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Econ 302

Homework #3

Due on Canvas by 11:59 pm, Monday, March 18th, 2024.

1.  (18 total points) Suppose there are two consumers, A and B.

The utility functions of each consumer are given by:

U_A(X,Y) = X^1/2*Y^1/2

U_B(X,Y) = X + 2Y

The initial endowments are:  

A: X = 2; Y = 4

B: X = 14; Y = 4

a) (12 points) Using an Edgeworth Box, graph the initial allocation (label it “W”) and draw the indifference curve for each consumer that runs through the initial allocation.  Be sure to label your graph carefully and accurately.

b) (2 points) What is the marginal rate of substitution for consumer A at the initial allocation?

c) (2 points) What is the marginal rate of substitution for consumer B at the initial allocation?

d) (2 points) Is the initial allocation Pareto Efficient?

2.  (14 total points)  Suppose there are two consumers, A and B, and two goods, X and Y.    Consumer A’s utility function is given by:

U_A(X,Y) = X^1/3*Y^2/3,

And consumer B’s utility function is given by

U_B(X,Y) = 4X + Y.

Suppose there is a total of 8 units of Good X and a total of 8 units of Good Y.  Using an Edgeworth Box, Illustrate the contract curve.  Be sure that the dimensions of the Edgeworth Box are correct, and that the Edgeworth Box is fully and accurately labeled.

3. (18 total points) Suppose there are two consumers, A and B, and two goods, X and Y.    Consumer A’s utility function is given by:

U_A(X,Y) = X + 4Y,

And consumer B’s utility function is given by

U_B(X,Y) = 2X + Y.

The initial endowments are:  

A: X = 4; Y = 2

B: X = 4; Y = 6

a) (12 points) Using an Edgeworth Box, graph the initial allocation (label it “W”) and draw the indifference curve for each consumer that runs through the initial allocation.  Be sure to label your graph carefully and accurately.

b) (6 points) On your graph from part a), using a highlighter, identify the core.