Review session for Midterm #1

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YU 1U 2Xf) On the same graph draw a second indifference curve U 2 , with U 2 >U 1 .(See above graph)3.21. Suppose a consumer’s preferences for two goods can be represented by the Cobb‐Douglas utilityfunction U = Ax α y β , where A, α, and β are positive constants. The marginal utilities are MU x = αAx α – 1 y βand MU y = βAx α y β – 1 . Answer all parts of Problem 3.15 for this utility function.a) Yes, the “more is better” assumption is satisfied for both goods since both marginal utilities arealways positive.b) Since we do not know the value of α , only that it is positive, we need to specify threepossible cases:When α < 1, the marginal utility of x diminishes as x increases.When α = 1, the marginal utility of x remains constant as x increases.When α > 1, the marginal utility of x increases as x increases.c)MRS x , yα −1αAxyα ββAxyβ=−1=αyβ xd) As the consumer substitutes x for y , the MRSx , ywill diminish because x is in the denominator anddrives down the entire fraction.e & f) The graph below depicts indifference curves for the case where A = 1 and α = β = 0.5.Thus0.5 0.5U ( x,y)= x y . Regardless, the indifference curves will never intersect either axis.6
Y450400350300250200150100500U 2U 10 5 10 15 20 25 30 35X3.24. One type of Cobb‐Douglas utility function is given by U(x,y) = x α y 1‐α , where MU x = αx α‐1 y 1‐α and MU y= (1‐α)x α y ‐α . Suppose that you are told that a person with Cobb‐Douglas preferences has an MRS x,y of 4when x = 4 and y = 8. What is the numerical value of α?First, the expression for MRS x,y isc)MRSx,yMU=MU==αxxyα −( 1−α)α y1−αx1 1−yαx yα−α(plugging in the MU’s and then rearranging)Since we know that MRS x,y = 4 when x = 4 and y = 8,d)α 84 =1−α4α2 =1−α(we set MRS equal to 4 and then plug in x,y values and solve for2 − 2α= αα =23α)7
Page 1 and 2: EconS 301 ‐ REVIEW EXERCISES FOR
Page 3 and 4: dQ = 10000 − 100P + 99P + 10000
Page 5: JellyU 1U 22124Peanut Butter3.15. C
Page 9 and 10: 80Clothing706050403020100U=72U=360
Page 11 and 12: y(10,6)(20,12)(5,3)4.7. Helen’s p
Page 13 and 14: all of his regular income on hambur
Page 15 and 16: ) Calculate his income and substitu
Page 17 and 18: c) Determine the numerical size of
Page 19 and 20: 5.28 Consider Noah’s preference f
Page 21 and 22: AP and MP with K=12001000000500000A
Page 23 and 24: Q = min(aK,bL)= min(λaK,λbL)= λm

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