Question

19. Suppose you find that MU1( x1,x2)=2x2 and MU2( x1,x2)=2x1. What is the rate at which the consumer is willing to trade good 2 for good 1 at bundle (2,4)? (Note: enter a positive number, i.e. enter the quantity of good 2 that the consumer is willing to give up for an additional—marginal—unit of good 1.)
20. Suppose you find that the expressions of the marginal utilities for a consumer are given by MU1( x1,x2)=1 and MU2( x1,x 2)=3. Then you can conclude that:
a. This consumer has Cobb-Douglas tastes
b. For this consumer good 1 and good 2 are perfect complements
c. For this consumer good 1 and good 2 are perfect substitutes
d. None of the above
21. Suppose a consumer is always willing to give up 5 units of good 2 for an additional unit of good 1. For this consumer:
a. Good 1 and good 2 are perfect complements
b. Good 1 and good 2 are perfect substitutes
c. Good 1 and good 2 are both essential goods
d. None of the above
22. Suppose a consumer is always willing to give up 4 units of good 2 for an additional unit of good 1. Which of the following utility functions represents the tastes of this consumer?

a. u(x1,x2)=min{4x1,x2}
b. u(x1,x2)=min{x1,4x2}
c. u(x1,x2)= x1+4x2
d. u(x1,x2)=4x1+x2
e. None of the above

25. Consider the following utility functions: u1(x1,x2)=x1+x2 ans u2(x1,x2)=3x1+3x2 Do they represent the same tastes?
a. Yes
b. No
c. There is not enough information to answer

Answer 1

19. MU1(x1,x2) = 2x2  MU2(x1,x2) = 2x1

To know the rate we need to know the MRS (Marginal rate of substitution) = MU1/ MU2 = 2x2/ 2x1 = x2/ x1

This is the MRS of well behaved preferenes. At bundle (2,4) MRS = 4/2 = 2/1.

At bundle (2,4) a consumer is willing to give up 2 units of good2 for having an additional unit of good1.

20. c) For this consumer good1 and good2 are perfect substitutes.

Since perfect substitutes are of the form: U = ax+ by where a and b are constants.

To find the MRS = -MUx/ MUy = -a/b. Here also in the question, MRS = -1/3 .

21) b) Both good1 and good2 are perfect substitutes as their rate of substitution is always same.

22) d) u(x1,x2)=4x1+x2 . Here MRS =dux1/ dux2 = 4/1 which implies a consumer is always willing to give up 4 units of good 2 for an additional unit of good 1.

23) a) Yes because second one is just the monotonic transformation of the first one. u1(x1,x2)=x1+x2 and u2(x1,x2)=3(x1+x2) = 3 (u1)