Micro Theory Problems and Practice Exams - Lake Forest College ...

MICRO THEORY PROBLEMS AND PRACTICE EXAMS
Companion Guide to Econ 210
This section contains over 100 problems. These problems represent an almost complete compilation of
nine years of exam questions.
Question 1
In the United States there is great demand for human organs for medical transplants. A person suffering
from kidney or liver failure, for example, can wait for many years before receiving a replacement organ.
At the same time, for ethical reasons it is illegal (and will remain illegal) for healthy people to sell their
organs. Rather, all transplanted organs come from people who agree to donate their organs upon their
death (and then die).
A. Explain in the simplest economic terms possible why the waiting list is so long.
B. Suppose someone proposed the following policy: a person with a failed organ can only put their name
on the list for a new organ if she or he willingly becomes an organ donor. Explain why this proposal
would not be likely to substantially reduce the waiting time.
C. Explain how the proposal could be altered slightly to make the proposal successful at substantially
reducing waiting times. That is, how might the proposal in part B be amended or changed slightly to
have the desired effect of reducing the waiting time for donated organs
Question 2
A supposedly important aspect of the “War on Terrorism” requires the U.S. to prevent terrorists from
smuggling weapons or chemicals into the United States in cargo containers that are shipped to the U.S. on
freight boats from all around the world, and in particular, from foreign ports that do not have tight
security. Thus, the Department of Homeland Security needs to determine how many cargo containers to
inspect and how thoroughly to inspect them. From an economic perspective, how should these decisions
be made
Question 3
Suppose six people get together to watch the Super Bowl. All six people like Pepsi a lot. When they get
together, there is one case of Pepsi, containing twelve cans of Pepsi.
A. Describe a Pareto efficient distribution of the Pepsi that is not very equitable.
B. Describe an equitable distribution of the Pepsi that is not Pareto efficient.
Question 4
Karl must purchase Big Macs in discrete units. The following table reports his weekly marginal
willingness to pay for each additional Big Mac.
Big Macs 1 2 3 4 5 6 7 8 9 10
MWTP $3.00 $2.50 $2.00 $1.50 $1.00 $0.80 $0.60 $0.40 $0.20 $0.00
A. If the price of Big Macs is $1.60, how many will Karl purchase each week, and how much surplus
does he receive How much surplus does he receive from the last Big Mac that he purchases
B. Suppose McDonalds increases the price of a Big Mac to $3.20 but then sells Big Macs as a 2-for-1.
That is, two Big Macs still cost $3.20, but consumers must purchase an even amount. How many Big
Macs will Karl now purchase How much surplus does he now receive
Question 5
Suppose the demand for Burger King Value Meals is p = 8 – 0.025Q where p is measured in dollars.
What is the elasticity of demand when Q = 200
1

Question 6
The demand for apples is Q = 2,000 – 1,000p and the current price for an apple is $1.20. What is the
elasticity of demand for apples
Question 7
Consider the following demand function for skateboards: Q D = 100 – 2p + 4p A – 3p B + 0.005Y.
A. Are skateboards and good A (whose price is represented by p A ) complements or substitutes
B. Are skateboards normal or inferior
C. Suppose the price of a skateboard is $100, the price of good A is $125, the price of good B is $75, and
average income is $5,000 per month. What is the cross-price elasticity of skateboards with respect to
good A
Question 8
Suppose Toys-R-Us faces demand for model airplanes in September of:
Q D = 35 – 5p – 0.5p G + 1.5p MC + 10Y,
where p is the price of a model airplane, p G and p MC represent prices of other goods, and Y is average
monthly household income in thousands of dollars
A. Is the good with a price of p G a complement to or a substitute for model airplanes
B. Is the good with a price of p MC a complement to or a substitute for model airplanes
C. Extra Credit: What do G and MC stand for
D. Are model airplanes a normal or an inferior good
E. Suppose p G = $2, p MC = $8, and average monthly income is $5,400 (i.e., average monthly income is
5.4 thousands of dollars). Rewrite the monthly demand for model airplanes in terms of just Q D and p.
F. Transform the demand function into an inverse demand function.
G. How many model airplanes will Toys-R-Us sell in September if it sets a price of $12
H. What is the elasticity of demand when price equals $12
I. At what price would the elasticity of demand equal -3
J. Which of the following demand functions: Q D = 50 – 5p – 0.5p G + 1.5p MC + 10Y or
Q D = 15 – 5p – 0.5p G + 1.5p MC + 10Y is more likely to be the monthly demand for model airplanes in
December
Question 9
When her income is $25,000 a year, Maggie spends $1,250 on sporting tickets annually. If her income
would increase to $40,000 a year, she would spend $1,500 on sporting tickets annually. What is her
income elasticity of sporting tickets
Question 10
The (inverse) market demand for CDs can be expressed as p = 50 – 0.01Q. What is the price elasticity of
demand for CDs at a price of $20
Question 11
Suppose the demand for cars is Q = 45000 – 5p – 2000p G + 500Y, where p is the price of a car, p G is the
price of a gallon of gas, and Y is the average yearly household income in thousands of dollars.
A. Suppose p = $10,000, p G = $2.50, and Y = $30. How many cars are demanded under these
conditions
B. Calculate the price elasticity of demand, the income elasticity of demand, and the cross-price
elasticity of demand between cars and gas under the same conditions as in part A.
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Question 12
The inverse supply curve for CD’s is p = 2 + 0.01Q S . What is the elasticity of supply when the price of a
CD is $14
Question 13
Consider the following industry demand and supply functions: Q D = 5000 – 20p and Q S = –400 + 4p.
A. Solve for the inverse demand function.
B. Solve for the inverse supply function.
C. Solve for the market equilibrium.
Question 14
The demand for home security systems is given by Q D = 4,000 – 10p. The supply of home security
systems is given by Q S = 20p – 2,000. What is the market equilibrium At the equilibrium price, what is
the elasticity of demand At the equilibrium price, what is the elasticity of supply
Question 15
The demand for and supply of yachts are Q D = 5000 – 0.01p and Q S = 0.04p – 10000. What is the market
equilibrium
Question 16
The demand for weekly airplane travel is p = 10000 – 20Q where p is measured in dollars. The supply of
weekly airplane travel is p = 2000 + 5Q. What is the market equilibrium What is the elasticity of
demand at the market equilibrium What is the elasticity of supply at the market equilibrium
Question 17
Consider the market for CDs. Monthly demand and supply are Q D = 2,500 – 50p and Q S = 150p – 300.
A. Solve for the inverse demand and inverse supply functions.
B. Solve for the equilibrium.
C. How many CDs are demanded and supplied under (i) a $16 price floor, (ii) a $16 price ceiling, (iii) a
$10 price floor, and (iv) a $10 price ceiling.
D. Suppose income increases causing demand to become Q D = 2,900 – 50p. Are CDs a normal or
inferior good Solve for the new equilibrium.
Question 18
The market for cars is described by: Q D = 2,500 – 0.1p and Q S = 0.05p – 500.
A. What is the market equilibrium
B. What is the elasticity of demand at the equilibrium
C. What is the elasticity of supply at the equilibrium
D. If the government sets a price ceiling of $14,000 per car, how many cars would be bought Is there a
shortage or a surplus of cars If so, how large is it
E. If the government sets a price floor of $14,000 per car, how many cars would be bought Is there a
shortage or a surplus of cars If so, how large is it
F. If the government sets a price ceiling of $24,000 per car, how many cars would be bought Is there a
shortage or a surplus of cars If so, how large is it
G. If the government sets a price floor of $24,000 per car, how many cars would be bought Is there a
shortage or a surplus of cars If so, how large is it
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Question 19
Presently each bag of dog food sells for $14. Moreover, the price elasticity of demand for dog food is
–0.6 while the price elasticity of supply of dog food is +1.8. Suppose the government starts to require
firms to pay a $4 excise tax for each bag of dog food that it sells. How much of the $4 tax will consumers
bear What is the new price consumers pay for a bag of dog food
Question 20
Best Buy faces weekly demand for its DVD movies of
Q D = 500 – 20p + 10p RGI – 5p RGII + Y
where Q D is the number of DVD movies, p is the price of each movie, p RGI and p RGII are the prices of two
related goods, and Y is average monthly income. The current values for the other prices and income are:
p RGI = $20, p RGII = $50, and Y = $650.
A. According to the demand equation, are DVD movies and the first other related good, whose price is
p RGI , complements or substitutes
B. Algebraically solve for the demand curve and the inverse demand curve.
C. Suppose Best Buy supplies DVD movies on a weekly basis according to Q S = 25p – 250.
Algebraically solve for the inverse supply curve.
D. Solve for the market equilibrium.
E. Calculate the elasticity of demand at the market equilibrium.
F. Calculate the elasticity of supply at the market equilibrium.
G. What percentage of a per-unit tax do consumers pay
H. What would the price of a DVD be following a tax of $4.50 per DVD
Question 21
Suppose the government imposes a $2 excise tax on each taxi ride provided in Chicago.
A. Under what condition(s) would the imposition of such a tax not result in the quantity of taxi rides
purchased in Chicago to fall That is, under what condition(s) will quantity demanded be unaffected
by the tax
B. If the condition(s) in part A are met, what will happen to the price of each taxi ride
Question 22
In response to a recent mad-cow disease scare, the U.S. Food and Drug Administration decided to require
all cows be tested for the disease. The test costs $500 per cow. With the test being administered,
however, consumers are confident in their food supply and do not change their willingness to pay for
beef. According to the standard model of supply and demand, how will the testing of cows affect the
supply of beef, the price of beef, and the total amount of beef purchased in the market
Question 23
Consider the market for gasoline in the United States. How did the equilibrium price and quantity change
in the wake of hurricanes Katrina and Rita, which left more than twenty-five percent of the infrastructure
for oil transportation and oil refining in the U.S. unusable at least for several months
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Question 24
A. What happens to the equilibrium price and quantity of hamburgers when the price of tacos, a
substitute, falls How have the supply and demand curves for hamburgers shifted Draw a graph
showing these shifts.
B. What happens to the equilibrium price and quantity of hamburgers when the price of cattle feed
increases How have the supply and demand curves for hamburgers shifted Draw a graph showing
these shifts.
C. What happens to the equilibrium price and quantity of hamburgers when non-labor income increases
How have the supply and demand curves for hamburgers shifted Clearly state any assumptions you
make. Draw a graph showing these shifts.
Question 25
Consider two goods: food and pollution. People like food but do not like pollution. Draw some
indifference curves for food and pollution. (Put food on the x-axis and pollution on the y-axis.) Label
three indifference curves so that consumers prefer IC 3 to IC 2 to IC 1 .
Question 26
Neil takes $40 to a Chicago Bears game to spend on beer and hotdogs. Each beer costs $4. Each hotdog
costs $5.
A. Draw Neil’s budget line. Label it BL A .
B. Suppose the price of each hotdogs falls to $4. Draw Neil’s new budget line. Label it BL B .
C. Suppose instead that Neil brings $60 with him to the game instead of $40. Draw his new budget line
using the original prices of $4 per beer and $5 per hotdog. Label it BL C .
D. Return to the original situation − income of $40 and prices of $4 per beer and $5 per hotdog.
Suppose Cook County levies a $1 excise tax (or quantity tax) on each beer. Draw Neil’s new budget
line. Label it BL D .
E. Return to the original situation − income of $40 and prices of $4 per beer and $5 per hotdog.
Suppose Cook County levies a 25% ad valorem tax on the purchase of all goods at Bears game. Draw
Neil’s new budget line. Label it BL E .
Question 27
Karla has to buy beer and pizza for a party. Parts A – C require you to draw Karla’s budget line under
different conditions. Be sure to state the slope of the budget line as well as both intercepts and all other
interesting points. Provide a separate graph for each part. Put beer on the X-axis.
A. Karla has $240 to spend. Each beer costs $3. Each pizza costs $12.
B. Karla has $150 to spend. Before paying taxes, each beer costs $2 and each pizza costs $10. The
government levies a $0.50 tax on each beer.
C. Karla has $320 to spend. Each beer costs $5. The regular price of a pizza is $15, but Karla receives a
$5 discount on every pizza she buys after buying 10 at the regular price.
Question 28
Consider a two-good, fixed price economy. The two goods are hammocks and swings. The price of each
hammock is $120. The price of each swing is $40. The director of a retirement community has $6,000 to
spend on furnishing the out-door patio area with hammocks and swings.
A. Draw the director’s budget line. (Put hammocks on the x-axis.) Label this budget line BL A .
B. Suppose the price of swings doubles. Draw the new budget line. Label this budget line BL B .
C. Ignoring part B, suppose someone gives the retirement community a gift of $3,000 to help it furnish
the patio. As a result of this gift, the administration of the retirement community decides to reduce its
budget for patio furniture from $6,000 to $4,200. With the gift of $3,000, therefore, the director’s
new budget is $7,200. Draw the new budget line. Label this budget line BL C .
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Question 29
Consider a two-good, fixed price economy. The two goods are sheets of music and guitar picks. The
price of each sheet of music is 60¢ regardless of what store Don goes to. There is a music store that Don
can walk to but that store does not sell guitar picks. Traveling to the next closest store, which does sell
guitar picks at $3 per pick, requires Don to purchase a $6 round-trip train ticket. Don does not care about
the time involved in traveling to either store. Don has a budget of $24. Graph Don’s budget line. Put
sheets of music on the x-axis.
Question 30
Consider a two-good economy with fixed prices. The goods are books and movies.
A. Graph the budget line when the price of each book is $40, the price of each movie is $12, and a
consumer has $120 to spend. Indicate the value of the intercepts and slope of the budget line. Label
the budget line BL A .
B. Graph a new budget line when the price of each movie decreases to $8 while the price of books and
the consumer’s budget remains fixed. Label this budget line BL B .
Question 31
As a financially strained college student, you are faced with the following situation. In return for your
tuition, Lake Forest College gives you a place to live, pays for your books and supplies, and lets you take
classes. Your own financial resources leave you with $120 to spend each month. The only goods which
you can buy are Pepsi (which is life sustaining) and cellular phone service (which is social-life
sustaining). Each can of Pepsi costs $1. If you sign on with the cellular service, they give you a phone
for free but charge a monthly access fee of $20. Additionally, you are charged 50 cents per minute for
each of the first 100 minutes you use the service. If you use more than 100 minutes, each minute after
your first 100 and up to a total of 200 is billed at a rate of 25 cents per minute. If you use more than 200
minutes, each minute in excess of 200 minutes is billed at 20 cents per minute.
A. If you use 50 minutes of airtime, how many cans of Pepsi will you be able to buy
B. Show that consuming 40 cans of Pepsi and using 140 minutes is on your budget line.
C. Draw your budget line.
D. Suppose, faced with all of the options on the budget line, your optimal choice is to buy 75 cans of
Pepsi and 50 minutes of airtime. Now, the phone company proposes to change its fee schedule. It
will eliminate its monthly fee, but charge a flat rate of $0.80 per minute. Should you, an economic
agent with well-behaved preferences, favor the new proposal by the phone company
Question 32
Best Buy sells DVDs and VHS tapes. Each DVD sells for $20 each.
A. Because of weak demand for VHS tapes, Best Buy sells the first four VHS tapes purchased by any
consumer at a price of $15 each, but sells each additional tape at the discounted price of $12 per tape.
Graph a consumer’s budget constraint if she has $120 to spend on DVDs and VHS tapes.
B. Repeat part A using the same information except that instead of giving the consumer a price break
after buying the first four VHS tapes, assume Best Buy sells each VHS tape for $15 to consumers
who buy at most four and sells each VHS tape (including the first four) to consumers who buy more
than four tapes at a price of $12 per tape.
C. Under the pricing scheme of part B, if someone has well-behaved preferences over DVDs and VHS
tapes, what is the greatest number of VHS tapes she might purchase with her $120 assuming she
purchases 4 or fewer tapes
Question 33
What would you predict to happen to the equilibrium price and quantity of computer chips if there is a
technological advance that allows computer chips to be made three times faster than is currently possible
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Question 34
According to our basic model of consumer behavior, how do indifference curves shift when income
increases
Question 35
Draw some indifference curves for two goods that are both disliked, such as pollution and traffic jams.
Question 36
Which of our four assumptions – completeness, transitivity, monotonicity, and diminishing returns – are
violated by perfect substitutes
Good 2
Perfect Substitutes
Good 1
Question 37
Nathan likes cookies and is always willing to eat more, but he does not care for peas. When his mom
gives him peas, Nathan casually drops them on the floor and let’s his dog eat them. (The dog likes peas
and is always willing to eat more.) As dropping peas on the floor is rather easy, doing so does not cause
Nathan any disutility. Graph Nathan’s indifference curves for cookies (x-axis) and peas (y-axis).
Question 38
Olivia’s preferences are well-behaved. Below are graphed five possible consumption bundles. Thus,
there are 10 two-way comparisons using all five bundles. Olivia reveals that she prefers E to A and
prefers D to E. What can you say about the other 8 possible comparisons
Good 2
Possible Consumption Bundles
D
A
E
B
C
Good 1
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Question 39
Regardless of his consumption level, Tony always receives the same happiness from consuming 3
minutes of long-distance as he does from consuming 2 minutes of dial-up.
A. Provide a utility function describing Tony’s preference ordering for long-distance and dial-up.
B. Using the utility function you gave in part A, which consumption bundle does Tony prefer: 15
minutes of long-distance and 32 minutes of dial-up or 24 minutes of long-distance and 28 minutes of
dial-up
C. Draw some of Tony’s indifference curves. (Put long-distance on the x-axis.)
D. What is Tony’s marginal rate of substitution for long-distance if he consumes 23 minutes of longdistance
and 201 minutes of dial-up
Question 40
Katy’s preferences for apples (a) and bananas (b) can be represented as: u(a,b) = 3a+5b.
A. What is Katy’s marginal rate of substitution between apples and bananas
B. Graph some of Katy’s indifference curves.
C. If the price of each apple is $0.25 and the price of each banana is $0.40, how many apples and
bananas will Katy buy when her income is $4.00
Question 41
Morty values going to 5 baseball games the same as he values going to 2 football games. Each baseball
game costs $10 and each football game costs $30. Morty’s sporting entertainment budget is $150 dollars.
A. Draw several of Morty’s indifference curves.
B. Draw Morty’s budget line. Is going to 4 baseball games and 4 football games on his budget line
C. What is Morty’s marginal rate of substitution of baseball games for football games at the point of
going to 4 baseball games and 4 football games
D. What is Morty’s optimal consumption bundle
Question 42
Due to a rather active baby, Maggie always uses 1 bib with every 12 jars of baby food.
A. Provide a utility function describing Maggie’s preference ordering for bibs and jars of baby food.
B. Using the utility function you gave in part A, which consumption bundle does Maggie prefer: 4 bibs
and 30 jars of food or 6 bibs and 15 jars of food
C. Draw some of Maggie’s indifference curves. (Put bibs on the x-axis.)
D. What is Maggie’s marginal rate of substitution for bibs when she consumes 9 bibs and 9 jars of food
Question 43
Kim’s preferences for apples (a) and bananas (b) can be represented as: u(a,b) = b + a 0.5 .
A. Graph some of Kim’s indifference curves.
B. What is Kim’s marginal rate of substitution between apples and bananas
C. Is v(a,b) = b 2 + a a monotonic transformation of u(a,b)
Question 44
Sandra’s preferences for cookies (c) and donuts (d) can be represented as u(c,d) = 2.5c 5 d 10 . Provide a
transformed utility function of Sandra’s preferences so that the exponents refer to income shares.
Question 45
For lunch, Joey eats cokes and sandwiches in equal proportions−1 coke for every 2 sandwiches. Joey has
$30 for the week. Each coke costs $1, and each sandwich costs $2.50. What is Joey’s optimal
consumption bundle
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Question 46
True or False: The preference ordering described by perfect complements is well-behaved. Explain.
Question 47
Under well-behaved preferences, will the marginal utility from consuming a good increase or decrease as
one’s consumption of that good increases That is, if x 1 ↑ → MU 1 ↑ or MU 1 ↓ Which assumption of wellbehaved
preferences guarantees this result
Question 48
One representation of Ben’s preferences for beer (b) and cigarettes (c) is v(b,c) = 32b 2 c 3 .
A. Using a monotonic transformation, Ben’s utility can be written as u(b,c) = b α c 1-α . What is the value
for α
B. Consider the bundle of 10 beers and 30 cigarettes, and use the new utility function, u(b,c), to answer
the following questions. Use the calculus formulas to answer questions a – c.
a. What is Ben’s marginal utility from beer
b. What is Ben’s marginal utility from cigarettes
c. What is Ben’s marginal rate of substitution for beer
Question 49
The marginal utility from buying one more Pepsi at a cost of $1 is 16 utils; whereas buying 1 more slice
of pizza at a cost of $2 yields 24 additional utils.
A. Which good is associated with the higher marginal utility
B. Which good is associated with the higher marginal utility per dollar
C. Which good will a utility maximizing economic agent purchase next
Question 50
Amy’s preferences for bags of chips (c) and cans soda (s) can be represented as: u(c, s) = c ¾ s ¼ . Each bag
of chips costs $2. Each can of soda costs $0.50. Amy has $12 per week to spend chips and soda.
A. Draw Amy’s budget line and highest possible indifference curve subject to her budget constraint.
Indicate her optimal consumption level of chips and soda.
B. Analytically solve for Amy’s optimal consumption level of chips and soda. (Be sure to go back to
your graph and label the optimal choices with your numerical answers.)
C. What is Amy’s marginal rate of substitution of soda for chips at her optimal consumption bundle
What is the market cost of 1 more bag of chips in terms of cans of soda
D. Show that consuming (c = 2, s = 16) is on Amy’s budget line. What is Amy’s marginal rate of
substitution of soda for chips at this point
E. Suppose Amy’s budget increases to $16 per week, how many bags of chips will she now consume
What is the income elasticity of chips in this example Are chips normal or inferior
Question 51
Amy’s preferences for bags of chips (c) and cans soda (s) can be represented as: u(c,s) = c 8 s 2 . Each bag
of chips costs $1. Each can of soda costs $0.75. Amy has $15 per week to spend on chips and soda.
Draw Amy’s budget line. How many bags of chips and cans of soda will Amy purchase each week to
maximize her utility.
Question 52
Craig has a budget of $13 to buy milk and tacos. Let x represent cartons of milk, and y represent tacos.
Each carton of milk costs 65¢. Each taco costs 25¢. What is the optimal consumption bundle if Craig’s
preference ordering can be captured by u(x,y) = x 93 y 31
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Question 53
A consumer’s preferences can be expressed with a utility function of u(x,y) = x 3 y 8 . She has income of
$44, and faces prices of p X = $4 and p Y = $2. How much of each good will she purchase in order to
maximize her utility
Question 54
Suppose preferences for x 1 and x 2 can be represented as:
U(x 1 , x 2 ) = 50x 1 13 x 2 52 .
A. Using monotonic transformations, U(x 1 , x 2 ) can be transformed into V(x 1 , x 2 ) = x 1 α x 2
1– α . What is the
value of α
B. Suppose the budget is $1,000, the price of x 1 is $10, and the price of x 2 is $80. What is the optimal
consumption bundle
C. Use the transformed utility function to calculate the following items at the optimal consumption
bundle: the marginal utility of x 1 , the marginal utility of x 2 , the marginal rate of substitution, and the
marginal rate of transformation.
Question 55
Suppose preferences can be represented by U(B,Z) = 5B 2 Z 3 where B represents the number of beers
consumed and Z equals the number of slices of pizza consumed. Each beer costs $2 and each slice of
pizza costs $4.
A. Transform U(B,Z) into a Cobb-Douglas function of the form B α Z 1– α . Interpret α.
B. Using the new utility representation, calculate the marginal utility for beer for the (B,Z) bundles (6,1),
(4,8), and (10,10).
C. Using the new utility representation, calculate the marginal utility for pizza for the (B,Z) bundles
(6,1), (4,8), and (10,10).
D. Calculate the marginal rate of substitution at the (B,Z) bundles (6,1), (4,8), and (10,10).
E. If the budget is $20, what is the optimal consumption bundle
Question 56
Preferences for CDs and DVDs can be represented by U(C,D) = C 0.25 D 0.75 where C is the number of CDs
and D is the number of DVDs. Each CD costs $12 while each DVD costs $20. There is a $240 budget.
A. Show that the (C,D) bundles of (15,3), (10,6), and (5,9) are on the budget line.
B. What is the optimal consumption bundle
C. For each of the three bundles listed in part A, calculate the MRS and the MRT.
Question 57
Consider an economy with two goods – gloves (g) and hats (h). Judy has Cobb-Douglas preferences for
gloves and hats according to u(g,h) = g 0.4 h 0.6 .
A. As a function of income (Y) and prices (p g and p h ), what are Judy’s demand curves for gloves and
hats
B. Let the price of each pair of gloves be $10 and the price of each hat be $12. What is Judy’s Engel
curves for hats. Graph her Engel curve for hats.
C. Let the price of each pair of gloves be $10 and the price of each hat be $12. What is Judy’s optimal
consumption bundle if she has a budget of $100
D. Let the price of each pair of gloves be $10 and the price of each hat be $12. What is the MRS and the
MRT of gloves in terms of hats if Judy consumes 50 pairs of gloves and 30 hats
E. How much money would Judy need to afford the proposed bundle in part D If she had that much
money, would she consume more than, exactly, or less than 50 pairs of gloves
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Question 58
Jack’s demand for DVD’s can be described as q = 250 – 2p – 10Y where p is the price of each DVD.
Graph Jack’s Engel curve holding p fixed at $20 per DVD for Y > $2. Are DVDs normal or inferior
How can you tell if DVDs are normal or inferior from the Engel curve
Question 59
Consider an individual decision maker who consumes two goods, x and y, in a 5:3 proportion (i.e., 5 x’s
are eaten with every 3 y’s). Prices are p x and p y , and the person’s income is Y.
A. Rigorously determine the person’s demand function for good x.
B. Graph the demand function for good x.
C. Graph the Engel curve associated with good x.
Question 60
0.4 0.6
Suppose Kate’s preferences for bales of hay (x 1 ) and bushels of oats (x 2 ) are u ( x1 , x2
) = x1
x2
.
A. Solve for and graph both of Kate’s demand curves (i.e., one demand curve for hay, and one demand
curve for oats) assuming that her income is $250.
B. Solve for and graph both of Kate’s Engel curves (i.e, one Engel curve for hay, and one Engel curve
for oats) assuming that p 1 = $4 and p 2 = $3.
C. Suppose Kate’s budget is $250, the price of each bale of hay is $4, and the price of each bushel of
oats is $3. What is Kate’s optimal consumption bundle of hay and oats
Question 61
Suppose Neil’s preferences for sheets of paper (x 1 ) and pencils (x 2 ) are perfect complements in a ratio of
20 sheets of paper with 1 pencil.
A. Solve for and graph Neil’s demand curve for paper assuming that his income is $40 and the price of
each pencil is 25¢.
B. Solve for and graph Neil’s demand curve for pencils assuming that his income is $40 and the price of
each sheet of paper is 5¢.
C. Solve for and graph both of Neil’s Engel curves assuming that each sheet of paper costs 5¢ and each
pencil costs 25¢.
D. Suppose Neil’s budget for paper and pencils is $40, each sheet of paper costs 5¢, and each pencil
costs 25¢. What is Neil’s optimal consumption of sheets of paper and pencils
Question 62
Suppose Joni treats her consumption of subway rides (s) and taxi rides (t) as perfect substitutes, where
each taxi ride can substitute for two subway rides (likewise, two subway rides can substitute for one taxi
ride).
A. Provide a utility function that represents Joni’s preference.
B. Solve for and graph Joni’s demand for subway rides assuming that her weekly budget for subway and
taxi rides is $120 and that each taxi ride costs $10.
C. Solve for and graph Joni’s demand for taxi rides assuming that her weekly budget for subway and taxi
rides is $120 and that each subway ride costs $2.
D. Solve for and graph both of Joni’s Engel curves assuming that the price of each subway ride is $2
while the price of each taxi ride is $10.
E. Suppose Joni’s weekly budget for subway and taxi rides is $120 and that each subway ride costs $2
while each taxi ride costs $10. What is Joni’s optimal consumption bundle of subway and taxi rides
for the week
11

Question 63
Consider a two-good, fixed prices model of consumer theory with well-behaved preferences. Assume
good 2 is a normal good. True or False: A decrease in the price of good 1 necessarily leads to a decrease
in the quantity demanded of good 2. Explain.
Question 64
The graph below represents the standard two-good consumer model. The consumer originally chose
consumption bundle A, then the price of good X fell and the consumer chose consumption bundle C. Is X
a normal good, an inferior good, or either Is Y a normal good, an inferior good, or either
Question 65
Consider the standard two-good, fixed prices model of consumer theory where the two goods are rice and
steak. Suppose that rice is a Giffen good.
A. Demonstrate using budget lines and indifference curves the change in quantity demanded for rice
when its price increases. Label all budget lines and indifference curves. Indicate on your graph the
substitution effect, income effect, and total effect.
B. Does rice violate the law of demand in this example
C. Graph a reasonable Engel curve for rice in this example
Question 66
Consider a model of worklife consumption (denoted by C 0 ) versus retirement consumption (denoted by
C 1 ). The consumer is endowed with $4 million of worklife income and $1.2 million of retirement
income. The consumer can save worklife income (to spend during retirement) at a guaranteed interest
rate of 25%. Alternatively, the consumer can borrow (to be financed out of retirement income) at an
interest rate of 50% in order to consume more during his worklife.
A. Draw the consumer’s budget line for consumption today versus consumption tomorrow. (Place C 0 on
the y-axis and C 1 on the x-axis.) Indicate the slope(s) of the budget line.
B. Might a consumer with well-behaved preferences borrow against his retirement income
C. Consider a consumer with well-behaved preferences who optimally chooses to save some income
today when the rate of return on savings is 25% and the rate of payment on borrowing is 50%. How
might this consumer adjust his savings/borrowing if the rate of payment on borrowing falls to 25%
D. Consider a consumer with well-behaved preferences who optimally chooses to not save or borrow
when the rate of return on savings is 25% and the rate of payment on borrowing is 50%. How might
this consumer adjust his savings/borrowing if the rate of payment on borrowing falls to 25%
Question 67
Assuming that consumption when young and consumption when old are both normal goods, it can be
shown that the effect on current savings from decreasing the capital gains tax rate is ambiguous. That is,
it is not clear if savings will increase or decrease following a cut in the capital gains tax rate. Why
12

Question 68
Consider the basic two-good consumer model where the two goods are consumption today (y-axis) and
consumption tomorrow (x-axis). Today’s income is Y. There is no income tomorrow other than what is
saved from today’s income. Individual savings does not earn interest. Rather, whatever is saved today is
placed in a lockbox. When tomorrow comes, the consumer opens the lockbox and consumes the money
in the box. The price of consuming in both time periods is $1. Parts A - C have you draw a budget line.
For each, specify the interesting points (including intercepts) and the slope.
A. Draw the budget line given the set-up above. Label it BL A .
B. Suppose the government requires the consumer to give the government S G where 0 < S G < Y. The
government puts this money in a lockbox for the consumer. When tomorrow comes, the government
returns S G to the consumer. The consumer is also allowed to put S I in a lockbox where 0 < S I < Y with
the condition that S G + S I ≤ Y. Neither S G nor S I earn interest. Draw the budget line. Label it BL B .
C. Suppose the government requires the consumer to give the government S G where 0 < S G < Y. The
government puts this money in a lockbox for the consumer. When the government returns the
consumer’s money to her tomorrow, however, the government gives the consumer 2S G . The
consumer is allowed to put S I in her own lockbox (i.e., personal savings) where 0 < S I < Y with the
condition that S G + S I ≤ Y. Again, S I does not earn interest. Draw the budget line. Label it BL C .
D. What can be said about the consumer’s ranking of BL A , BL B , and BL C assuming “nice” preferences
Question 69
The U.S. military posts a wage and recruits people who are willing to be a soldier at that wage (i.e., the
U.S. has a “voluntary” army). There has been some discussion about raising the pay of soldiers in order
to get more people to willingly enter the military (that is, to improve recruitment) and to entice those who
do enter to remain in the military longer (that is, to improve retention). As an economist, comment
separately on the effect increasing military pay will have on the recruitment and retention of soldiers.
Question 70
Consider someone who values consumption (c) and leisure (l). Both goods are normal. The person faces
a wage of $8 per hour and has no non-labor income.
A. If this person has well-behaved preferences and currently does not work, what is his reservation
wage
B. Is it likely that an increase in the person’s non-labor income (e.g., through a lump-sum welfare
payment) will entice the person to start working
C. Instead of a lump-sum transfer, is it possible for a wage subsidy (e.g., through the earned income tax
credit) to entice the person to start working
Question 71
Tina has 112 hours each week to devote to leisure and/or work. Tina faces an after-tax hourly wage of
$10 per hour for the first 40 hours of work each week. Any hours she works in excess of 40 hours is
considered overtime, which is paid at “time and a half” so that her after-tax overtime hourly wage is $15.
Tina must earn any money that she spends on consumption goods. Graph Tina’s weekly budget line
showing what consumption-leisure bundles Tina can afford.
Question 72
Consider the basic labor supply model in which workers get utility from eating consumption and leisure.
The hourly wage is w, each worker can work T hours each week, and the price of a unit of consumption is
$1. Assume both consumption and leisure are normal goods.
A. What use is it to assume consumption and leisure are normal goods. (That is, what does this
assumption tell us about consumption and leisure)
B. Under these assumptions, will hours worked by poor, single mothers currently working part-time
necessarily increase if Congress increases the minimum wage
13

Question 73
Calculate the marginal rate of technical substitution for the following three production technologies.
A. f(K,L) = 12K 1/4 L 1/3 .
B. f(K,L) = 4K + 3L.
C. f(K,L) = min{4K, 3L}.
Question 74
The firm’s total cost function written in units of output, q, is: C(q) = 1200 + 6q 2 .
A. Derive the algebraic expression for each of the following: variable costs, fixed costs, average total
costs, average variable costs, average fixed costs, the marginal cost curve, the short-run supply curve,
and the long-run supply curve.
B. Plot total costs, variable costs, and fixed costs on the same graph.
C. Plot average total cost, average variable costs, average fixed costs, and marginal costs on the same
graph.
Question 75
A firm’s total cost function written in units of output, q, is: C(q) = 5000 + 10q.
A. Algebraically solve for the firm’s variable cost curve, fixed costs, average total cost curve, average
variable cost curve, average fixed cost curve, and marginal cost curve.
B. Graph the firm’s average total costs, average variable costs, and marginal costs on the same graph.
Question 76
Provide values for boxes A – E in the table below.
Quantity Price
Total
Revenue
Total
Cost Profit
Marginal
Cost
Marginal
Revenue
0 --------- --------- $50.00 -$50.00 --------- ---------
1 $25.00 $25.00 $60 -$35.00 $10.00 $25.00
2 $24.00 $48.00 $69 -$21.00 $9.00 $23.00
3 $23.00
4 A $4.00 $19.00
5 B
6 $118.50 $96.75 $6.25
7 $18.50 $6.00
8 $17.25 C $5.75
9 $16.00 D $29.25
10 $147.50
11 $13.50 $128.00
12 E $135.00 -$1.50
13 $11.00 $0.75
Question 77
Graph several isoquants associated with the production function: q = f(x 1 , x 2 ) = min{3x 1 , x 2 }. Given
factor prices of w 1 and w 2 , what is the cost function
Question 78
Graph several isoquants associated with the production function: q = f(x 1 , x 2 ) = 2x 1 + 3x 2 . Given factor
prices of w 1 and w 2 , what is the cost function
14

Question 79
What is the cost function associated with a production process that turns 5 units of x 1 and 0.25 units of x 2
into 32 units of output, when the cost of each unit of x 1 is $25 and the cost of each unit of x 2 is $12.
Question 80
What is the cost function associated with a production process that repeatedly turns 2 units of x 1 and 5
units of x 2 into 3 units of output, when each unit of x 1 costs $20 and each unit of x 2 costs $4
Question 81
Fisher Price can sell as many Little People Houses as it likes at a price of $27.99 each. If Fisher Price
makes 100 houses, the average total cost of production is $20.25 per house. If Fisher Price makes 101
houses, the average total cost of production is $20.34. Should Fisher Price make and sell the 101 st house
Why or why not
Question 82
Joni drives a big yellow taxi in Chicago where she can charge a price of $1.25 per mile. She is willing to
work 8 hours a day. During an 8 hour day, she will receive payment for driving a total of 300 miles. Her
cost of operating her taxi is $0.25 per mile in gas, $0.40 per mile in general maintenance, and $50 in
insurance each day. Joni has the option of working at McDonalds for 8 hours a day earning $5.15 per
hour. She has no other employment options. What is Joni’s daily profit from driving a taxi cab
Question 83
A firm earns $10,000 profit from selling 200 units of output. The firm’s fixed costs are $12,000 and its
average variable cost per unit sold is $13. At what price is each unit of output sold
Question 84
Analyze the validity of the following statement. A profit maximizing firm will remain open in the shortrun
as long as it can recuperate its fixed costs.
Question 85
Suppose Ripon College is a price taker. Its fixed costs are $4 million per year. The marginal cost per
student is $7,000 as long as the College enrolls 1300 or fewer students. The marginal cost is $12,000 per
student for every student over 1300 that the college enrolls . How many students should Ripon College
enroll if it receives tuition of $11,000 from each student who enrolls
Question 86
The costs of recording and producing a music album’s master tape are quite large, say $5 million. Once
the master tape is produced, the cost of actually producing each CD for sale is $2. We also observe CD
prices falling over time. For example, when Mariah Carey released the album "Butterfly" in September
of 1997, a CD sold for $17.99. A year and a half later, the same album could be bought for $12.88. If the
marginal cost of producing a CD is always $2, why do we observe the price of the same CD falling over
time Does this mean Mariah Carey is not profit maximizing
Question 87
The yearly production function for a profit-maximizing firm is q = f(L) = 100L, where L is the number of
workers the firm hires each year. The price of output depends on how much is sold according to the
following schedule: p(q) = 1000 − 0.25q. Each worker costs $40,000 for the year. How much labor
should the firm hire to maximize profits How many units of output will be produced At what price
will each unit of output sell How much profit will the firm earn
15

Question 88
Explain why a firm will never choose to produce at a quantity where its marginal revenue is negative.
Question 89
Consider a firm that employs labor and capital. Each unit of labor costs $15 and each unit of capital costs
$5. The firm’s production function is q = f(K,L) = 0.5K 0.2 L 0.6 . Given this production function, the MRTS
equals –3K / L.
A. Does the production function exhibit decreasing, constant, or increasing returns to scale
B. How many units of labor and capital should the firm employ if it wants to minimize the cost of
making 128 units of output
Question 90
Suppose a firm faces a constant selling price of $3 and has a total costs of 2 + 4q.
A. What are the algebraic expressions for the firm’s fixed cost, variable costs, and marginal costs
B. What is the short-run profit maximizing action of the firm How much is produced How much
profit does the firm earn in the short run
C. As the firm goes to the long-run, what is the profit maximizing action of the firm How much is
produced How much profit does the firm earn
Question 91
Bob’s Apple Orchard faces perfectly elastic demand for apples at a price of $2 per bag. Let q represent
the number of bags of apples produced and sold by Bob’s. Bob’s total cost for producing bags of apples
is C(q) = 1000 + q + 0.0025q 2 . How many bags of apples should the orchard sell to maximize profits
How much profit will the orchard earn
Question 92
Central Perk’s total cost of producing cups of coffee is C(q) = 2q + 0.01q 2 . Demand for Central Perk
coffee is p(q) = 10 – 0.015q. If Central Perk is a profit maximizing firm, how much coffee will it sell
What price will it charge How much profit will it earn
Question 93
Al makes desks. The (inverse) demand curve for Al’s desks is p(q) = 1000 − 10q. Al’s total costs of
production are C(q) = 3,500 + 100q + 5q 2 . How many desks should Al make in order to maximize
profits What price will he charge How much profit will he earn
Question 94
The (inverse) demand curve for widgets is p(q) = 200 – 5q. Widgets are produced by a monopolist for
which total costs are C(q) = 4q 2 – 16q + 24.
A. What is the firm’s average total cost curve
B. Assuming the monopolist maximizes her profits, how many widgets will the firm produce At what
price does the monopolist sell widgets How much profit does the monopolist earn
16

Question 95
Suppose volleyballs are produced in a perfectly competitive market. In 2003, the market for volleyballs
was in long-run equilibrium wherein the price of each volleyball was $5 and two million volleyballs were
produced each year by forty firms producing 50,000 balls each. Then, Misty May and Kerri Walsh won
the gold medal in women’s beach volleyball for the U.S.A. in the summer of 2004. As a result, volleyball
became very popular throughout the country (and will continue to remain popular).
A. What would you expect to happen to the price of volleyballs, total quantity of volleyballs sold, the
number of volleyballs produced by each volleyball-making firm, and the number of volleyballmaking
firms in the short run.
B. What would you expect to happen to the price of volleyballs, total quantity of volleyballs sold, the
number of volleyballs produced by each volleyball-making firm, and the number of volleyballmaking
firms in the long run. Be as precise as possible.
Question 96
Suppose the market for milk is perfectly competitive and, given current technology, is in long-run
equilibrium. Discuss in words and show with graphs what the effects would be if the Food and Drug
Administration releases new evidence that drinking milk each day helps prevent getting sick. Be sure to
comment on the effects the announcement will have in the short run and long run on (i) the quantity of
milk produced by each farmer, (ii) the quantity of milk produced in the entire industry, (iii) the price of
milk, (iv) each farmer’s profits, (v) entry and/or exit of firms, (vi) the market demand curve, and (vii) firm
cost curves.
Question 97
The market for fertilizer is perfectly competitive. Each bag of fertilizer sells at a price of $20. The total
cost to Fred’s Fertilizing Factory of producing q bags of fertilizer is C(q) = 125 + 5q + 0.05q 2 . How
many bags of fertilizer should Fred make in the short run to maximize profits How much profit does
Fred earn How much profit will Fred earn in the long run
Question 98
Suppose beets are produced in a perfectly competitive industry. The price of each 10 pound bag of beets
is $1.80. A typical farmer’s yearly cost function in dollars is C(q) = 180,000 + 0.3q + 0.000002q 2 where
q is the number of ten- pound bags of beets the farmer produces during the year. Given this cost function,
the marginal cost for each bag of beets is MC(q) = 0.30 + 0.000004q. For the current year, the farmer is
in the short run.
A. How many bags of beets should the farmer make during the year How much profit does the farmer
earn for the year
B. Suppose instead that the farmer’s fixed costs are $680,000. How many bags of beets should the
farmer make during the year How much profit does the farmer earn for the year
Question 99
Alison makes chairs. Inverse demand for Alison’s chairs is p = 800 − 15q where p is the price of a chair
and q is the number of chairs sold. Alison’s total cost of producing q chairs is C(q) = 500 + 200q + 15q 2 .
How many chairs will Alison make in the short run to maximize profits What price will she charge
Question 100
In 2007, the market for household robots is small and uncompetitive due to patents of new technologies.
In the long run, however, patents will expire and it is likely that the market for household robots will be
very competitive. At that time, people will eventually be able to purchase a robot that does all household
chores – cooking, cleaning, washing clothes, etc. The cost of paying an actual person, not a robot, to do
these for a household will be about $65,000 per year by the time the market for household robots is
competitive. What do you expect the long-run cost of a household robot to be Why
17

Question 101
The market for apartments in Lake Forest is competitive. Demand is captured by Q D = 430 – 0.05p while
supply is captured by Q S = 0.15p – 110. Suppose the city of Lake Forest imposes a price ceiling of
$1,200. Following the imposition of the price ceiling, how many apartments will be supplied How
many apartments will be demanded By how much is producer surplus reduced due to the price ceiling
Question 102
Currently the yearly market demand and supply for fire extinguishers are Q D = 18,000 – 200p and
Q S = 50p – 250 respectively.
A. Solve for the competitive equilibrium. How much surplus do consumers and producers receive
How much is total surplus
B. In an attempt to get more fire extinguishers to be purchased each year, the government places a price
ceiling of $35 on each extinguisher. How many fire extinguishers will be purchased when the price
ceiling is in place Calculate consumer surplus, producer surplus, total surplus, and deadweight loss
under the $35 price ceiling.
C. Was the government successful in achieving its goal Can you suggest an intervention that would be
more successful
Question 103
The inverse demand curve for a gallon of milk can be expressed as p = 5 – 0.001Q D . Similarly, the
inverse supply curve for a gallon of milk can be expressed as p = 2 + 0.002Q S .
A. What is the competitive equilibrium How much surplus do consumers and producers receive
B. Suppose the government imposes a price ceiling of $3.80 per gallon of milk. How large is the
quantity surplus or quantity shortage associated with such a price ceiling
C. What is the value of producer surplus under the price ceiling
D. What is the value of consumer surplus under the price ceiling
E. Compared to the competitive equilibrium, has the price ceiling collectively helped the (potential)
consumers of milk
F. Compared to the competitive equilibrium, has the price ceiling collectively helped the (potential)
producers of milk
Question 104
Suppose industry demand is Q = 50 – 0.20p. A patent gives a monopolist complete control of the
industry. The monopolist’s costs are C(q) = 4q 2 + 16q + 221. How much should the monopolist produce
to maximize her profits What price will she charge How much profit will the monopolist earn
18

Question 105
The graph below shows the industry demand curve for computers. The marginal cost of producing a
computer is $1,000 and there are no fixed costs of production.
A. If Dell is the only computer manufacturer, at what price will Dell sell computers How many
computers will it sell How much profit will Dell earn
B. If computers are produced in a perfectly competitive industry, at what price will computers be
sold How many computers will be sold in total How much profit will each firm earn
C. What is the dollar value of the deadweight loss associated with monopoly versus a perfectly
competitive
Question 106
Consider our classroom discussion of monopolies.
A. Explain why monopoly is never consumer efficient.
B. Explain why a natural monopoly is producer efficient.
C. If the government gives a natural monopolist (such as ComEd) a monopoly franchise, why doesn’t
the government require that the firm sell the good at its marginal cost of production so that the market
is consumer efficient
Question 107
A monopolist faces inverse demand of p = 40 – 0.025q and total costs of C(q) = 150 + 2q + 0.05q 2 so that
its marginal cost curve is MC(q) = 2 + 0.1q. How many units of output will the monopolist produce to
maximize its profit What price does the monopolist charge How much profit is earned
Question 108
The Lake Forest Water Company (LFWC) is a natural monopoly. It has fixed costs of $2 million per
week. Its marginal cost of refining and distributing 100 gallons of water is $25. Weekly demand for
household tap water in Lake Forest can be written as p = 100 – 0.0005q where q is each 100 gallons of
water.
A. What price will LFWC set for a gallon of water How many gallons of water will LFWC provide
each week How much profit will LFWC earn each week
B. Compared to a competitive water market in which price would equal marginal cost, how much
inefficiency is created by LFWC’s monopoly power
19

Question 109
Consider a two-player game. The normal form of the game is listed below, with player one’s payoffs
listed first. Both players act to maximize their payoffs.
Player
One
Player Two
C1 C2 C3 C4 C5
R1 ( 2 , 2 ) ( 2 , 3 ) ( 3 , 1 ) ( 6 , 5 ) ( 4 , 3 )
R2 ( 1 , 3 ) ( 1 , 1 ) ( 2 , 1 ) ( 3 , 4 ) ( 5 , 6 )
R3 ( 7 , 5 ) ( 4 , 8 ) ( 3 , 9 ) ( 2 , 3 ) ( 3 , 3 )
R4 ( 8 , 4 ) ( 6, 6 ) ( 4 , 8 ) ( 2 , 2 ) ( 1 , 2 )
R5 ( 9 , 3 ) ( 8 , 4 ) ( 5, 7 ) ( 1 , 2 ) ( 3 , 3 )
A. What are all of the pure strategy Nash Equilibria to the game
B. What are all of the Pareto efficient outcomes to the game
C. Suppose Player One chooses her action first. Player Two then chooses her action after seeing what
Player One has done. What is the likely outcome to this game
Question 110
Consider the following two player game. Player One’s available strategies are Top and Bottom. Player
Two’s available strategies are Left, Middle, and Right. As ususal, Player One’s payoffs are listed first.
Player One
Player Two
Left Middle Right
Top 2 , 50 5 , 20 4 , 10
Bottom 10 , 10 2 , 4 10 , 5
A. What is a Nash Equilibrium if both players choose their actions simultaneously
B. If Player One chooses her action after seeing Player Two’s action, what is an equilibrium to the
game
C. What are the Pareto Optimal outcomes of the game
Question 111
Consider the following normal form game.
Player 1
Player 2
Left Right
Top 10 , 10 12 , 8
Bottom 8 , 12 α , α
What values for α would make the above game a Prisoners Dilemma
20

Question 112
Find all pure-strategy Nash equilibrium to the simultaneous move game with the following normal form
representation..
Player 1
Player 2
V W X Y Z
A 9 , 4 3 ,5 0 , 1 9 , 1 7 , 6
B 2 , 6 4 , 6 7 , 0 2 , 3 3 , 3
C 4 , 4 1 , 4 4 , 7 7 , 6 6 , 6
D 3 , 8 2 , 8 8 , 5 4 , 6 5 , 5
E 7 , 7 4 , 2 8 , 9 8 , 5 3 , 8
Question 113
For each of the eight characteristics of industry structures given below, list whether it is associated with
Perfect Competition, Monopoly, and/or Monopolistic Competition. Write Y if the characteristic is
associated with the industry structure. Write N if the characteristic is not associated with the industry
structure. Fill in all 24 boxes.
Profits are zero in the long run.
The industry is consumer efficient in the long run.
The industry is consumer efficient in the short run.
Supply curves are essentially marginal cost curves.
Entry into the industry is prohibited in the short run.
Entry into the industry is prohibited in the long run.
Each firm faces a downward sloped demand curve.
A firm might find it profitable to advertise its product.
Perfect
Competition
Monopoly
Monopolistic
Competition
Question 114
Suppose that the marginal cost of mining gold is $500 per pound (there are no fixed costs), and the
demand for gold is described by the schedule below.
Price: $300 $400 $500 $600 $700 $800 $900 $1,000
Quantity: 5,000 4,400 3,800 3,200 2,600 2,000 1,400 800
A. If there are many suppliers of gold, what would be the market price of gold and how many pounds of
gold would be sold
B. If there was only one supplier of gold, what would be the market price, quantity sold, and profit
C. If there are only two countries that successfully form a cartel and split production evenly, what would
be the market price of gold, how many pounds of gold does each country mine, and what is each
country’s profit
D. Show that both countries in part C have an incentive to cheat on the cartel’s collusive agreement.
21

Question 115
General observation suggests two empirical facts: (1) Pepsi and Coke dominate the soft drink industry,
and (2) Pepsi and Coke products are sold essentially at the same price. True, there are sale prices, but
Pepsi’s best sale price is the same as Coke’s best sale price, and both companies offer their best sale price
frequently.
A. Given these facts, the predictions from economic theory suggest that Pepsi and Coke could be a
Cartel, engaged in Bertrand competition, or engaged in Cournot competition. Explain why all three
market structures are possible given the facts above.
B. How might you, as an economist for the Federal Trade Commission, go about determining which of
the three forms of oligopoly best describes the competitive practices between Coke and Pepsi
Question 116
The daily global market for oil is described by p = 160 – 0.25Q where Q is total industry output (in
millions of barrels) and p is the price of each barrel. The marginal cost of producing a barrel of oil is $10
in all countries. Suppose all oil producing countries are members of OPEC. OPEC decides to limit
production to 300 million barrels per day, which maximizes joint profits for OPEC. Under this limitation,
OPEC agrees that Mexico will produce 5 million barrels each day.
A. What is Mexico’s daily variable profit from oil if it and all OPEC countries abide by the agreement
B. Show that Mexico could increase its daily profit by cheating on the agreement.
C. Suppose OPEC is successful in limiting daily supply to 300 million barrels. How much deadweight
loss arises because of this policy in comparison to the perfectly competitive market that would exist
in the absence of OPEC
Question 117
Graph a market with a negative consumption externality but no production externality. Label the private
demand and supply curves and the social demand and supply curves. Indicate how much quantity is
produced under the private outcome. Indicate how much quantity is produced under the socially efficient
outcome. Indicate the dead weight loss associated with the externality.
Question 118
Most museums receive public funds to offset some of their expenses.
A. Are museums public goods
B. Whether or not museums are public goods, governments may want to subsidize museums for other
economic reasons. Why
Question 119
The table below lists the amount of pollution each of 4 firms emits during production. The table also lists
each firm’s cost of cleaning up each unit of its own pollution. The government wants to limit pollution to
200 units. Thus, each firm is given 50 tradable permits, and each permit allows the firm to emit 1 unit of
pollution without cleaning it up. Firms are required to pay to clean up all of its pollution for which it does
not have a permit. Assuming that firms do not respond to regulation by producing less output (and thus
pollute less), fill-in the remainder of the table. At what price do permits trade
Firms: A B C D
Pre-Regulation Units of Pollution: 100 75 200 100
Cost of Cleaning Up Each Unit of Pollution: $25 $100 $50 $75
Permits Given: 50 50 50 50
Permits Bought:
Permits Sold:
Total Permits Held After Trading:
22

PRACTICE QUESTIONS TEST ONE
Question 1
The cost of a daily pass to Disneyland is $40. At this price, Disneyland’s total monthly revenue is $8
million. Disneyland decides to cut prices one month to $30 per pass. During that month, 220,000 people
visited Disneyland.
A. Approximately what is the elasticity of demand for Disneyland
B. Would you advise Disneyland to keep its price at $30 per person or return its price to $40 per person
C. Why might these numbers be a bit misleading when making long-term projections
Question 2
What is your best estimate of the elasticity of demand for ice cream cones What is your best estimate of
the elasticity of demand for Dairy Queen ice cream cones Explain both answers in terms of their relation
to each another.
Question 3
Consider the market for air travel. Recently, Northwest Airlines and Delta Airlines both filed for Chapter
11 bankruptcy. Chapter 11 bankruptcy allows these firms to reorganize their debt structure, financial
obligations, and labor contracts to the firms’ advantage, while allowing the firms to continue to operate.
A. What effect does the option of Chapter 11 bankruptcy have on the equilibrium price and quantity of
air travel
B. In contrast to Chapter 11 bankruptcy, the firm is actually dissolved under Chapter 7 bankruptcy.
Comment on the different effects Chapter 7 bankruptcy would have on the market for air travel in
contrast to Chapter 11 bankruptcy.
C. If the problem with the airline industry is that prices are too low due to over-capacity, which
bankruptcy law, Chapter 11 or Chapter 7, would be better for the industry in the long run
Question 4
Due to an increased frequency of malpractice law suits, doctors are paying higher premiums for
malpractice insurance. What effect will this have on the cost and availability of medical services Draw
a graph to illustrate your answer.
Question 5
Cable service costs $50 per month, and almost every household buys cable. Comcast is the only cable
provider and earns huge profits each year. Lake County decides to impose a $5 per month excise tax on
cable service. After the tax is imposed, almost all households continue their service, and the government
collects $4 million in taxes each month. True or False: The profits Comcast receives for operating in
Lake county will fall by roughly $4 million.
Question 6
Suppose the market for DVD movies can be described by p = 40 – 0.5Q D and p = 10 + 2Q S .
A. What is the equilibrium
B. What are the elasticity of supply and elasticity of demand at the equilibrium
C. Suppose the government levies a $5 tax on every DVD sold. What is the new price consumers pay
for a DVD What price (net of taxes) do firms receive for each DVD How much tax revenue does
the government receive
D. What percent of the $5 tax is paid by consumers What percent is paid by firms
23

Question 7
The monthly demand for pizza is Q D = 900 – 50p and the monthly supply of pizzas is Q S = 100p – 300
where p is the price of each pizza.
A. Solve for the inverse demand and inverse supply equations.
B. Solve for the market equilibrium.
C. What is the elasticity of demand and elasticity of supply at the market equilibrium
D. What price would consumers pay if the government imposes a $3 tax on each pizza sold
E. What percentage of the $3 per pizza tax do firms pay
F. How much revenue does the government receive from a $3 excise tax
Question 8
Provide accurate and complete mathematical definitions of the following properties regularly assumed
about preferences: completeness, convexity, monotonicity, and transitivity.
Question 9
Consider the preference ordering captured by the “thick” indifference curves below. Which of our four
assumptions – completeness, transitivity, monotonicity, and diminishing returns – are violated by thick
indifference curves (Thick indifference curves, unlike well-behaved indifference curves, have a
thickness or width, so geometrically they are not officially lines.)
Good 2
Thick Indifference Curves
Good 1
Question 10
Suppose Tom’s preferences for two goods can be described as perfect substitutes whereby Tom is always
indifferent between consuming 3 units of good one or 5 units of good two. Provide a utility function
representation of Tom’s preferences.
Question 11
Suppose Sean has $48. Each beer costs $2 and each pizza costs $8.
A. Draw Sean’s budget line, label it BL 1 . Label the intercepts. What is the slope of BL 1
B. Suppose the price of beer increases to $4 each. Draw Sean’s new budget line, label it BL 2 .
24

PRACTICE QUESTIONS FOR TEST TWO
Question 1
Olivia views cookies and bags of fish crackers as perfect substitutes in a 3:1 ratio. That is, 3 cookies give
her the same utility as 1 bag of fish crackers.
A. Graph some of Olivia’s indifference curves. (Put cookies on the x-axis and fish crackers on the y-
axis.)
B. What is Olivia’s marginal rate of substitution when consuming 10 cookies and 2 bags of crackers
What is her marginal rate of substitution when consuming 2 cookies and 10 bags of crackers
C. Suppose Olivia has $5 to spend on these goods. Each cookie costs $0.20, while each bag of crackers
costs $0.75. How many of each good should she buy to maximize her utility
D. Let Y represent Olivia’s budget, p 1 represent the price of each cookie, and p 2 represent the price of
each bag of crackers. In terms of these three variables, what is Olivia’s optimal consumption bundle
Question 2
Nathan views boxes of milk and cookies as perfect complements in a 1:4 ratio. That is, Nathan always
drinks 1 box of milk with every 4 cookies that he eats (and vice versa).
A. Graph some of Nathan’s indifference curves. (Put milk on the x-axis and cookies on the y-axis.)
B. What is Nathan’s marginal rate of substitution when consuming 10 boxes of milks and 2 cookies
What is his marginal rate of substitution when consuming 2 boxes of milk and 10 cookies
C. Suppose Nathan has $5 to spend on these goods. Each box of milk costs $0.80, while each cookie
costs $0.05. How many of each good should he buy to maximize his utility
D. Let Y represent Nathan’s budget, p 1 represent the price of each box of milk, and p 2 represent the price
of each cookie. In terms of these three variables, what is Nathan’s optimal consumption bundle
Question 3
Suppose preferences for x 1 and x 2 can be represented as: U(x 1 ,x 2 ) = 5x 1 12 x 2 24 .
A. Using a monotonic transformation, U(x 1 ,x 2 ) can be transformed into V(x 1 ,x 2 ) = x 1 α x 2
1– α . What is the
value of α
B. Suppose the budget is $1,200, the price of x 1 is $50, and the price of x 2 is $80. What is the optimal
consumption bundle
C. Use the transformed utility function to calculate the marginal utility of x 1 , the marginal utility of x 2 ,
the marginal rate of substitution, and the marginal rate of transformation at the optimal consumption
bundle.
Question 4
Consider a two-good, fixed price economy. The two goods are bread and cheese. Everybody has a
budget of $50. The price of a loaf of bread is $1.25. The price of a pound of cheese is $4.
A. Ann has Cobb-Douglas preferences for bread and cheese in which she associates a 70% income share
to bread and a 30% income share to cheese. How much bread and cheese does Ann purchase with her
$50
B. Bryan is indifferent between eating bread and cheese. In particular, he always receives the same
utility from eating 2 loaves of bread as he does from eating 1 pound of cheese. How much bread and
cheese does Bryan purchase with his $50
C. Cathy always consumes one half pound of cheese with four tenths of a loaf of bread. Any bread or
cheese consumed in addition to this proportion gives Cathy no utility. How much bread and cheese
does Cathy purchase with her $50
25

Question 5
Shelly has well-behaved preferences. Her budget allows her to afford exactly 30 tablets of cold medicine
(x-axis) and 7 boxes of Kleenex (y-axis). At this bundle, however, the slope of her budget line is -0.25
while her MRS for cold tablets is -0.20. Should Shelly purchase more than 30, exactly 30, or less than 30
tablets of cold medicine
Question 6
Karen’s preferences for butterscotch chips (b) and chocolate chips (c) can be expressed as u(b,c) = 5b 2 c 3 .
The price of each chip is 5¢ for butterscotch and 8¢ for chocolate. Karen has $12 to spend on chips.
A. Draw Karen’s budget line. (Put butterscotch chips on the x-axis.)
B. If Karen buys 80 butterscotch chips, how many chocolate chips can she afford
C. What is the marginal rate of transformation for butterscotch chips
D. What is the marginal rate of substitution for butterscotch chips if Karen consumes 100 butterscotch
chips and 100 chocolate chips
E. What is Karen’s optimal consumption bundle What is Karen’s marginal rate of substitution for
butterscotch chips at her optimal consumption bundle
Question 7
Suppose Richard always consumes shoes and suits in a fixed 2:5 proportion. That is, he always buys two
pairs of shoes with five suits.
A. Draw some of Richard’s indifference curves. (Put shoes on the x-axis.)
B. What is Richard’s MRS for shoes when consuming 8 pairs of shoes and 5 suits
C. What is Richard’s MRS for shoes when consuming 5 pairs of shoes and 8 suits
For parts D – F, assume that the price of each pair of shoes is $50 and the price of each suit is $180.
D. Graph Richard’s budget line when he has $9,000 to spend.
E. Solve for Richard’s optimal consumption bundle given his $9,000 budget.
F. Solve for and graph Richard’s Engle curve for shoes. Let Y denote Richard’s budget.
Question 8
Toll ways are roads that people need to pay to use. Suppose that workers who commute to work by
driving on the toll way are charged $1.50 each day. Of course, commuters can choose to use alternative
routes that are not toll ways for free, but these routes may increase commute time.
A. One senator proposes increasing the toll charge to $3 per day. He claims that the higher toll charge
will result in greater tax revenue. A different senator, however, is opposed to the higher toll. She
claims that the higher toll will lead to fewer people using the toll way, and ultimately lead to less, not
more, tax revenue. Are both of these arguments plausible If not, why not If yes, explain what
factors will determine which scenario comes about
B. In a compromise, the daily toll on commuters is raised from $1.50 to $2.25. In order to learn more
about the effect of the toll on driving patterns, the state hires a few economists from Knox College to
analyze the data. The economists define poor commuters to be those earning less than $50,000 per
year and rich commuters to be those earning more than $50,000 per year. According to this
classification, 80% of all workers are poor and 20% are wealthy. Before the toll increase, 32% of
poor commuters and 63% of wealthy commuters used the toll way. After the toll was increased to
$2.25 per day, 18% of poor commuters and 68% of wealthy commuters used the toll way. The
economists concluded that toll ways are normal goods for poor commuters as this group used toll
ways less after the price increased, but that toll ways are Giffen goods for wealthy commuters as this
group used toll ways more after the price increased. Are the economists from Knox College correct
in their assessment that toll ways are Giffen goods for wealthy commuters If yes, explain what must
be happening in terms of the substitution and income effects for poor vs. wealthy commuters. If the
economists from Knox College are wrong, what part of the model or data are they misinterpreting or
considering incorrectly
26

Question 9
Suppose beer and slices of pizza are perfect complements in a 2:5 ratio so that 2 beers are always
consumed with 5 slices of pizza.
A. Assuming the budget is $20 and the price of each slice of pizza is $2, derive the demand curve for
beer.
B. Assuming the price of each beer is $5 and the price of each slice of pizza is $2, derive the Engel curve
for beer.
Question 10
A. Explain the substitution effect.
B. Explain the income effect.
C. When leisure is a normal good, explain why the income effect goes against the substitution effect.
D. Demonstrate using budget lines and indifference curves and explain in terms of income and
substitution effects the change in quantity demanded for a normal good when its price increases.
E. Demonstrate using budget lines and indifference curves and explain in terms of income and
substitution effects the change in quantity demanded for a Giffen good when its price decreases.
Question 11
In a standard two-good economy, if good one is normal and good two is inferior, is it true that the two
goods must then behave like substitutes when the price of good one falls
Question 12
Consider a consumer model of optimal choice using two normal goods – education and consumption.
Each credit hour of education costs p E . Presently p E = $5,000. Each person, however, can apply for
government aid based on his or her financial situation. He or she will then receive a per-credit
government subsidy of between $0 and $5,000. Thus, someone who receives no subsidy continues to pay
$5,000 per credit, while education is free for someone who receives a per-credit subsidy of $5,000. The
more typical case, however, is between these two extremes. For example, someone who receives a
$1,200 per-credit subsidy would have to pay $3,800 per education credit.
A. Using income and substitution effects, show intuitively that the optimal amount of education
increases (or at least does not decrease) as the government subsidy increases. Recall that both goods
are normal.
B. When is it likely (or for whom is it likely) that an increase in the subsidy for which an individual is
eligible will not affect the amount of education purchased
C. Consider the following two empirical facts.
i. Children from wealthier households are much more likely to purchase more education,
especially a college education, than children from poorer households.
ii. Children from poorer households will receive a much higher education subsidy than
children from wealthier households.
Your answer in part A should have concluded that someone is more likely to purchase more
education when his or her subsidy increases. Given this prediction, how is it that children of
wealthier households actually purchase more education than children of poorer households even
though the children from poorer households are eligible for larger subsidies
27

Question 13
Consider a two-good consumer model where the goods are consumption today (C 0 ) and consumption
tomorrow (C 1 ). The consumer is given Y 0 dollars of income today. The selling price of each unit of
consumption is $1 in each time period. The consumer can invest any savings, S, from today until
tomorrow at a guaranteed interest rate, i, so that her income tomorrow, Y 1 , equals (1+i)S. Assume
throughout that C 0 is inferior while C 1 is a normal good.
A. Mathematically, how does S relate to C 0 and Y 0
B. Graph the consumer’s budget line with tomorrow’s consumption on the x-axis and today’s
consumption on the y-axis. Label this budget line BL 1 .
C. What is the slope of BL 1 Mark a point A on BL 1 and draw an indifference curve (label it IC 1 ) that
indicates that A is the consumer’s optimal consumption bundle given BL 1 .
D. Suppose the government increases the interest rate by lowering the capital gains tax rate. Graph the
consumer’s new budget line (label it BL 2 ). What is the slope of BL 2 Mark a point B on BL 2 and
draw an indifference curve (label it IC 2 ) that indicates that C is the consumer’s optimal consumption
bundle given BL 2 . (Keep in mind that C 0 is inferior and C 1 is normal.)
E. When the interest rate increases, how do C 0 , C 1 , S, and the consumer’s utility change That is, for
each of these 4 items, can you say for certain if they increase or decrease Keep in mind that C 0 is
inferior and C 1 is normal.
28

PRACTICE QUESTIONS FOR EXAM THREE
Question 1
A firm’s total cost function written in units of output, q, is: C(q) = 4q 2 + 2q + 2500.
A. Algebraically solve for the firm’s variable cost curve, fixed costs, average total cost curve, average
variable cost curve, average fixed cost curve, and marginal cost curve.
B. Graph the firm’s average total costs, average variable costs, and marginal costs on the same graph.
Question 2
Consider the cost function: C(q) = 30 + 50q. What are the algebraic expressions for F, VC(q), AFC(q),
AVC(q), AC(q), and MC(q)
Question 3
Provide values for boxes A – H in the table below.
Quantity Price
Total
Revenue
Total
Cost Profit
Marginal
Cost
Marginal
Revenue
0 --------- --------- $50.00 -$50.00 --------- ---------
1 $25.00 $25.00 $60.00 -$35.00 $10.00 $25.00
2 $24.00 $48.00 $69.00 -$21.00 $9.00 $23.00
3 $23.00 B
4 A $4.00 $19.00
5 C
6 $118.50 $96.75 $6.25
7 $18.50 $6.00
8 $17.25 D $5.75
9 $16.00 E $29.25
10 $147.50
11 $13.50 $128.00
12 F $135.00 -$1.50
13 $11.00 G $0.75 H
Question 4
Graph several isoquants associated with the production function: q = f(x 1 , x 2 ) = min{5x 1 , 4x 2 }. Given
factor prices of w 1 and w 2 , what is the cost function
Question 5
Below are six economic concepts (i – vi) that can all be graphed and eight possible descriptions (A – H).
Associate with each concept all descriptions that apply to that concept. Each description can be used
more than once or not at all, and a concept may be associated with more than one description.
Concepts
Descriptions
i. Isoquants A. Typically graphed with labor on the x-axis and capital on the y-axis.
ii. Isocost Lines
B. Constant slope in the typical case.
iii. Marginal Product of Labor C. Has a zero slope when profits are maximized.
iv. SR Total Costs
D. Usually graphed with quantity on the x-axis and dollars on the y-axis.
v. SR Average Variable Costs E. Negatively sloped in the typical case.
vi. SR Average Fixed Costs F. Assumes at least one factor of production is being held fixed.
G. Positively sloped in the typical case.
H. Can be used to determine when labor exhibits diminishing returns.
29

Question 6
Graph several isoquants associated with the production function: q = f(x 1 x 2 ) = min { 3x 1 , 2x 2 }. Given
competitive factor markets that yield factor prices of w 1 = $12 and w 2 = $30, what is the cost function
Question 7
Andrea currently owns a piano for her own playing enjoyment. She also works 15 hours a week at the
Kaplan tutoring center earning $15 per hour. She only works at Kaplan during the school year, which is
36 weeks long. She is considering quitting Kaplan and teaching piano lessons instead. If she gave piano
lessons, she would need to pay $10 each week to get the piano tuned. Andrea could quit Kaplan and
teach piano lessons after school every day for 3 hours, Monday through Friday. She would do this for the
same 36 week stretch and receive $20 per hour from her piano students. What is the dollar value of the
yearly economic profit Andrea gains by quitting Kaplan and teaching piano lessons
Question 8
A firm employs capital and labor to produce its product. Suppose factor prices are $12.50 per unit of
labor and $50 per unit of capital. Currently the firm employs an optimal amount of capital and labor to
make 24,000 units of output as cheaply as possible. Given this optimal bundle of factor inputs, the
marginal product of labor is 30 units of output and the average product of labor is 40 units of output.
What is the marginal product of capital
Question 9
A firm uses capital, K, and labor, L, in it production process, both of which the firm purchases from
competitive factor markets. The firm also sells its output, q, in a competitive product market. Presently,
the price of capital is $50 per unit, the price of labor is $10 per unit, and the firm can sell each unit of
output for $20. The firm’s production function is described by q = f(K,L) = min{20K, L}, and the firm is
required to produce 2,000 units of output. How much capital does the firm purchase How much labor
does the firm purchase How much output does the firm produce How much profit does the firm earn
Question 10
A firm uses capital, K, and labor, L, in it production process, both of which the firm purchases from
competitive factor markets. The firm also sells its output, q, in a competitive product market. Presently,
the price of capital is $50 per unit, the price of labor is $10 per unit, and the firm can sell each unit of
output for $20. The firm’s production function is described by q = f(K,L) = 20K + L, and the firm is
required to produce 1,000 units of output. How much capital does the firm purchase How much labor
does the firm purchase How much output does the firm produce How much profit does the firm earn
Question 11
Consider a firm that employs labor (L) and capital (K) to make output (q). Each unit of labor costs $10
and each unit of capital costs $2. The firm’s production function is q = KL. Given this production
function, the firm’s marginal rate of technical substitution for any factor input bundle is MRTS = –K / L.
A. Does the production function exhibit diminishing marginal returns to labor
B. Does the production function exhibit decreasing, constant, or increasing returns to scale
C. Draw the firm’s isoquant associated with q = 180.
D. How many units of labor and capital should the firm employ if it wants to minimize the cost of
making 180 units of output
E. Draw the firm’s isocost curve associated with spending $120 on factor inputs.
30

Question 12
Parrot Jungle, a tourist attraction in Miami, is a monopolistically competitive firm. Daily demand for
Parrot Jungle is p = 36 − 0.05q where p is the price of admission and q is the number of people admitted.
Parrot Jungle’s daily total costs are C(q) = 5,000 + 0.01q 2 . What price should Parrot Jungle set to
maximize profits How many people visit Parrot Jungle each day What are Parrot Jungle’s daily
profits
Question 13
ABC Records has paid the fixed capital cost of $500,000 associated with having Joni Mitchell record her
next album. Burning, packaging, and shipping each CD costs ABC Records $2. ABC has a contract with
Joni Mitchell whereby ABC pays Mitchell $3 for every CD it sells. Finally, ABC must pay an
entertainment tax of $1 for each CD it sells.
A. Specify ABC’s total cost function. What is ABC’s marginal cost curve
B. Suppose demand for the Mitchell CD can be expressed as p = 30 – 0.00005q. How many CDs will
ABC sell in order to maximize its profit At what price will each CD sell How much profit will
ABC earn from the CD How much income does Mitchell receive from the CD
C. Is the contract between Mitchell and ABC records efficient That is, could you write a contract so
that Mitchell and ABC both earn more than they did in part B If not, why not If yes, specify one
such contract.
Question 14
Annie’s Pear Orchard can sell as many pears as it likes at a price of $8.63 per bushel. Each week, Annie
spends $500 on rent and other necessary maintenance items that are out of her control. Annie also incurs
variable costs of production according to VC(q) = 0.13q + 0.005q 2 .
A. Algebraically solve for C(q), AC(q), AVC(q), and MC(q)
B. Graph MC(q), AC(q), and AVC(q) as accurately as possible on the same graph.
C. How many pounds of pears should Annie make each week to maximize her profits How much profit
does Annie earn each week
D. Instead of a price of $8.63 per bushel, suppose Annie faces a price of $1.43 per bushel. How many
pounds of pears (if any) should Annie make each week to maximize her profits How much profit
does Annie earn each week
Question 15
Suppose wheat is produced in a perfectly competitive market. Currently farmers are making zero
economic profits. Then demand for wheat shifts out due to a severe corn shortage. Describe what
happens in the wheat market in the short run. Describe what happens in the wheat market in the long run.
Include in your analysis comments at the industry and firm level on price, quantity, and profits.
Question 16
Suppose the market for calculators is perfectly competitive. The current price for a calculator is $12.
Texas Instruments’ (TI) weekly total cost function is C(q) = 2500 + 2q + 0.1q 2 , where q is the number of
calculators it makes in a week. Given this cost function, TI’s marginal cost function is MC(q) = 2 + 0.2q.
A. How many calculators should TI make in a week to maximize its profits How much profit does it
earn for the week
B. Suppose TI’s weekly fixed cost did not equal $2,500. At what level of fixed costs would TI earn
weekly profit of $0
C. Suppose TI’s weekly fixed cost did not equal $2,500. At what level of fixed costs would TI choose to
shutdown in the short run
31

Question 17
Oliver receives a constant price of $20 for each broom that he makes and sells. He can sell as many
brooms as he likes at this price. Oliver’s monthly cost function is C(q) = 5000 + 8q + 0.005q 2 .
A. How many brooms should Oliver sell each month to maximize his profits
B. How much profit does Oliver earn each month
C. If Oliver’s fixed costs increased to $50,000 per month, explain as precisely as possible how your
answers to parts A and B would change
D. Suppose price does not equal $20, but instead fluctuates. At what price would Oliver be indifferent
between staying open and shutting down
Question 18
A monopoly faces demand of q = 346 – 0.02p and costs of C(q) = 50,000 + 500q + 10q 2 .
A. Solve for the firm’s marginal revenue curve and marginal cost curve.
B. What is the profit maximizing quantity and price
C. How much profit does the firm earn
D. How much deadweight loss is associated with the monopolist compared to the efficient outcome
Question 19
A monopoly faces costs of of C(q) = 320 + 10q + 2q 2 and demand for its product of q = 50.8 – 0.4p.
A. How many units of output does the monopolist make to maximize its profit What price does the
monopolist charge How much profit does the monopolist earn
B. Suppose the monopolist could pay a local sports hero $1,200 to advertise its product. It is expected
that demand for the product would increase to q = 76 – 0.4p. Should the monopolist pursue this
advertising opportunity
Question 20
Glaxo-Smith-Kline (GSK) has a patent on Glisimnex, a drug that can help treat a form of cancer. GSK’s
cost of making q tablets of Glisimnex each month is C(q) = 18750 + 5q + 0.025q 2 . Monthly demand for
Glisimnex, which can be expressed as an inverse demand function, is p(q) = 180 - 0.01q. How many
tablets of Glisimnex should GSK make each month What price will it charge for each tablet How
much profit will it earn each month
32

PRACTICE QUESTIONS FOR FINAL EXAM
Question 1
The farm lobby is headed to Washington D.C. in hopes of getting Congress to set higher price floors for
all agricultural goods. When interviewed by CNN, the leader of the farm lobby was asked what target
price floor the lobby was hoping to get enacted. His response was “The higher, the better.”
A. Is this true That is, is a higher price floor always better for producers
B. In the United States, agricultural price floors are usually also accompanied with a promise by the
government to purchase (at the price floor) any goods that farmers fail to sell in the marketplace.
Does your answer to A hold up when both of these policies – a price floor and a promise to purchase
all of the quantity surplus – are in place
Question 2
The market for apartments in Lake Forest is competitive, with demand of Q D = 420 – 0.05p and supply of
Q S = 0.10p – 60. Suppose the city of Lake Forest imposes a price ceiling of $2,800. Following the
imposition of the price ceiling, how many apartments will be supplied How many apartments will be
demanded By how much is producer surplus reduced due to the price ceiling How much deadweight
loss is caused by the price ceiling
Question 3
Consider an oligopoly with two firms. The market inverse demand curve is p = 160 – 2Q. The two firms
make identical products, have no fixed costs, and face a marginal cost of 40 per unit produced.
A. Suppose the oligopoly is engaged in Bertrand competition. What is the equilibrium price How
much output does each firm make How much profit does each firm earn
B. Suppose the two firms form an enforceable cartel. What is the equilibrium price How much output
does each firm make How much profit does each firm earn
Question 4
The total yearly (inverse) demand for motorcycles is p = 70,000 – 5Q. Harley Davidson and Yamaha are
the only makers of motorcycles. Each year, each company decides how many motorcycles to make, and
the total made determines the market price. Each company has a total cost of production of 10,000q.
A. If the two companies collude to maximize joint profits, how many motorcycles will each company
make (assuming they split production and profits equally) and how much profit does each company
earn
B. Assuming that Yamaha sticks to this optimal colluding level of production, show that Harley
Davidson can increase its profits by deviating from the agreement and making more motorcycles.
Question 5
Consider an industry in which there are two firms with no fixed costs. Both firms face a constant
marginal cost of $7 and the industry inverse demand curve is p = 187 – 2Q.
A. If the firms successfully form a cartel, what price will the cartel set How much quantity will be
made in the industry How much profit will the cartel earn
B. If the firms are engaged in Bertrand competition, what market price will come about How much
output will be produced in total How much profit will each firm earn
Question 6
Provide very brief descriptions/definitions of the following concepts by completing the sentence.
A. Schumpeterian Growth is the idea that
B. Natural monopoly exists whenever
C. Monopolistic competition is described by the following three properties:
D. Cournot competition requires that
33

Question 7
The following payoff matrix represents payoffs from a game in which there are 2 players each with 4
possible actions. The first number in each box is Player One’s payoff, and the second number is Player
Two’s payoff.
Player One
Player Two
B1 B2 B3 B4
A1 12 , 0 12 , 1 3 , 3 10 , 0
A2 9 , 9 8 , 8 4 , 10 8 , 10
A3 4 , 5 9 , 4 5 , 5 9 , 0
A4 6 , 6 5 , 6 1 , 7 50 , 6
A. What are the pure strategy Nash equilibria to the game
B. List all of the Pareto optimal outcomes to the game.
Question 8
Consider the following normal form game.
Player 1
Player 2
Left Center Right
Top 5 , 4 6 , 9 7 , 2
Middle 8 , 9 4 , 9 2 , 7
Bottom 3 , 5 7 , 6 5 , 5
A. What is the predicted outcome of the above game when considering dominant strategies
B. List all of the pure-strategy Nash equilibria to the above game.
Question 9
Consider the following normal form game.
Player 1
Player 2
A B C D E
W 6 , 3 2 , 9 5 , 5 8 , 9 7 , 9
X 4 , 2 9, 2 2 , 5 2 , 0 6 , 4
Y 0 , 0 7 , 7 5 , 2 9 , 9 5 , 1
Z 7 , 19 3 , 4 7 , 3 4 , 5 1 , 2
List all of the pure strategy Nash equilibria to the above game.
34

Question 10
Consider the following sequential game.
Left
1
Right
In
2 2
Out
In
Out
10 , 40 20 , 30 5 , 100 100 , 5
What is the sub-game perfect equilibrium to the above game
Question 11
The table below lists the amount of pollution each of 4 firms emits during production and each firm’s cost
of cleaning up each unit of its own pollution. The government wants to limit pollution to 300 units. Thus,
each firm is given 75 tradable permits, and each permit allows the firm to emit 1 unit of pollution without
cleaning it up. Firms are required to pay to clean up all of its pollution for which it does not have a permit.
Firms: A B C D
Pre-Regulation Units of Pollution: 160 240 200 400
Cost of Cleaning-Up Each Unit of Pollution: 40 25 30 20
Permits Given: 75 75 75 75
Permits Bought:
Permits Sold:
Total Permits Held After Trading:
A. Fill in the remainder of the table assuming that firms do not respond to regulation by producing less
output (and thus pollute less). At what price do permits trade
B. What would have been the cost of reducing pollution to 300 units if the government had not used
pollution permits but rather required each firm to produce at most 75 units of pollution What is the
cost of reducing pollution to 300 units under the permit scheme
35

EXAM #1 – ECON 210: INTERMEDIATE MICRO
Professor Lemke
February 14, 2011
1. Consider the market for cranberry juice. The market starts in equilibrium. Then it is discovered that
cranberries contain antioxidants, which help in improving one’s health. In response to the news that
cranberries contain antioxidants:
a. How will the demand for cranberry juice change Why
b. How will the supply of cranberry juice change Why
c. How will the equilibrium price and quantity of cranberry juice change Provide a graph of
the changes. (Let 0 denote the original equilibrium, and let 1 denote the new equilibrium.)
2. On February 2, Jewel/Osco predicted that its demand for snow shovels was Q D = 200 – 10p.
a. What is the inverse demand equation
b. What is the elasticity of demand if Jewel sets the price to $12 per shovel
3. The yearly market for bottles of glue in the Lake Forest College Bookstore can be described with the
following demand and supply functions: Q D = 1,000 – 200p and Q S = 200p – 200.
a. What is the market equilibrium (Price and quantity.)
b. At the market equilibrium, it can be shown that the price elasticity of demand is –1.5 and that
the price elasticity of supply is +1.5. Suppose Lake Forest College decides to fund a new
program by imposing a $2 excise tax on each bottle of glue sold in the bookstore.
i. What price will students now pay for a bottle of glue
ii. What price will the bookstore now receive, net of the tax, for a bottle of glue
iii. How much revenue will the college collect because of the excise tax on glue
4. Jeff is taking a group of 8-year-olds to the movies. The tickets were free, and Jeff has $60 to spend
on popcorn and soda. Each bag of popcorn costs $4 and each soda costs $3. Graph Jeff’s budget line.
(Put popcorn on the x-axis.) What is the marginal rate of transformation that Jeff faces
5. A big-box store sells two products – plastic crap and junky trinkets. The store offers two pricing
schemes. Under scheme A, each unit of plastic crap and each junky trinket costs $2. Under scheme
B, a customer can pay a $50 membership fee, the benefit of which is that the prices of both goods are
reduced to $1.
a. On one graph, provide three budget lines for scheme A when income is $80, $100, and $120.
b. On one graph, provide three budget lines for scheme B when income is $80, $100, and $120.
c. When will a consumer pay the membership fee
6. A person values books (x 1 ) and movies (x 2 ) as perfect substitutes whereby each book takes on the
same value as three movies.
a. Provide a utility function capturing these preferences.
b. Graph some indifference curves.
c. What is the person’s marginal rate of substitution (of books in terms of movies) when
consuming 20 books and 21 movies
7. A person values gallons of paint (x 1 ) and paint brushes (x 2 ) as perfect complements whereby 5 gallons
of paint are consumed in tandem with every 2 paint brushes.
a. Provide a utility function capturing these preferences.
b. Graph some indifference curves.
c. What is the person’s marginal rate of substitution (of gallons of paint in terms of paint
brushes) when consuming 30 gallons of paint and 10 paint brushes.
36

EXAM #1 ANSWERS
Professor Lemke
February 14, 2011
1. Consider the market for cranberry juice. The market starts in equilibrium. Then it is discovered that
cranberries contain antioxidants, which help in improving one’s health. In response to the news that
cranberries contain antioxidants:
a. How will the demand for cranberry juice change Why
The new information regarding cranberries will increase (shift out) the demand for cranberry
juice, because people will have a greater preference for cranberry juice.
b. How will the supply of cranberry juice change Why
The supply of cranberry juice will not change. The supply of any product only depends on
the production costs of the good. As the health benefits of cranberry juice do not affect the
production cost of cranberry juice, the new information has no effect on the supply of
cranberry juice.
c. How will the equilibrium price and quantity of cranberry juice change Provide a graph of
the changes. (Let 0 denote the original equilibrium, and let 1 denote the new equilibrium.)
As demand increases but supply remains the same, the new equilibrium in the market for
cranberry juice will result in a higher price (P 1 > P 0 ) and more cranberry juice being sold (Q 1
> Q 0 ) . See the graph below.
Price
D 0 D 1 S 0
P 1
P 0
Q 0 Q 1 Cranberry Juice
2. On February 2, Jewel/Osco predicted that its demand for snow shovels was Q D = 200 – 10p.
a. What is the inverse demand equation
Q D = 200 – 10p → 10p = Q D – 200 → p = 0.1Q D – 20 (Inverse Demand)
b. What is the elasticity of demand if Jewel sets the price to $12 per shovel
At a price of $12, Q D = 200 – 10(12) = 120 = 80. From the demand equation, we also have
that ∂Q D / ∂p = –10. The elasticity of demand is now straightforward to calculate:
⎛
⎜
∂Q
ε =
⎝ ∂p
D
⎞⎛
⎟⎜
p
⎠⎝
Q
D
⎞
⎟ =
⎠
⎛ 12 ⎞
⎜ ⎟
⎝ 80 ⎠
( −10) = −1.5.
37

3. The yearly market for bottles of glue in the Lake Forest College Bookstore can be described with the
following demand and supply functions: Q D = 1,000 – 200p and Q S = 200p – 200.
a. What is the market equilibrium (Price and quantity.)
Q D = Q S
1,000 – 200p = 200p – 200
400p = 1,200
p* = $3
Q* = 1,000 – 200(3) = 200(3) – 200 = 400 bottles of glue.
b. At the market equilibrium, it can be shown that the price elasticity of demand is –1.5 and that
the price elasticity of supply is +1.5. Suppose Lake Forest College decides to fund a new
program by imposing a $2 excise tax on each bottle of glue sold in the bookstore.
i. What price will students now pay for a bottle of glue
As demand and supply are both linear, we know that
⎛ η ⎞ ⎛ 1.5 ⎞ ⎛ 1 ⎞
∆p
= ⎜ ⎟ × ∆t
= ⎜ ⎟ × 2 = ⎜ ⎟ × 2 = $1.
⎝η
− ε ⎠ ⎝1.5
− ( −1.5)
⎠ ⎝ 2 ⎠
As price changes by $1, students pay $4 after the tax has been imposed.
ii. What price will the bookstore now receive, net of the tax, for a bottle of glue
As students now pay $4 per bottle of glue and the tax on each bottle is $2, the
bookstore receives a net price of $4 – $2 = $2 per bottle of glue following the tax.
iii. How much revenue will the college collect because of the excise tax on glue
At the new consumer price of $4, we have that Q D = 1,000 – 200(4) = 200 bottles of
glue are demanded. (Alternatively, at the new after-tax price of $2, Q S = 200(2) –
200 = 200 bottles of glue are supplied.) With 200 bottles now being bought and sold,
and given a $2 excise tax, total revenue collected from the tax is 200 × $2 = $400.
4. Jeff is taking a group of 8-year-olds to the movies. The tickets were free, and Jeff has $60 to spend
on popcorn and soda. Each bag of popcorn costs $4 and each soda costs $3. Graph Jeff’s budget line.
(Put popcorn on the x-axis.) What is the marginal rate of transformation that Jeff faces
With a $60 budget, the max popcorn that can be afforded is $60 ÷ $4 = 15 bags and the max soda is
$60 ÷ $3 = 20 sodas. As prices never change, the budget line is a straight line with constant slope. In
particular, the slope of the budget line is the MRT = –p popcorn ÷ p soda = –$4 ÷ $3 = –1.33.
Soda
20
Slope = –1.33
15 Popcorn
38

5. A big-box store sells two products – plastic crap and junky trinkets. The store offers two pricing
schemes. Under scheme A, each unit of plastic crap and each junky trinket costs $2. Under scheme
B, a customer can pay a $50 membership fee, the benefit of which is that the prices of both goods are
reduced to $1.
a. On a single graph, provide three budget lines for scheme A when income is $80, $100, and
$120.
As both prices are $2, the consumer can purchase a max of 40 of either good when having an
$80 budget, 50 when having a $100 budget, and 60 when having an $120 budget.
Trinkets
60
50
40
Budget Lines for Scheme A
BL $80 BL $100 BL $120
40 50 60 Crap
b. On a single graph, provide three budget lines for scheme B when income is $80, $100, and
$120.
As both prices are now $1 but one must pay the $50 membership fee, the consumer can
purchase a max of 30 of either good when having an $80 budget, 50 when having a $100
budget, and 70 when having an $120 budget.
Trinkets 70 Budget Lines for Scheme B
50
30 BL $80 BL $100 BL $120
c. When will a consumer pay the membership fee
30 50 70 Crap
Under Scheme A, both prices are $2. Therefore, the total number of units of goods that can
be purchased (of either good or in some combination) is Y ÷ 2. Under Scheme B, both prices
are $1, but the membership fee must be paid. Therefore, the total number of units of goods
that can be purchased (of either good or in combination is (Y – 50) ÷ 1 = Y – 50. The
consumer prefers Scheme B, therefore, if Y – 50 > Y ÷ 2, which reduces to
Y – 50 > Y / 2 → 2Y – 100 > Y → Y > 100.
Thus, the consumer prefers scheme B whenever her budget is greater than (or equal to) $100.
39

6. A person values books (x 1 ) and movies (x 2 ) as perfect substitutes whereby each book takes on the
same value as three movies.
a. Provide a utility function capturing these preferences.
As 1 book (x 1 ) always provides the same value as 3 movies (x 2 ), according to our notation in
class we have that a = 1 and b = 3. Therefore, a valid utility function for these perfect
substitute preferences is
x2
u ( x1,
x2)
= x1
+ .
3
b. Graph some indifference curves.
Movies 9
6
3
1 2 3 Books
c. What is the person’s marginal rate of substitution (of books in terms of movies) when
consuming 20 books and 21 movies
As all indifference curves has the same constant slope under perfect substitutes, the MRS at
any bundle is always the same: MRS = –b / a = –3 / 1 = –3. Thus, when consuming 20
books and 21 movies, the MRS is –3.
40

7. A person values gallons of paint (x 1 ) and paint brushes (x 2 ) as perfect complements whereby 5 gallons
of paint are consumed in tandem with every 2 paint brushes.
a. Provide a utility function capturing these preferences.
As 5 gallons of paint (x 1 ) is always consumed in tandem with 2 paint brushes (x 2 ), according
to our notation in class we have that a = 5 and b = 2. Therefore, a valid utility function
for these perfect complement preferences is
b. Graph some indifference curves.
⎧ x1
x2
⎫
u ( x1,
x2)
= max⎨
, ⎬ .
⎩ 5 2 ⎭
Paint Brushes
6
Ray of Slope b / a = 0.4
4
2
5 10 15 Gallons of Paint
c. What is the person’s marginal rate of substitution (of gallons of paint in terms of paint
brushes) when consuming 30 gallons of paint and 10 paint brushes.
Under perfect substitutes, the MRS is always negative infinity above the ray (i.e., having
excess paint brushes) and is always 0 on and below the ray (i.e., having excess paint). As 10
paint brushes can be used with 25 gallons of paint (i.e., [10 ÷ 2] × 5 = 25), the proposed
bundle of 30 gallons of paint and 10 paint brushes is associated with excess paint. Therefore,
the MRS at this bundle equals 0.
41

EXAM #1 – ECON 210: INTERMEDIATE MICRO
Professor Lemke
February 20, 2012
1. Explain how the following events affect the market equilibrium (both price and quantity). In your
answer, explain in words and show with a graph what happens.
a. Suppose a new, popular, and successful diet promotes eating low-carb foods. What happens
to the equilibrium in the market for cheese For the record, cheese is a low-carb food.
b. Suppose the price of aluminum falls by half due to the finding of new deposits. What
happens to the equilibrium in the market for aluminum-coated frying pans For the record,
the production of aluminum-coated frying pans requires considerable amounts of aluminum.
2. Following natural disasters (such as hurricanes), the government frequently enacts “No Price
Gauging” laws. For example, following a natural disaster when people need “recovery goods” such
as power generators, clean water, or batteries, the government prohibits firms from selling these items
at a price significantly higher than what these goods were selling at before the disaster. Consider an
extremely devastating disaster for which the effects last for at least three months and therefore the No
Price Gauging law remains in effect for at least three months as well. At the same time, though the
devastation was severe, suppose the roads are opened relatively quickly so that during the three
months of recovery, goods can still be shipped into the area at the same cost and as easily as they had
been shipped into the area before the disaster.
a. Using words and a graph, what would happen to the price of one of these “recovery” goods
such as power generators, clean water, or batteries following the natural disaster if the
government did not impose the No Price Gauging law
b. During the three months of recovery, the No Price Gauging law would help some (potential)
consumers. Explain why.
c. During the three months of recovery, the No Price Gauging law would hurt some (potential)
consumers. Explain why.
3. Draw a budget line when income is $100, the price of good 1 is $10, and the price of good 2 is $5.
Include both intercepts and the slope in your graph.
4. Consider the budget line drawn in the graph below, and know that the price of Good 2 = $4.00.
Budget Line
Good 2
Slope = –2
10
Good 1
a. How much of Good 2 can the consumer afford if he buys none of Good 1
b. How much income does the consumer have
c. What is the price of Good 1
42

5. Consider a situation with $100 of income and two goods – bottles of glue and all other goods. The
price of all other goods is always $1 per unit. The Craft Store sells bottles of glue for $2 per bottle,
unless the purchaser is willing to buy more than 40 bottles in which case the Craft Store charges $1
per bottle for all of the bottles purchased (not just the bottles purchased after the 40 th ). Thus, among
the infinite possibilities, the consumer could purchase 20 bottles at $2 per bottle, leaving $60 to be
spent on all other goods. Alternatively, the consumer could purchase 70 bottles at $1 per bottle,
leaving $30 to be spent on all other goods. Graph the consumer’s budget line. Be sure to include all
intercepts, interesting points, and slopes.
6. Consider a market for iPhones described by the following supply and demand functions.
Supply: Q S = 4P – 120
Demand: Q D = 480 – 2P
a. Solve for the inverse supply function and the inverse demand function.
b. Solve for the market equilibrium.
c. Suppose the government imposes a $30 excise tax on firms. What is the new market
equilibrium, including the new price consumers pay for an iPhone, the new price firms
receive for an iPhone after paying the tax, and the quantity of iPhones now bought and sold in
equilibrium Moreover, what portion of the $30 excise tax do consumers bear What
portion of the $30 excise tax do firms bear How much revenue does the tax generate for the
government
7. For Mylie, downloading 7 songs always yields the same amount of happiness as does downloading
two episodes of The Office. Thus, for Mylie, song downloads and episodes of The Office are perfect
substitutes.
a. Graph several of Mylie’s indifference curves. (Put songs on the x-axis and episodes of The
Office on the y-axis.)
b. Provide a utility function representing Mylie’s preferences.
c. What is Mylie’s MRS at the consumption bundle of 19 songs and 43 episodes of The Office
8. Aramark, in planning for a party, expects guests to always want to consume 9 pieces of sushi with 2
pieces of tempura. Thus, from Aramark’s perspective, sushi and tempura are perfect complements.
a. If the price of each piece of sushi is $3, the price of each piece of tempura is $4, and
Aramark’s budget for the party is $700, how many pieces of sushi and how many pieces of
tempura should Aramark purchase
b. Provide a utility function representing Aramark’s preferences.
c. What is the MRS for sushi (so sushi is graphed on the x-axis) at the consumption bundle of
360 pieces of sushi and 60 pieces of tempura
43

9. Arthur and Baxter both have well-behaved preferences for cake (x-axis good) and donuts (y-axis
good), though they differ in their valuation of both goods. The graphs below include some of
Arthur’s indifference curves and some of Baxter’s indifference curves. Both graphs are on the same
scale, so they are comparable.
Arthur’s Indifference Curves
Baxter’s Indifference Curves
Donuts
Donuts
Cakes
Cakes
According to the indifference curves graphed above, does Arthur place a greater value on cake than
does Baxter or does Baxter place a greater value on cake than does Arthur Explain.
44

EXAM #1 – ECON 210: INTERMEDIATE MICRO – ANSWERS
Professor Lemke
February 20, 2012
1. Explain how the following events affect the market equilibrium (both price and quantity). In your
answer, explain in words and show with a graph what happens.
a. Suppose a new, popular, and successful diet promotes eating low-carb foods. What happens
to the equilibrium in the market for cheese For the record, cheese is a low-carb food.
The successful diet doesn’t affect the cost of producing cheese, so the supply curve is
unaffected. On the other hand, the successful diet will increase the demand for cheese as
people are attracted to the diet and therefore have a greater preference for cheese. When
supply stays fixed and demand increases, the equilibrium price will increase and the
equilibrium quantity will increase. Both of these changes are captured in the graph below.
Price of Cheese
The Market for Cheese
S
P 1
P 0
D 0
D 1
Q 0
Q 1
Quantity of Cheese
b. Suppose the price of aluminum falls by half due to the finding of new deposits. What
happens to the equilibrium in the market for aluminum-coated frying pans For the record,
the production of aluminum-coated frying pans requires considerable amounts of aluminum.
The fall in the price of aluminum doesn’t affect preferences for aluminum-covered pans or
income or the price of other goods, so demand does not change in response to this news.
However, when the price of aluminum falls, the cost of making aluminum-coated pans falls
as the price of an input fell. Thus, supply shifts out in response to the news. When demand
stays fixed and supply increases, the equilibrium price for aluminum-coated pans falls and the
equilibrium quantity of aluminum-coated pans increases. Both of these changes are captured
in the graph below.
45

Price of Aluminum-
Coated Pans
The Market for Aluminum-Coated Pans
S 0
P 0
S 1
P 1
D
Q 0
Q 1
Quantity of Aluminum-
Coated Pans
2. Following natural disasters (such as hurricanes), the government frequently enacts “No Price
Gauging” laws. For example, following a natural disaster when people need “recovery goods” such
as power generators, clean water, or batteries, the government prohibits firms from selling these items
at a price significantly higher than what these goods were selling at before the disaster. Consider an
extremely devastating disaster for which the effects last for at least three months and therefore the No
Price Gauging law remains in effect for at least three months as well. At the same time, though the
devastation was severe, suppose the roads are opened relatively quickly so that during the three
months of recovery, goods can still be shipped into the area at the same cost and as easily as they had
been shipped into the area before the disaster.
a. Using words and a graph, what would happen to the price of one of these “recovery” goods
such as power generators, clean water, or batteries following the natural disaster if the
government did not impose the No Price Gauging law
Following a natural disaster, demand for recovery goods increases while supply is unaffected
as the cost of shipping goods into the region has not changed. Thus, when demand increases
and supply remains unchanged, price will increase as will equilibrium quantity.
Price of
Recovery Good
The Market for a Recover Good
S
P 1
P 0
D 0
D 1
Q 0
Q 1
Quantity of Recovery Good
46

. During the three months of recovery, the No Price Gauging law would help some (potential)
consumers. Explain why.
Given the new equilibrium in part (a), notice that a No Price Gauging law is simply a price
ceiling imposed on a market. Therefore, the (potential) consumers who benefit from the No
Price Gauging law are those who actually purchase the good at the artificially low price.
c. During the three months of recovery, the No Price Gauging law would hurt some (potential)
consumers. Explain why.
The problem with price ceilings is that they lead to shortages. In this case, more consumers
want power generators, clean water, batteries, etc. than are being supplied to the market by
firms. Thus, the (potential) consumers who are hurt by the No Price Gauging law are those
consumers who are willing to pay an even higher price for the good but can’t do so and thus
can’t buy the good as firms do not supply enough to meet demand.
3. Draw a budget line when income is $100, the price of good 1 is $10, and the price of good 2 is $5.
Include both intercepts and the slope in your graph.
The math should be relatively straightforward, so here I only draw the graphs.
Good 2
20
Budget Line
Slope = -2
10
Good 1
47

4. Consider the budget line drawn in the graph below, and know that the price of Good 2 = $4.00.
Budget Line
Good 2
Slope = –2
10
Good 1
a. How much of Good 2 can the consumer afford if he buys none of Good 1
As the slope is -2 and the x-axis intercept is 10, this means that the y-intercept is 10*(2) = 20.
Thus, the consumer can purchase 20 units of Good 2 if he doesn’t buy any of Good 1.
b. How much income does the consumer have
As the price of Good 2 is $4.00 per unit and the consumer can afford to purchase 20 units of
Good 2, the consumer has 20*($4) = $80 of income.
c. What is the price of Good 1
As the slope is -2, the price of Good 2 = $4, and the slope equals –P 1 /P 2 , we can solve -2 = -
P 1 /4 to find that the price of Good 1 is $8.
5. Consider a situation with $100 of income and two goods – bottles of glue and all other goods. The
price of all other goods is always $1 per unit. The Craft Store sells bottles of glue for $2 per bottle,
unless the purchaser is willing to buy more than 40 bottles in which case the Craft Store charges $1
per bottle for all of the bottles purchased (not just the bottles purchased after the 40 th ). Thus, among
the infinite possibilities, the consumer could purchase 20 bottles at $2 per bottle, leaving $60 to be
spent on all other goods. Alternatively, the consumer could purchase 70 bottles at $1 per bottle,
leaving $30 to be spent on all other goods. Graph the consumer’s budget line. Be sure to include all
intercepts, interesting points, and slopes.
This is not a kink problem, but rather price depends on quantity. The first 40 bottles of glue cost 40 x
$2 = $80, leaving $20 for all other goods. At the other extreme, one could buy no glue and spend all
$100 on all other goods. On this portion of the budget line, the slope = -2.
When buying more than 40 bottles of glue, the consumer can buy 100 bottles of glue (and no other
good) or 40 + ε bottles of glue, leaving $60 – ε for spending on all other goods. On this portion of the
budget line, the slope = -1.
See the graph on the next page.
48

All Other Goods
Budget Line
100
Slope = –2
60
Slope = –1
20
0
0
40
100
Bottles of Glue
6. Consider a market for iPhones described by the following supply and demand functions.
Supply: Q S = 4P – 120
Demand: Q D = 480 – 2P
a. Solve for the inverse supply function and the inverse demand function.
Inverse Supply: Q S = 4P – 120 Inverse Demand: Q D = 480 – 2P
4P = Q S + 120
2P = 480 – Q D
P = 0.25Q S + 30 P = 240 – 0.5Q D .
b. Solve for the market equilibrium.
Market Equilibrium: Q S = Q D
4P – 120 = 480 – 2P
6P = 600
P* = $100 => Q* = 4(100) – 120 = 480 – 2(100) = 280 units.
Thus, in equilibrium, 280 iPhones will be sold at a price of $100 per phone.
c. Suppose the government imposes a $30 excise tax on firms. What is the new market
equilibrium, including the new price consumers pay for an iPhone, the new price firms
receive for an iPhone after paying the tax, and the quantity of iPhones now bought and sold in
equilibrium Moreover, what portion of the $30 excise tax do consumers bear What
portion of the $30 excise tax do firms bear How much revenue does the tax generate for the
government
Using the inverse supply curve, the new supply curve is P = 0.25Q S + 60 as it shifts up by the
amount of the tax.
New Market Equilibrium: 0.25Q S + 60 = 240 – 0.5Q D
0.75Q = 180
Q* = 240 => P* = 0.25(24) + 60 = 240 – 0.5(240) = $120.
Thus, under the tax, 240 iPhones will be sold at a price of $120 per phone ($90 received by
firms). From this, we have that consumers bear $20 ($120 - $100) of the $30 tax while firms
bear the remaining $10 of the $30 tax. In the end, the tax generates 240 x $30 = $7,200 of tax
revenue.
49

7. For Mylie, downloading 7 songs always yields the same amount of happiness as does downloading
two episodes of The Office. Thus, for Mylie, song downloads and episodes of The Office are perfect
substitutes.
a. Graph several of Mylie’s indifference curves. (Put songs on the x-axis and episodes of The
Office on the y-axis.)
Episodes of The Office
8
6
4
Slope = –2/7 for all Indifference Curves
2
7 14 21 28
Song Downloads
b. Provide a utility function representing Mylie’s preferences.
Let x 1 be songs and x 2 be downloads of the Office. Then, as 7 songs always yields the same
amount of happiness as 2 episodes, one utility function that represents these preferences is:
x1
x2
u ( x1
, x2
) = + .
7 2
c. What is Mylie’s MRS at the consumption bundle of 19 songs and 43 episodes of The Office
As Mylie treats song downloads and episodes of The Office as perfect substitutes, her MRS is
always -2/7 regardless of consumption bundle. In particular, at the bundle of 19 songs and 43
episodes of The Office, her value of another song, which is her MRS, is -2/7 th of an episode.
50

8. Aramark, in planning for a party, expects guests to always want to consume 9 pieces of sushi with 2
pieces of tempura. Thus, from Aramark’s perspective, sushi and tempura are perfect complements.
a. If the price of each piece of sushi is $3, the price of each piece of tempura is $4, and
Aramark’s budget for the party is $700, how many pieces of sushi and how many pieces of
tempura should Aramark purchase
Consider a bundle to be 9 pieces of sushi and 2 pieces of tempura. The cost of a bundle is
then 9 x $3 + 2 x $4 = $35. Given Aramark’s $700 budget, it can afford to purchase
$700 ÷ $35 = 20 such bundles. Thus, Aramark should purchase 20 x 9 = 180 pieces of sushi
and 20 x 2 = 40 pieces of tempura.
b. Provide a utility function representing Aramark’s preferences.
Let x 1 be pieces of sushi and x 2 be pieces of tempura. Then, party guests always want to
consume 9 pieces of sushi with 2 pieces of tempura, one utility function that represents these
preferences is:
⎧ x1
x2
⎫
u ( x1
, x2
) = min⎨
, ⎬ .
⎩ 9 2 ⎭
c. What is the MRS for sushi (so sushi is graphed on the x-axis) at the consumption bundle of
360 pieces of sushi and 60 pieces of tempura
Given Aramarks preferences of 9 pieces of sushi to 2 pieces of tempura, providing 360 pieces
of sushi should be accompanied with (360 ÷ 9) x 2 = 80 pieces of tempura. As the proposed
bundle comes with 60 pieces of tempura, there is not enough tempura in the bundle (or there
is excess sushi). Thus, Aramark would not be willing to trade any of its tempura for any
amount of sushi. Thus, Aramark’s MRS for sushi is 0 at the proposed bundle.
51

9. Arthur and Baxter both have well-behaved preferences for cake (x-axis good) and donuts (y-axis
good), though they differ in their valuation of both goods. The graphs below include some of
Arthur’s indifference curves and some of Baxter’s indifference curves. Both graphs are on the same
scale, so they are comparable.
Arthur’s Indifference Curves
Baxter’s Indifference Curves
Donuts
Donuts
Cakes
Cakes
According to the indifference curves graphed above, does Arthur place a greater value on cake than
does Baxter or does Baxter place a greater value on cake than does Arthur Explain.
Notice that Arthur’s indifference curves are more steeply sloped at any bundle compared to Baxter’s
indifference curves. In particular, if one graphs both indifference curves on the same graph, at any
bundle A, we would have the following.
Donuts
Arthur’s IC
A
Baxter’s IC
Cakes
At bundle A, Arthur’s indifference curve is more steeply sloped than is Baxter’s. This means that
Arthur’s MRS is greater than Baxter’s. This means that Arthur always places a greater value on
cakes than does Baxter.
52

EXAM #2 – ECON 210: INTERMEDIATE MICRO
Professor Lemke
March 18, 2011
1. Marian’s preferences for flowers (x) and jewelry (y) can be expressed as v(x, y) = 2x 4 y 36 . Each flower
costs $2.50 and each unit of jewelry costs $20.
a. Transform Marian’s preferences into u(x, y) = x α y 1–α where 0 < α < 1.
b. What is Marian’s marginal utility for flowers under the transformed utility function when
consuming 10 units of flowers and 40 units of jewelry
c. What is Marian’s marginal rate of substitution of flowers in terms of jewelry when
consuming 10 units of flowers and 40 units of jewelry
d. What is Marian’s marginal rate of transformation of flowers in terms of jewelry when
consuming 10 units of flowers and 40 units of jewelry
e. Suppose Marian’s significant other knows Marian’s preferences and chooses to spend $200
on flowers and jewelry for Marian. How many flowers and how much jewelry will Marian’s
significant other purchase for her
2. Scott has $72 and faces prices of p 1 = $5 and p 2 = $6. Scott’s preferences can be written as:
⎧ x1
⎫
u ( x1,
x2
) = min⎨
, 3x2
⎬ .
⎩ 2 ⎭
What is Scott’s optimal consumption bundle
3. Lori always places the same value on 1 piece of cake as she does on 4 donuts. Lori has $9 to spend,
and the price of each piece of cake is $3 while the price of each donut is $0.60.
a. Given Lori’s preferences, income, and the above prices, what is Lori’s optimal consumption
bundle
b. Suppose the price of donuts increases but Lori doesn’t change her consumption decision.
What can be said about the new price of donuts
4. Consider a standard two-good consumption model for beer and pretzels. Norm and Cliff, two
friendly bar patrons, who have identical incomes and face the same prices, both have well-behaved
preferences. Norm’s preference for beer, however, is stronger than Cliff’s preference for beer at all
possible consumption bundles.
a. You are told that one of the barmates optimally chooses to consume 5 beers and 2 bowls of
pretzels while the other chooses to consume 7 beers and 1 bowls of pretzels. Which person is
associated with the consumption bundle of 5 beers and 2 bowls of pretzels Explain.
b. You are told that Cliff’s MRS (in absolute value) is always greater than Norm’s MRS (in
absolute value). Under this characterization, which good – beer or pretzels – is being graphed
on the x-axis Explain.
c. On a single graph, provide some indifference curves for Cliff and some indifference curves
for Norm (labeled clearly) that incorporate the information given in part b.
53

5. Consider a standard two-good model. Bruce’s optimal demand for good 1 is
x 1 = Y
10 p p
.
For the record, you should notice that this is not the optimal demand that comes about from having
preferences according to Cobb-Douglas, perfect complements, or perfect substitutes. For each of the
questions below, be sure to explain your answer clearly and completely.
a. Does Bruce treat the two goods (x 1 and x 2 ) as complements or substitutes
b. Graph Bruce’s demand curve for good 1 assuming that Y = $500 and p 2 = $5. Does Bruce’s
demand for good 1 satisfy the law of demand
c. Graph Bruce’s Engel curve for good 1 assuming p 1 = $2 and p 2 = $5. Does Bruce consider
good 1 to be a normal or inferior good
6. Consider the standard Consumption Today – Consumption Tomorrow model with an income
endowment of Y 0 today and no income endowment tomorrow. Thus, consumption tomorrow is
financed completely out of consumption today, and borrowing is not allowed. Let i be the real
interest rate between the two periods, t be the capital gains tax rate, and r be the real after-tax interest
rate between the two periods.
a. What is it specifically in the first sentence above that leads the second sentence to conclude
that “borrowing is not allowed”
b. State r as a function of i and t. State p 1 , the price of consumption tomorrow (period 1), as a
function of r. How do r and p 1 change when the capital gains tax rate is increased Do these
relationships make intuitive sense
c. What are the mathematical relationships between endowed income (Y 0 ), consumption today
(C 0 ), consumption tomorrow (C 1 ), savings (S), and the after-tax rate of return (r) Hint: You
can answer this by providing two mathematical equations.
d. Assuming consumption today is an inferior good, use income and substitution effects to
demonstrate potential changes in consumption today (C 0 ), consumption tomorrow (C 1 ), and
savings (S) when the capital gains tax rate is increased.
7. For each part below, draw a budget line for our standard consumption – leisure model that reflects the
general conditions given. Thus, you will draw a budget line for part A, and you will draw a second
budget line on a separate graph for part B. Label all aspects of your graphs as much as possible.
a. Draw a typical weekly budget line assuming a person earns a higher wage when working
overtime. That is, the first 40 hours of work is paid at one wage while all hours worked past
40 hours are paid a higher wage. Assume there are 98 hours each week that can be divided
between work and leisure.
b. Draw a typical budget line for an hourly worker in the United States who faces a progressive
marginal income tax schedule. Assume the worker has 5,000 hours each year to be divided
between work and leisure. Recall that a progressive tax system raises marginal tax rates with
income. For simplicity, assume there are three marginal tax rates and that a worker who
works 5,000 hours each year would earn enough money to pay at least some tax at the highest
marginal rate.
1
2
54

EXAM #2 ANSWERS
Professor Lemke
March 18, 2011
1. Marian’s preferences for flowers (x) and jewelry (y) can be expressed as v(x, y) = 2x 4 y 36 . Each flower
costs $2.50 and each unit of jewelry costs $20.
a. Transform Marian’s preferences into u(x, y) = x α y 1–α where 0 < α < 1.
From class we know that α = 4 ÷ (4 + 36) = 0.1. Therefore, u(x, y) = x 0.1 y 0.9 .
b. What is Marian’s marginal utility for flowers under the transformed utility function when
consuming 10 units of flowers and 40 units of jewelry
1−α
⎛ y ⎞ ⎛ 40 ⎞
Flowers = x, and so MU x = α⎜
⎟ = 0.1⎜
⎟ ≈ 0. 3482 .
⎝ x ⎠ ⎝ 10 ⎠
c. What is Marian’s marginal rate of substitution of flowers in terms of jewelry when
consuming 10 units of flowers and 40 units of jewelry
⎛ α ⎞⎛
y ⎞ ⎛ 0.1⎞⎛
40 ⎞
MRS = −⎜
⎟⎜
⎟ = −⎜
⎟⎜
⎟ ≈ −0.444
.
⎝1−
α ⎠⎝
x ⎠ ⎝ 0.9 ⎠⎝
10 ⎠
d. What is Marian’s marginal rate of transformation of flowers in terms of jewelry when
consuming 10 units of flowers and 40 units of jewelry
0.9
⎛ ⎞
⎜
px
⎛ $2.50 ⎞
MRT = − ⎟ = −⎜
⎟ = −0.125
.
⎝
p y ⎠ ⎝ $20 ⎠
e. Suppose Marian’s significant other knows Marian’s preferences and chooses to spend $200
on flowers and jewelry for Marian. How many flowers and how much jewelry will Marian’s
significant other purchase for her
αY
(0.1)($200)
x* = =
= 8
$2.50
p x
(1 − α)
Y (0.9)($200)
and y* = =
= 9 .
$20
p y
Therefore, the optimal bundle is 8 flowers and 9 units of jewelry.
2. Scott has $72 and faces prices of p 1 = $5 and p 2 = $6. Scott’s preferences can be written as:
⎧ x1
⎫
u ( x1,
x2
) = min⎨
, 3x2
⎬ .
⎩ 2 ⎭
What is Scott’s optimal consumption bundle
Scott’s preferences are perfect complements, with 2 units of x 1 always being consumed with ⅓ units
of x 2 . The price of this bundle is 2p 1 + (⅓)p 2 = 2($5) + (⅓)($6) = $12. The income level of $72
allows $72 ÷ $12 = 6 such bundles being consumed. Therefore Scott consumes 6 × 2 = 12 units of
good 1 and 6 × ⅓ = 2 units of good 2.
55

3. Lori always places the same value on 1 piece of cake as she does on 4 donuts. Lori has $9 to spend,
and the price of each piece of cake is $3 while the price of each donut is $0.60.
a. Given Lori’s preferences, income, and the above prices, what is Lori’s optimal consumption
bundle
Lori’s preferences are perfect substitutes. The market cost of 1 piece of cake is $3. The
market cost of 4 donuts is 4 × $0.60 = $2.40. As $2.40 < $3, Lori spends all of her money on
donuts and none of it on cake. Lori consumes 0 pieces of cake and $9 ÷ $0.60 = 15 donuts.
b. Suppose the price of donuts increases but Lori doesn’t change her consumption decision.
What can be said about the new price of donuts
As Lori doesn’t change her consumption decision, the cost of 4 donuts must remain less than
the cost of 1 piece of cake. That is, 4p d < $3, which requires p d < $0.75. Therefore, we know
that the new price of donuts is above $0.60 and is less than $0.75.
4. Consider a standard two-good consumption model for beer and pretzels. Norm and Cliff, two
friendly bar patrons, who have identical incomes and face the same prices, both have well-behaved
preferences. Norm’s preference for beer, however, is stronger than Cliff’s preference for beer at all
possible consumption bundles.
a. You are told that one of the barmates optimally chooses to consume 5 beers and 2 bowls of
pretzels while the other chooses to consume 7 beers and 1 bowls of pretzels. Which person is
associated with the consumption bundle of 5 beers and 2 bowls of pretzels Explain.
As the two bar patrons have well-behaved preferences, identical incomes, and face the same
prices, Norm’s optimal consumption bundle will always include as much or more beer than
Cliff’s optimal consumption bundle. Therefore, we know that Cliff’s optimal bundle is 5
beers and 2 bowls of pretzels (and Norm’s bundle is 7 beers and 1 bowl of pretzels).
b. You are told that Cliff’s MRS (in absolute value) is always greater than Norm’s MRS. Under
this characterization, which good – beer or pretzels – is being graphed on the x-axis
As Cliff’s MRS is greater than Norm’s MRS for the x-axis good, Cliff’s marginal value of the
x-axis good exceeds Norm’s valuation at all possible consumption bundles. As we are told
that Norm always has a stronger preference for beer, the x-axis good must be pretzels.
c. On a single graph, provide some indifference curves for Cliff and some indifference curves
for Norm (labeled clearly) that incorporate the information given in part b.
Beer
IC 1
Cliff
IC2 Cliff
IC 3Cliff
IC 3
Norm
IC 2
Norm
IC 1
Norm
Pretzels
56

5. Consider a standard two-good model. Bruce’s optimal demand for good 1 is
x 1 = Y
10 p p
.
For the record, you should notice that this is not the optimal demand that comes about from having
preferences according to Cobb-Douglas, perfect complements, or perfect substitutes. For each of the
questions below, be sure to explain your answer clearly and completely.
a. Does Bruce treat the two goods (x 1 and x 2 ) as complements or substitutes
1
As the price of good 2 increases, the optimal value of x 1 falls. (Plug in some numbers if you
don’t see this directly: if Y = 10 and p 1 = 1, then p 2 = $0.50 → x 1 = 2 and p 2 = $1.00 → x 1 =
1.) Moreover, if x 1 falls when p 2 increases, x 1 and x 2 are, by definition, complements.
b. Graph Bruce’s demand curve for good 1 assuming that Y = $500 and p 2 = $5. Does Bruce’s
demand for good 1 satisfy the law of demand
Substituting: x 1 = 500/(10 × $5 × p 1 ) = 10/p 1 . Rearranging: p 1 = 10/x 1 .
Price of good 1
5
Demand Curve
2
2 Good 1
c. Graph Bruce’s Engel curve for good 1 assuming p 1 = $2 and p 2 = $5. Does Bruce consider
good 1 to be a normal or inferior good
Substituting: x 1 = Y/(10 × $2 × $5) = Y/100. Rearranging: Y = 100x 1 .
Income
Engel Curve
Slope =100
Good 1
As the Engel curve has a positive slope, Bruce considers Good 1 to be normal.
57

6. Consider the standard Consumption Today – Consumption Tomorrow model with an income
endowment of Y 0 today and no income endowment tomorrow. Thus, consumption tomorrow is
financed completely out of consumption today, and borrowing is not allowed. Let i be the real
interest rate between the two periods, t be the capital gains tax rate, and r be the real after-tax interest
rate between the two periods.
a. What is it specifically in the first sentence above that leads the second sentence to conclude
that “borrowing is not allowed”
As there is no endowment income in the second period (tomorrow), the agent has nothing to
borrow against (i.e., the agent has no assets in the second period with which to repay a loan
from the first period). Therefore, there cannot be any borrowing.
b. State r as a function of i and t. State p 1 , the price of consumption tomorrow (period 1), as a
function of r. How do r and p 1 change when the capital gains tax rate is increased Do these
relationships make intuitive sense
Let S be savings. Without taxes, S grows by iS from the first period to the second. If the
agent pays a capital gains tax rate of t, the net growth is iS – iSt = (1 – t)iS. Therefore, r = (1
– t)i.
Given r, p 1 = 1/(1 + r) = 1/(1 + (1 – t)i).
When t↑ → r↓ → p 1 ↑. These relationships make intuitive sense. When the tax rate goes up,
the real rate of return (r) falls. And when the real rate of return falls, consumption tomorrow
gets more expensive, which means that p 1 must increase.
c. What are the mathematical relationships between endowed income (Y 0 ), consumption today
(C 0 ), consumption tomorrow (C 1 ), savings (S), and the after-tax rate of return (r) Hint: You
can answer this by providing two mathematical equations.
S = Y 0 – C 0 and C 1 = (1 + r)S = (1 + r)(Y 0 – C 0 ).
d. Assuming consumption today is an inferior good, use income and substitution effects to
demonstrate potential changes in consumption today (C 0 ), consumption tomorrow (C 1 ), and
savings (S) when the capital gains tax rate is increased.
First note that consumption tomorrow must be normal as consumption today is inferior.
(IE) t ↑ → p 1 ↑ → Real Income ↓ → C 1 ↓ (normal), C 0 ↑ (inferior) → S ↓
(SE) t ↑ → p 1 ↑ → C 1 ↓, C 0 ↑ → S ↓.
Taking the IE and SE together, we see that when consumption today is inferior, an increase in
the capital gains tax rate is predicted to lower consumption tomorrow, increase consumption
today, and lower savings. There is no ambiguity in any of the three variables in this case.
58

7. For each part below, draw a budget line for our standard consumption – leisure model that reflects the
general conditions given. Thus, you will draw a budget line for part A, and you will draw a second
budget line on a separate graph for part B. Label all aspects of your graphs as much as possible.
a. Draw a typical weekly budget line assuming a person earns a higher wage when working
overtime. That is, the first 40 hours of work is paid at one wage while all hours worked past
40 hours are paid a higher wage. Assume there are 98 hours each week that can be divided
between work and leisure.
Consumption
Weekly Budget Line
|slope| > w
|slope| = w
58 98 Leisure
b. Draw a typical budget line for an hourly worker in the United States who faces a progressive
marginal income tax schedule. Assume the worker has 5,000 hours each year to be divided
between work and leisure. Recall that a progressive tax system raises marginal tax rates with
income. For simplicity, assume there are three marginal tax rates and that a worker who
works 5,000 hours each year would earn enough money to pay at least some tax at the highest
marginal rate.
Yearly Budget Line
Consumption
|slope| = (1 – t 2 )w
|slope| = (1 – t1)w
|slope| = w
5,000 Leisure
The graph above assumes that the lowest tax rate is t 0 = 0, in which range the worker earns an
after-tax hourly wage of w. Once enough money is earned, the worker pays a marginal tax
rate of t 1 > 0, in which range the worker’s after-tax wage is (1 – t 1 )w. Finally, if the worker
continues to earn enough money (by working enough hours), he will eventually face a
marginal tax rate of t 2 where t 2 > t 1 . In this range the worker’s after-tax wage is (1 – t 2 )w.
59

EXAM #2 – ECON 210: INTERMEDIATE MICRO
Professor Lemke
March 9, 2012
1. Consider the Cobb-Douglas utility function: u ( x1,
x2
) = x1
x2
. The price of good 1 is $15, while
the price of good 2 is $10. The consumer has a budget of $300.
a. What is the marginal rate of substitution of good 1 for good 2 at the consumption bundle (8,
6)
b. What is the marginal rate of transformation of good 1 for good 2 at the consumption bundle
(8, 6)
c. What is the optimal consumption bundle
2. Consider a consumer whose preference can be described by the following utility function:
2 / 5
{ 3x
}
1 , x 2 ) min 1 ,
2
3/ 5
u ( x = x .
a. Write the optimal demand for x 1 and x 2 as a function of prices and income.
b. Assume the price of good 1 is $30 and income is $60. Provide and graph the inverse demand
function for good 2.
c. Assume the price of good 1 is $30 and the price of good 2 is $5. Provide and graph the Engel
curve for good 2.
3. When shopping for her family, Claire treats kiwis (k) and mangos (m) as perfect substitutes, where
five kiwis can substitute for two mangos (and likewise, two mangos can substitute for five kiwis).
Thus, one utility function that represents Claire’s preferences is
u(k, m) = 0.2k + 0.5m.
a. What is Claire’s demand function for kiwis when her budget is $30 and the price of each
mango is $0.80. Graph this demand function.
b. What is Claire’s Engel curve for kiwis when the price of each kiwi is $0.20 and the price of
each mango is $0.80. Graph this Engel curve.
c. What is the Claire’s optimal demand when her budget is $20, the price of each kiwi is $0.20,
and the price of each mango is $0.80.
4. When asked why she supported expanding the Earned Income Tax Credit (EITC) but did not support
offering a lump-sum transfer as policy to help the poor, a famous economist responded “Because the
lump-sum transfer is not associated with a substitution effect, but the EITC is.” Explain what the
economist meant by this and why this led her to have a policy preference for the EITC but not for the
lump-sum transfer.
5. Assuming consumption today and consumption tomorrow are both normal goods, we showed in class
that a reduction in the capital gains tax rate could result in greater or less savings today. Explain or
reproduce this result. Be thorough and careful.
60

6. The following graph shows optimal choice following an increase in the price of good 1. All items
before the price increase are labeled with a superscript 0, while all items following the price increase
are labeled with a superscript 1. All items are labeled as we labeled them in class.
Good 2
IC 1
IC 0 BL 1
●
●
BL 0
Good 1
a. On the graph, draw in the hypothetical budget line and clearly label the substitution, income,
and total effects for good 1 from the price increase.
b. According to your graph, is good 1 normal, inferior but not Giffen, or Giffen Explain.
c. According to your graph, are goods 1 and 2 complements or substitutes Explain.
61

7. Below are nine graphs, and ten descriptions of the graphs. There is only one way to uniquely map all
nine graphs into all ten descriptions, which is the task at hand.
Good 2
PANEL 1
Income
PANEL 2
Price of
Good 1
PANEL 3
Good 1
Good 1
Good 1
Price of
Good 1
PANEL 4
Good 2
PANEL 5
Income
PANEL 6
Good 1
Good 1
Good 1
PANEL 7
PANEL 8
Income Price of
Good 2
Good 1
PANEL 9
Good 1
Good 1
Good 1
Circle the number of the graph that corresponds with the descriptions below.
A standard budget line…………………………….. 1 2 3 4 5 6 7 8 9 None
A price-consumption curve for normal goods……. 1 2 3 4 5 6 7 8 9 None
An income-consumption curve for normal goods… 1 2 3 4 5 6 7 8 9 None
A demand curve under Cobb-Douglas preferences… 1 2 3 4 5 6 7 8 9 None
A demand curve under perfect complements……… 1 2 3 4 5 6 7 8 9 None
A demand curve under perfect substitutes………… 1 2 3 4 5 6 7 8 9 None
A demand curve for a Giffen good………………… 1 2 3 4 5 6 7 8 9 None
An Engel curve for a necessity……………………. 1 2 3 4 5 6 7 8 9 None
An Engel curve for a normal good………………… 1 2 3 4 5 6 7 8 9 None
An Engel curve for an inferior good………………. 1 2 3 4 5 6 7 8 9 None
62

EXAM #2 – ECON 210: INTERMEDIATE MICRO -- ANSWERS
Professor Lemke
March 9, 2010
1. Consider the Cobb-Douglas utility function: u ( x1,
x2
) = x1
x2
. The price of good 1 is fixed at
$15, while the price of good 2 is fixed at $10. The consumer has a budget of $300.
a. What is the marginal rate of substitution of good 1 for good 2 at the consumption bundle (8, 6)
⎛
MRS = −⎜
⎝
α ⎞⎛
x
2
⎟
1 ⎜
− α ⎠ x1
⎝
⎞ ⎛ 2 / 5 ⎞⎛
6 ⎞
⎟ = −⎜
⎟⎜
⎟ = −
⎠ ⎝ 3 / 5 ⎠⎝
8 ⎠
1
.
2
2 / 5
3/ 5
b. What is the marginal rate of transformation of good 1 for good 2 at the consumption bundle (8,
6)
MRT = −
p
p
1
2
15
= − = −1.5.
10
c. What is the optimal consumption bundle
x
αY
(2 / 5)(300)
= = p 15
*
1 =
1
8.
x
(1 − α)
Y
=
p
(3 / 5)(300)
=
10
*
2 =
2
18.
2. Consider a consumer whose preference can be described by the following utility function:
{ 3x
}
u ( x = x .
1 , x 2 ) min 1 ,
a. Write the optimal demand for x 1 and x 2 as a function of prices and income.
Given the utility function, a = 1/3 and b = 1 meaning that the consumer must consume onethird
unit of good 1 with one unit of good 2. Optimal demands, therefore, are:
x
*
1
aY Y / 3 Y
= =
= and
ap + bp ( p / 3) + p p + 3p
1
1
2
2
1
* bY Y 3Y
x2
= =
= .
ap + bp ( p / 3) + p p + 3p
1
2
2
2
1
1
2
2
63

. Assume the price of good 1 is $30 and income is $60. Provide and graph the inverse demand
function for good 2.
Given p 1 = 30 and Y = 60, demand for good 2 is
x
*
2
= 3(60)
30 + 3p
. Solving this for p yields 2
2
60
p 2 = −10
. x
Graphing the inverse demand curve for good 2, we have:
Price of
Good 2
Demand Curve for Good 2
2
6 Good 2
c. Assume the price of good 1 is $30 and the price of good 2 is $5. Provide and graph the Engel
curve for good 2.
* 3Y
3Y
Y
Given p 1 = 30 and p 2 = 5, demand for good 2 is x 2 = = = . Solving this for Y
30 + 3(5) 45 15
yields Y = 15x 2 . Graphing the Engel curve for good 2, we have:
Income
Engel Curve for Good 2
Slope = 15
Good 2
64

3. When shopping for her family, Claire treats kiwis (k) and mangos (m) as perfect substitutes, where
five kiwis can substitute for two mangos (and likewise, two mangos can substitute for five kiwis).
Thus, one utility function that represents Claire’s preferences is
u(k, m) = 0.2k + 0.5m.
a. What is Claire’s demand function for kiwis when her budget is $30 and the price of each mango
is $0.80. Graph this demand function.
Demand depends on relative prices. Five kiwis cost 5p k . Two mangos cost 2p m = 2 × $0.80 =
$1.60. Therefore, Claire spends all of her budget on kiwis as long as 5p k < 1.60, which requires
p k < $0.32. If the price of each kiwi is greater than $0.32, Claire will not buy any kiwis.
Therefore, her demand curve for kiwis is:
Graphing this function, we have:
⎧ 30
⎪ if
p
⎪
k
k * = ⎨
⎪ 0 if
⎪
⎩
pk
< 0.32
p > 0.32
Demand Curve for Kiwis
k
Price of
Kiwis
$0.32
Kiwis
b. What is Claire’s Engel curve for kiwis when the price of each kiwi is $0.20 and the price of each
mango is $0.80. Graph this Engel curve.
As p k = $0.20, which is less than $0.32, Claire spends her entire budget on kiwis. Therefore, k* =
Y/p k = Y/0.20 = 5Y. Solving for Y we have Y = 0.20k. Graphing this:
Income
Engel Curve for Kiwi
Slope = $0.20
Kiwi
65

c. What is the Claire’s optimal demand when her budget is $20, the price of each kiwi is $0.20, and
the price of each mango is $0.80.
As the price of kiwis is less than $0.32, Claire spends her entire budget on kiwis. Therefore,
with a budget of $20, Claire buys k* = 20/0.2 = 100 kiwis and m* = 0 mangos.
4. When asked why she supported expanding the Earned Income Tax Credit (EITC) but did not support
offering a lump-sum transfer as policy to help the poor, a famous economist responded “Because the
lump-sum transfer is not associated with a substitution effect, but the EITC is.” Explain what the
economist meant by this and why this led her to have a policy preference for the EITC but not for the
lump-sum transfer.
A substitution effect, in terms of labor supply, only occurs when the price of leisure (i.e., the wage
rate) changes. As a lump-sum transfer doesn’t affect the wage rate, it cannot be associated with a
substitution effect. As a result, a lump-sum transfer is only associated with an income effect, which
would lead a person to want to leisure more (and work less). Alternatively, the EITC is associated
with a 40% wage subsidy, which essentially increases one’s wage by 40%. Thus, the EITC is
associated with a substitution effect. In particular:
↑ wage subsidy → ↑ wage rate → ↑ price of leisure → ↓ leisure (& ↑ hours worked).
Ultimately, the economist prefers expanding the EITC over offering a lump-sum transfer, because
expanding the EITC may encourage more people to start working while offering a lump-sum transfer
will never have a positive effect on employment.
5. Assuming consumption today and consumption tomorrow are both normal goods, we showed in class
that a reduction in the capital gains tax rate could result in greater or less savings today. Explain or
reproduce this result. Be thorough and careful.
The tax change has the following effects:
↓ capital gains tax rate → ↑ real interest rate → ↓ price of consumption tomorrow.
Given the decrease in the price of consumption tomorrow, we have:
(SE) ↓ price of consumption tomorrow → ↓ consumption today, ↑ consumption tomorrow.
(IE) ↓ price of consumption tomorrow → ↑ consumption today and ↑ consumption tomorrow as both
are normal goods.
Now, one must look at consumption today to see what happens to savings. According to the
substitution effect, consumption today falls, so savings increases. However, according to the income
effect, consumption today increases, so savings decreases. Thus, as the effect on saving is
ambiguous, it is unclear whether a lowering of the capital gains tax rate would increase or decrease
savings.
66

6. The following graph shows optimal choice following an increase in the price of good 1. All items
before the price increase are labeled with a superscript 0, while all items following the price increase
are labeled with a superscript 1. All items are labeled as we labeled them in class.
Good 2
IC 1
1
x 2
SE
x 2
●
●
x 2
0
●
TE
IC 0 BL 1
IE
SE
BL H
BL 0
x 1
1
x 1
SE
x 1
0
Good 1
a. On the graph, draw in the hypothetical budget line and clearly label the substitution, income,
and total effects for good 1 from the price increase.
The optimal point on the hypothetical budget line ( x 1 ) must be on IC 0 up and to the left
from the original optimal bundle. From there, the substitution effect is from the origin al
0 SE
point, x 1 , to x 1 . The income effect if from x SE 1 to x 1 1 .
b. According to your graph, is good 1 normal, inferior but not Giffen, or Giffen Explain.
As drawn above (and as it would be drawn by almost anyone), good 1 is normal because the
SE 1
income effect goes in the same direction as the substitution effect. That is, from x 1 to x 1 ,
all that is happening is that income is being reduced, and optimal demand for good 1 is also
falling. This is what is required for a good to be normal.
c. According to your graph, are goods 1 and 2 complements or substitutes Explain.
According to the graph, quantity demanded of good 2 increased when the price of good 1
increased. This is the definition of goods 1 and 2 being substitutes.
SE
67

7. Below are nine graphs, and ten descriptions of the graphs. There is only one way to uniquely map all
nine graphs into all ten descriptions, which is the task at hand.
Good 2
PANEL 1
Income
PANEL 2
Price of
Good 1
PANEL 3
Good 1
Good 1
Good 1
Price of
Good 1
PANEL 4
Good 2
PANEL 5
Income
PANEL 6
Good 1
Good 1
Good 1
PANEL 7
PANEL 8
Income Price of
Good 2
Good 1
PANEL 9
Good 1
Good 1
Good 1
a. A standard budget line…………………………….. 1 2 3 4 5 6 7 8 9 None
b. A price-consumption curve for normal goods……. 1 2 3 4 5 6 7 8 9 None
c. An income-consumption curve for normal goods… 1 2 3 4 5 6 7 8 9 None
d. A demand curve under Cobb-Douglas preferences… 1 2 3 4 5 6 7 8 9 None
e. A demand curve under perfect complements……… 1 2 3 4 5 6 7 8 9 None
f. A demand curve under perfect substitutes………… 1 2 3 4 5 6 7 8 9 None
g. A demand curve for a Giffen good………………… 1 2 3 4 5 6 7 8 9 None
h. An Engel curve for a necessity……………………. 1 2 3 4 5 6 7 8 9 None
i. An Engel curve for a normal good………………… 1 2 3 4 5 6 7 8 9 None
j. An Engel curve for an inferior good……………. 1 2 3 4 5 6 7 8 9 None
68

EXAM #3 – ECON 210: INTERMEDIATE MICRO
Professor Lemke
April 15, 2011
1. A firm’s production function is f(K, L) = 20K 1/4 L 5/4 . Each unit of capital costs the firm $2,000, while
each unit of labor costs the firm $24,000.
a. Does the firm experience increasing, constant, or decreasing returns to scale How do you know
b. In terms of K and L, what is the firm’s marginal rate of technical substitution
c. Graph the firm’s $60,000 isocost line.
d. If the firm maximizes profit by employing capital to the point where the marginal product of
capital is 480, what is the marginal product of the optimal amount of labor the firm employs
2. VisCom Industrial, better known as VCI, sells color printer cartridges in a perfectly competitive
market. Presently the price of color printer cartridges is $45 per cartridge. VCI’s cost function is
C(q) = 25,000 + 5q + 0.02q 2 where q is the number of cartridges that VCI manufactures. How many
cartridges should VCI manufacture and sell in order to maximize its short run profits (Provide a
complete answer!)
3. Market demand for a good is Q = 1,200 – 5p.
a. When the industry is controlled be a monopolist, the cost function is C(q) = 4,000 + 0.1q 2 . What
is the firm’s marginal cost function
b. The monopolist chooses its output to maximize profits. How much output will the monopolist
choose to sell At what price will it sell each unit of output How much profit will the
monopolist earn each period
c. Suppose instead that the market is perfectly competitive. (Assume the monopolist’s marginal
cost function is the now the industry supply curve.) How many units of output will be produced
in the entire industry under perfect competition At what price will each unit of output sell
d. How much dead-weight loss is associated with monopoly (part b) compared to perfect
competition (part c) for this industry
4. Consider a market with no externalities. According to our statement of the First Welfare Theorem,
therefore, we are considering a market in which consumers and firms “take into account all social
costs and benefits when valuing the consumption and production of goods.”
a. Draw a picture of an efficient market, labeling consumer surplus and producer surplus. What is it
about this picture (in particular, what is missing from this picture) that indicates the market is
efficient
b. Draw a picture of a market with a price floor. Indicate all of the important welfare concepts.
What is it about this picture that indicates the market is inefficient
c. The picture you drew in part b looks very much like the picture one draws for monopoly.
However, in class it was claimed that producer surplus under a price floor may or may not be
greater than producer surplus under competition but that producer surplus under a monopolistic
market had to be greater than producer surplus under a competitive market. Explain this claim.
69

5. Soybeans are sold in a perfectly competitive industry. The industry is presently in long-run
equilibrium. In the present equilibrium, the following hold (along with the variable representation):
the price of soybeans is $5 per bushel (p = $5), there are 5,000 soybean farmers (N = 5,000), each
soybean farmer produces 40,000 bushels (q = 40,000), 200 million bushels of soybeans are produced
in total (Q = 200 million), and each firm receives $0 profits (π = $0).
a. A negative finding regarding the health risks of soybeans then leads to an immediate and
permanent decrease in the market demand for soybeans. For each of the five variables, indicate
(by circling your answer) which value might come about in the short run in response to the
negative demand shock. (Circle only one value per variable.)
Short-Run Variable Values
Price = p $4 $5 $6
Number of Firms = N 4,000 5,000 6,000
Firm quantity = q 38,000 40,000 42,000
Industry quantity = Q 190 million 200 million 210 million
Firm profits = π –$12,000 $0 $12,000
b. For each of the five variables, indicate (by circling your answer) which value might come about
in the long run following the demand shock. (Circle only one value per variable.)
Long-Run Variable Values
Price = p $4 $5 $6
Number of Firms = N 4,000 5,000 6,000
Firm quantity = q 38,000 40,000 42,000
Industry quantity = Q 160 million 200 million 240 million
Firm profits = π –$12,000 $0 $12,000
c. Following the eventual return to long-run equilibrium, another shock occurs, and after the market
for soybeans works through that shock, long-run equilibrium is once again obtained. This time,
however, the price of a bushel of soybeans is now $2 per bushel. Which of the following shocks
could have caused this long-run change, and why: an increase in the demand for soybeans; an
increase in the price of soybean seeds; a decrease in the cost of farm workers; a technological
advancement in the fertility of soybean seeds
70

EXAM #3 ANSWERS
Professor Lemke
April 15, 2011
1. A firm’s production function is f(K, L) = 20K 1/4 L 5/4 . Each unit of capital costs the firm $2,000, while
each unit of labor costs the firm $24,000.
a. Does the firm experience increasing, constant, or decreasing returns to scale How do you know
The firm experiences increasing returns to scale because the production function is a Cobb-
Douglas production function in which the exponents sum to greater than 1. In particular, the
exponents are 1/4 and 5/4, which sum to 1.5.
b. In terms of K and L, what is the firm’s marginal rate of technical substitution
We know from the notes that for a Cobb Douglass production function f(K, L) = AK α L β is :
βK
MRTS = − α L
c. Graph the firm’s $60,000 isocost line.
⎛ 5K
⎞
⎜ ⎟
4 5K
= −
⎝ ⎠
= −
⎛1L
⎞ L
⎜ ⎟
⎝ 4 ⎠
.
As $60,000 can purchase 2.5 = $60,000/$24,000 units of labor or 30 = $60,000/$2,000 units of
capital, the $60,000 isocost line is:
Capital
30
$60,000 Isocost Line
2.5 Labor
d. If the firm maximizes profit by employing capital to the point where the marginal product of
capital is 480, what is the marginal product of the optimal amount of labor the firm employs
Profit maximization requires
MP
w
L
MPk
MPL
480
= ⇒ = ⇒ MPL
r 24,000 2,000
= 5,760 .
Thus, at these factor prices, if the firm employs capital to the point where the marginal product of
capital is 480, it will employ labor to the point where the marginal product of labor is 5,760.
71

2. VisCom Industrial, better known as VCI, sells color printer cartridges in a perfectly competitive
market. Presently the price of color printer cartridges is $45 per cartridge. VCI’s cost function is
C(q) = 25,000 + 5q + 0.02q 2 where q is the number of cartridges that VCI manufactures. How many
cartridges should VCI manufacture and sell in order to maximize its short run profits (Provide a
complete answer!)
As it is a perfectly competitive industry and price equals $45, VCI’s marginal revenue equals $45. As
VCI’s cost function is C(q) = 25,000 + 5q + 0.02q 2 , its marginal cost function is MC(q) = 5 + 0.04q.
So now, to maximize profits:
Step 1. Set MR = MC to solve for q*.
MR = MC
45 = 5 + 0.04q
0.04q = 40
q* = 1,000 cartridges.
Step 2. Because the market is perfectly competitive, we know that p* = $45 per cartridge.
Step 3. At q* = 1,000 and p* = $45, VCI’s revenues are R(1,000) = 1,000 × $45 = $45,000. At
the same time, VCI’s total costs are C(1,000) = 25,000 + 5(1,000) + 0.02(1,000) 2 =
$50,000. Therefore VCI’s profits, when it produces 1,000 color printer cartridges is
π(1,000) = R(1,000) – C(1,000) = $45,000 – $50,000 = –$5,000.
Step 4.
As profit is negative, the shut-down rule must be checked. If the firm stays open, it will
produce 1,000 cartridges and lose $5,000 in profit. If the firm shuts down, it produces 0
cartridges and loses its fixed costs of $25,000. As VCI would rather lose $5,000 than
lose $25,000, VCI will opt to remain open, produce 1,000 cartridges, and earn –$5,000 in
profit.
72

3. Market demand for a good is Q = 1,200 – 5p.
a. When the industry is controlled be a monopolist, the cost function is C(q) = 4,000 + 0.1q 2 . What
is the firm’s marginal cost function
The firm’s marginal cost function is MC(q) = 0.2q.
b. The monopolist chooses its output to maximize profits. How much output will the monopolist
choose to sell At what price will it sell each unit of output How much profit will the
monopolist earn each period
The monopolist faces market demand, so 5p = 1,200 – q so that p = 240 – 0.2q. Therefore the
monopolist’s marginal revenue is MR = 240 – 0.4q.
Setting MR = MC to find Q* MON :
240 – 0.4q = 0.2q
0.6q = 240
Q* MON = q* = 400.
Therefore, p* MON = 240 – 0.2(400) = $160. The monopolist’s revenue is R(400) = 400 × $160 =
$64,000. The monopolist’s costs are C(400) = 4,000 + 0.1(400) 2 = $20,000. Therefore, the
monopolist’s profits each period are π(400) = R(400) – C(400) = $64,000 – $20,000 = $44,000.
Note, for part d below, that the firm’s marginal cost when making 400 units of output is
MC(400) = 0.2(400) = $80.
c. Suppose instead that the market is perfectly competitive. (Assume the monopolist’s marginal
cost function is the now the industry supply curve.) How many units of output will be produced
in the entire industry under perfect competition At what price will each unit of output sell
Under perfect competition, price equals marginal cost:
At Q* PC = 600, p* PC = 240 – 0.2(600) = $120.
p = MC
240 – 0.2Q = 0.2Q
0.4Q = 240
Q* PC = 600
d. How much dead-weight loss is associated with monopoly (part b) compared to perfect
competition (part c) for this industry
Given the above results, we have:
DWL = (½)(p* MON – MC(Q* MON ))(Q* PC – Q* MON ) = (½)($160 – $80)(600 – 400) = $8,000.
73

4. Consider a market with no externalities. According to our statement of the First Welfare Theorem,
therefore, we are considering a market in which consumers and firms “take into account all social
costs and benefits when valuing the consumption and production of goods.”
a. Draw a picture of an efficient market, labeling consumer surplus and producer surplus. What is it
about this picture that indicates the market is efficient
The market below is efficient because there is no dead-weight loss.
Efficient Market
$ Supply
p*
CS
PS
Q* Quantity
Demand
b. Draw a picture of a market with a price floor. Indicate all of the important welfare concepts.
What is it about this picture that indicates the market is inefficient
The market below is inefficient because of the existence of dead-weight loss.
Price Floor
$ Supply
DWL
CS
Price Floor
p Floor
PS
Demand
Q Floor Q*
Quantity
c. The picture you drew in part b looks very much like the picture one draws for monopoly.
However, in class it was claimed that producer surplus under a price floor may or may not be
greater than producer surplus under competition but that producer surplus under a monopolistic
market had to be greater than producer surplus under a competitive market. Explain this claim.
When the government imposes a price floor, it does not necessarily do it in such a way that helps
firms. (Think if it set the price floor of a gallon of milk to $5,000. This certainly would not help
dairy farmers.) However, when the market is controlled by a monopolist, the monopolist chooses
the price that maximizes its profits. Therefore it must be that profits are greater under the
monopoly price than under the competitive price. Moreover, we showed in class that maximizing
profits is the same as maximizing producer surplus, so as we know that profits are maximized
under the monopoly price, producer surplus must also be maximized under that price. Therefore
we know that producer surplus is greater under monopoly than under competition.
74

5. Soybeans are sold in a perfectly competitive industry. The industry is presently in long-run
equilibrium. In the present equilibrium, the following hold (along with the variable representation):
the price of soybeans is $5 per bushel (p = $5), there are 5,000 soybean farmers (N = 5,000), each
soybean farmer produces 40,000 bushels (q = 40,000), 200 million bushels of soybeans are produced
in total (Q = 200 million), and each firm receives $0 profits (π = $0).
a. A negative finding regarding the health risks of soybeans then leads to an immediate and
permanent decrease in the market demand for soybeans.
Short-Run Variable Values
Price = p $4 $5 $6 Price falls due to the negative demand shock.
Number of Firms = N 4,000 5,000 6,000 Firms cannot exit (or enter) in the short run.
Firm quantity = q 38,000 40,000 42,000 Existing firms produce less when the price falls.
Industry quantity = Q 190 mil 200 mil 210 mil
Less is produced in the industry, because each firm
produces less.
Firm profits = π –$12,000 $0 $12,000
Firms lose money in the short run because price
falls.
b. Return to the long run following the demand shock.
Long-Run Variable Values
Price = p $4 $5 $6
Following a demand shock, the long-run price
returns to the original long-run price.
Number of Firms = N 4,000 5,000 6,000 Firms exit in the long run due to short-run neg π.
Firm quantity = q 38,000 40,000 42,000 Firm quantity returns to the original q MES output.
Industry quantity = Q 160 mil 200 mil 240 mil Total industry output falls b/c some firms exited.
Firm profits = π –$12,000 $0 $12,000 Perf. Comp. firm profits always equal $0 in the LR.
c. Following the eventual return to long-run equilibrium, another shock occurs, and after the market
for soybeans works through that shock, long-run equilibrium is once again obtained. This time,
however, the price of a bushel of soybeans is now $2 per bushel. Which of the following shocks
could have caused this long-run change, and why: an increase in the demand for soybeans; an
increase in the price of soybean seeds; a decrease in the cost of farm workers; a technological
advancement in the fertility of soybean seeds
A decrease in the long-run competitive price cannot come about from a demand shock (ruling out the
first). An increase in a factor price would increase, not decrease, the long-run price (ruling out the
second). The third is a possibility – when the price of a factor of production falls, the cost function falls
and in particular the minimum average cost must fall. As long-run price equals the minimum average
cost, such a change could cause a decrease in the long-run price (making the third shock a possibility).
The fourth is also a possibility – a technological advancement is reflected by an improved cost function,
and in particular by a lower minimum average cost. As long-run price equals the minimum average cost,
such advancement could cause a decrease in the long-run price (making the fourth shock a possibility).
75

EXAM #3 – ECON 210: INTERMEDIATE MICRO
Professor Lemke
April 16, 2011
1. A firm’s production function is f(K, L) = 20K 1/4 L 5/4 . Each unit of capital costs the firm $2,000, while
each unit of labor costs the firm $24,000.
a. Does the firm experience increasing, constant, or decreasing returns to scale How do you know
b. In terms of K and L, what is the firm’s marginal rate of technical substitution
c. Graph the firm’s $60,000 isocost line.
d. If the firm maximizes profit by employing capital to the point where the marginal product of
capital is 480, what is the marginal product of the optimal amount of labor the firm employs
Hint: There is an easy way and a hard way to get this answer. I would suggest doing it the easy
way, but if you don’t see that way, the hard way with brute force mathematics will work.
2. VisCom Industrial, better known as VCI, sells color printer cartridges in a perfectly competitive
market. Presently the price of color printer cartridges is $45 per cartridge. VCI’s cost function is
C(q) = 28,800 + 5q + 0.02q 2 where q is the number of cartridges that VCI manufactures.
a. How many cartridges should VCI manufacture and sell in order to maximize its short run
profits Provide a complete answer!
b. What will be the long-run price of color printer cartridges and how many cartridges will each
firm produce Hint: This takes a bit of thinking and math to figure out.
3. A firm faces an inverse demand function of p = 240 – 0.2q. The firm’s cost function is
C(q) = 4,000 + 0.1q 2 . How much output will the firm choose to sell in the short run in order to
maximize its profits At what price will it sell each unit of output How much profit will the firm
earn in the short run
4. In class, we drew a picture that represented the “Gains to Trade” from having free trade when the
domestic country would be a net importer of the good.
a. Draw a similar graph of the domestic market under free trade when the domestic country
would be a net exporter of the good. Indicate the areas associated with consumer surplus,
producer surplus, and gains to trade. (Hint: I am willing to give you a hint on this problem
for 2 points. Call me over or come to my desk for the hint.)
b. Draw a new graph (similar to part a) of the domestic market assuming the domestic
government taxes domestic producers t for each unit of the good that they export. Indicate
the areas associated with consumer surplus, producer surplus, tax revenue, and dead-weight
loss.
5. A firm’s production function is f(K, L) = min{ 4K, 0.2L}. What is the firm’s cost function if the price
of each unit of capital is $40 and the price of each unit of labor is $12
6. A firm’s cost function is C(q) = 5q + 3q 2 .
a. Algebraically solve for F, VC(q), AC(q), AVC(q), and MC(q).
b. Graph AC(q), AVC(q), and MC(q) as accurately as possible on the same graph.
c. Given this cost function, under what condition(s) on price will the firm shut down in the short
run Under what condition(s) on price will the firm exit in the long run
76

7. Soybeans are sold in a perfectly competitive industry. The industry is presently in long-run
equilibrium. In the present equilibrium, the following hold:
• The price of soybeans is $5 per bushel: p = $5.
• There are 5,000 soybean farmers: N = 5,000.
• Each soybean farmer produces 40,000 bushels: q = 40,000.
• Total production equals 200 million bushels of soybeans: Q = 200 million.
• Each firm receives $0 profits: π = $0.
Then suppose a negative finding regarding the health risks of soybeans leads to an immediate and
permanent decrease in the market demand for soybeans.
To answer the questions below, you can draw a graph if you want though a graph is not required and
a graph by itself is not sufficient to answer the question. You need to explain in words how things
change.
a. Indicate how each of the variables listed above changes (if at all) in the short run. When possible,
give a precise number for the variable. For example, in a situation in which the price of soybeans
doesn’t change, you could write, “The price of soybeans is unaffected by the demand shock, so p
= $5.” Of course, if the price of soybeans increases to an unknown price, you would write “The
price of soybeans increases because of the demand shock, so p > $5.”
b. Indicate the long-run value for each of the five variables indicated above in relation to the original
long-run equilibrium. Again, if possible, specify the actual number the variable will take on.
c. Following the eventual return to long-run equilibrium, another shock occurs, and after the market
for soybeans works through that shock, long-run equilibrium is once again obtained. This time,
however, the price of a bushel of soybeans is now $2 per bushel. Which of the following shocks
could and could not have caused this long-run change, and why:
i. A decrease in the cost of farm workers.
ii. An increase in the demand for soybeans
iii. An increase in the price of soybean seeds.
iv. A technological advancement in the fertility of soybean seeds.
77

EXAM #3 ANSWERS – ECON 210: INTERMEDIATE MICRO
Professor Lemke
April 16, 2012
1. A firm’s production function is f(K, L) = 20K 1/4 L 5/4 . Each unit of capital costs the firm $2,000, while
each unit of labor costs the firm $24,000.
a. Does the firm experience increasing, constant, or decreasing returns to scale How do you know
The firm experiences increasing returns to scale because the production function is a Cobb-
Douglas production function in which the exponents sum to greater than 1. In particular, the
exponents are 1/4 and 5/4, which sum to 1.5.
b. In terms of K and L, what is the firm’s marginal rate of technical substitution
We know from the notes that for a Cobb Douglass production function f(K, L) = AK α L β is :
βK
MRTS = − α L
c. Graph the firm’s $60,000 isocost line.
⎛ 5K
⎞
⎜ ⎟
4 5K
= −
⎝ ⎠
= −
⎛1L
⎞ L
⎜ ⎟
⎝ 4 ⎠
.
As $60,000 can purchase 2.5 = $60,000/$24,000 units of labor or 30 = $60,000/$2,000 units of
capital, the $60,000 isocost line is:
Capital
30
$60,000 Isocost Line
2.5 Labor
d. If the firm maximizes profit by employing capital to the point where the marginal product of
capital is 480, what is the marginal product of the optimal amount of labor the firm employs
Profit maximization requires
MP
w
L
MPk
MPL
480
= ⇒ = ⇒ MPL
r 24,000 2,000
= 5,760 .
Thus, at these factor prices, if the firm employs capital to the point where the marginal product of
capital is 480, it will employ labor to the point where the marginal product of labor is 5,760.
78

2. VisCom Industrial, better known as VCI, sells color printer cartridges in a perfectly competitive
market. Presently the price of color printer cartridges is $45 per cartridge. VCI’s cost function is
C(q) = 28,800 + 5q + 0.02q 2 where q is the number of cartridges that VCI manufactures.
a. How many cartridges should VCI manufacture and sell in order to maximize its short run
profits Provide a complete answer!
As it is a perfectly competitive industry and price equals $45, VCI’s marginal revenue equals
$45. As VCI’s cost function is C(q) = 28,800 + 5q + 0.02q 2 , its marginal cost function is
MC(q) = 5 + 0.04q. So now, to maximize profits:
Step 1. Set MR = MC to solve for q*.
MR = MC
45 = 5 + 0.04q
0.04q = 40
q* = 1,000 cartridges.
Step 2. Because the market is perfectly competitive, we know that p* = $45 per cartridge.
Step 3. At q* = 1,000 and p* = $45, VCI’s revenues are R(1,000) = 1,000 × $45 = $45,000. At
the same time, VCI’s total costs are C(1,000) = 28,800 + 5(1,000) + 0.02(1,000) 2 =
$53,800. Therefore VCI’s profits, when it produces 1,000 color printer cartridges is
π(1,000) = R(1,000) – C(1,000) = $45,000 – $53,800 = –$8,800.
Step 4.
As profit is negative, the shut-down rule must be checked. If the firm stays open, it will
produce 1,000 cartridges and lose $8,800 in profit. If the firm shuts down, it produces 0
cartridges and loses its fixed costs of $28,800. As VCI would rather lose $8,800 than
lose $28,800, VCI will opt to remain open, produce 1,000 cartridges, and earn –$8,800.
b. What will be the long-run price of color printer cartridges and how many cartridges will each
firm produce Hint: this takes a bit of math to figure out.
In the long run, we know that a perfectly competitive industry results in p = MC = min AC.
We already have that MC = 5 + 0.04q. Using the cost function, we see that
C(
q)
28,
800 5q
0.
02q
28,
800
AC = = + + = + 5 + 0.
02q
.
q q q q q
28,
800
Setting these two equations equal to one another yields + 5 + 0.
02q
= 5 + 0.
04q
.
q
Grouping and isolating q yields 0.02q 2 = 28,800. Thus, q 2 = 1,440,000, or q* = 1,200. At a
quantity of 1,200, the firm’s marginal cost is 5 + 0.04(1,200) = $53. Finally, we have the
answer: the long-run price for a bushel of soybeans is $53, at which price each soybean
farmer makes 1,200 bushels of soybeans.
2
79

3. A firm faces an inverse demand function of p = 240 – 0.2q. The firm’s cost function is
C(q) = 4,000 + 0.1q 2 . How much output will the firm choose to sell in the short run to maximize its
profits At what price will it sell each unit of output How much profit will the firm earn in the short
run
The firm’s marginal revenue is MR = 240 – 0.4q. The firm’s marginal cost curve is also easily
determined: MC(q) = 0.2q. Setting MR = MC to find q*:
240 – 0.4q = 0.2q
0.6q = 240
q* = 400.
Therefore, p* = 240 – 0.2(400) = $160. The firm’s revenue is R(400) = 400 × $160 = $64,000. The
firm’s costs are C(400) = 4,000 + 0.1(400) 2 = $20,000. Therefore, the firm’s profits each period are
π(400) = R(400) – C(400) = $64,000 – $20,000 = $44,000.
4. In class, we drew a picture that represented the “Gains to Trade” from having free trade when the
domestic country would be a net importer of the good.
a. Draw a similar graph of the domestic market under free trade when the domestic country
would be a net exporter of the good. Indicate the areas associated with consumer surplus,
producer surplus, and gains to trade.
The graph is too difficult to draw in Word.
b. Draw a graph of the domestic market assuming the domestic government taxes domestic
producers t for each unit of the good that they export. Indicate the areas associated with
consumer surplus, producer surplus, tax revenue, and dead-weight loss.
The graph is too difficult to draw in Word.
5. A firm’s production function is f(K, L) = min{ 4K, 0.2L}. What is the firm’s cost function if the price
of each unit of capital is $40 and the price of each unit of labor is $12
As this production function represents fixed factors, we know that there will be a constant marginal
cost for all units of production. We will figure out this marginal cost in two different ways.
One unit of output requires 0.25 units of capital as 4 × 0.25 = 1 and 5 units of labor as 0.2 × 5 = 1.
The cost of these inputs is 0.25 × r + 5 × w = 0.25 × $40 + 5 × $12 = $70. Therefore, the cost
function is C(q) = 70q.
Alternatively, notice that making 20 units of output requires 5 units of capital (as 4 × 5 = 20) and 100
units of capital (as 0.2 × 100 = 20). The cost of 20 units of output, therefore, is 5×$40 + 100×$12 =
$1,400. Therefore, each unit itself costs $1,400 ÷ 20 = $70. Therefore the cost function is
C(q) = 70q.
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6. A firm’s cost function is C(q) = 5q + 3q 2 .
a. Algebraically solve for F, VC(q), AC(q), AVC(q), and MC(q).
F = 0
VC(q) = 5q + 3q 2 .
AC(q) = C(q) ÷ q = 5 + 3q.
AVC(q) = VC(q) ÷ q = 5 + 3q. (So notice that AC = AVC.)
MC(q) = 5 + 6q.
b. Graph AC(q), AVC(q), and MC(q) as accurately as possible on the same graph.
$
MC = 5 + 6q
AC = AVC = 5 + 3q
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quantity
c. Given this cost function, under what condition(s) on price will the firm shut down in the short
run Under what condition(s) on price will the firm exit in the long run
Notice that minimum AC equals minimum AVC as AC equals AVC. Therefore, the shutdown
rule (which uses minimum AVC) is the same as the exit rule (which uses minimum AC). In
particular:
• Shut down in the short run if price is less than $5.
• Exit in the long run if price is less than $5.
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7. Soybeans are sold in a perfectly competitive industry. The industry is presently in long-run
equilibrium. In the present equilibrium, the following hold:
• The price of soybeans is $5 per bushel: p = $5.
• There are 5,000 soybean farmers: N = 5,000.
• Each soybean farmer produces 40,000 bushels: q = 40,000.
• Total production equals 200 million bushels of soybeans: Q = 200 million.
• Each firm receives $0 profits: π = $0.
Then suppose a negative finding regarding the health risks of soybeans leads to an immediate and
permanent decrease in the market demand for soybeans.
a. Indicate how each of the variables listed above changes (if at all) in the short run. When possible,
give a precise number for the variable. For example, in a situation in which the price of soybeans
doesn’t change, you could write, “The price of soybeans is unaffected by the demand shock, so p
= $5.” Of course, if the price of soybeans increases to an unknown price, you would write “The
price of soybeans increases because of the demand shock, so p > $5.”
A permanent decrease in demand (in the short run) leads to:
• A fall in price below $5.
• N = 5,000 as entry and exit is not allowed in the short run.
• Each firm’s quantity, q, falls below 40,000 bushels in the short run as the marginal bushel
is less profitable as prices have fallen.
• Total industry quantity, Q falls in the short run as all firms produce less; i.e., Q SR < 200
million bushels.
• Firm profits fall as prices and quantities have fallen: π SR < $0.
b. Indicate the long-run value for each of the five variables indicated above in relation to the original
long-run equilibrium. Again, if possible, specify the actual number the variable will take on.
For the market to return to long run equilibrium after the permanent negative demand shock and
negative short run profits, some firms exit the industry, shifting industry supply in. This drives
price up and returns the industry to zero profits. Specifically, returning to long run equilibrium:
• Price returns to $5.
• N < 5,000 as firms exit in the long run.
• Each firm’s quantity, q, returns to 40,000 bushels in the long run.
• Total industry quantity, Q falls even more in the long run because of exiting firms; i.e.,
Q LR < Q SR < 200 million bushels.
• Firm profits return to $0: π LR = $0.
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c. Following the eventual return to long-run equilibrium, another shock occurs, and after the market
for soybeans works through that shock, long-run equilibrium is once again obtained. This time,
however, the price of a bushel of soybeans is now $2 per bushel. Which of the following shocks
could and could not have caused this long-run change, and why:
i. A decrease in the cost of farm workers.
This is a possible reason long-run price fell. Specifically, when the price of a factor
of production falls, the cost function falls and in particular the minimum average cost
must fall. As long-run price equals the minimum average cost, such a change could
cause a decrease in the long-run price (making the third shock a possibility).
ii. An increase in the demand for soybeans
A decrease in the long-run competitive price cannot come about from a demand
shock (ruling out this explanation).
iii. An increase in the price of soybean seeds.
An increase in a factor price would increase, not decrease, the long-run price (ruling
out this explanation).
iv. A technological advancement in the fertility of soybean seeds.
A technological advancement is reflected by an improved cost function, and in
particular by a lower minimum average cost. As long-run price equals the minimum
average cost, such advancement could cause a decrease in the long-run price (making
this explanation a possibility).
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