Econ 444 Problem Set #1

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Problem 1. Suppose that, in a large city, 100 identical street vendors compete in a
competitive market for ice-cream.
1. Fore each vendor i, total cost of producing qi ice-cream is, Ci(qi) = qi + 1qi2. 4
2. What is the marginal cost function of each firm?
3. Given your answer from above, how many units of ice-cream will each vendor
produce if offered a price of $5 per ice-cream? What is the marginal revenue
of the firm at this price?
4. What is the aggregate supply curve for this market?
5. Let demand for ice-cream be Q = 1600−100P , what is the short run equilibrium
price?
6. What is the total quantity of ice-cream sold in short-run equilibrium?
7. In the long run, would you expect this industry to experience entry or exit?
Explain your answer.
Problem 2. In the same city as before, a new fast prepare ice-cream (FI) tech-
nology is discovered. Firms using this new technology have a total cost function
CFI(q ) = 2q + 1 q2. While the 100 existing firms keep their old, regular ice-cream ii i20i
(RI), technology, ten new firms enter using FI technology. The ice-cream produced by the
two technologies tastes exactly the same to consumers (that is, ice-cream is
homogeneous). You may assume there is free entry in both technologies in the long run.
Econ 444: Problem Set #1 2

1. The promoters of FI technology point out that although it may appear more
expensive at first, it benefits from greater ”economies of scale” than RI.
Explain what they mean, feel free to use a numerical example.
2. What is the individual supply curve of a firm using FI technology?
3. Given that there are now 100 RI firms and 10 FI firms, what is the aggregate
supply curve for this market?
4. What is the new short-run equilibrium price in this market?
5. Is the market in long-run equilibrium? Explain why or why not.
6. You are hired as a consultant by a firm using FI technology. What do you
suggest they do?
Problem 3. Suppose Global Shoveling Co. has gained exclusive rights to shovel snow in
State College. The demand for shoveling is given by Q = 3000 − 30P . The total cost
function for shoveling is C(Q) = 6Q for Q miles of road.
1. What is the marginal cost function for Global Shoveling Co.?
2. Write down the monopolist’s maximization problem, assume the monopolist
3. chooses how much road to shovel.
4. How much road should Global Shoveling Co. shovel in State College?
5. What is the price at this level of output?
6. Is this outcome efficient? If so, why? If not, what is the efficient level of
output?
7. What is the Lerner Index for Shoveling services in State College? What about
the HHI?
8. Suppose the demand for shoveling services in State College was instead
given by Qd = 3000 − 100P . How would Global Shoveling Co. Lerner index
change? Would this lead to a more or less efficient outcome? Explain.
Econ 444: Problem Set #1 3 Problem 4. The following firms compete within the same
industry:

Name
ACME Industries Beta Inc.
Caltech
Douglass Ltd. Gramen Inc. Houghton Enterprises Jenentech
1. Use this information to calculate CR3
2. Calculate CR5 for the industry.
3. What is the HHI for the industry?
Sales (millions) 50 18 18 4 11 22 5
4. Can you use this information alone to calculate the Lerner Index? Explain why or why
not. What information would you need?
Problem 5. True or False. In each part, state whether the sentence is true or false and
explain your assertion. You will receive half the credit for the correct answer and half the
credit for the correct explanation.
1. In a perfectly competitive market, firms produce optimally at the point where
marginal revenue equals marginal cost.
2. A monopolist may sometimes produce on the inelastic portion of the demand
curve.
3. In equilibrium, the quantity produced by a monopolist is greater when (downward
sloping) demand is more inelastic.