Question

Round answers to 5 decimal places. Suppose there are two consumers, A and B, and two goods, X and Y. Consumer A is given an initial endowment of 3 units of good X and 7 units of goodY. Consumer B is given an initial endowment of 8 units of good X and 5 units of good Y. ConsumerA’s utility function is given by:UA(X, Y) =X^1/2 Y^1/2 and Consumer B’s utility function is given byUB(X, Y) =X^1/5 Y^4/5. Therefore, the marginal utilities are as follows:

MU X/A= 1/2X^-1/2 Y^1/2

MU Y/A= 1/2X^1/2 Y^−1/2

MU XB= 1/5X^−4/5 Y^3/4

MU YB= 4/5X^1/5 Y^−1/5

1) How much of each good does consumer A demand in equilibrium?

2) How much of each good does consumer B demand in equilibrium?

3) What is the MRS for consumer B at the competitive equilibrium?

4) Illustrate the situation in an Edgeworth Box. Be sure to label your box carefully andaccurately. Identify the initial endowment and label it M. Identify the competitive equilibrium and label it C. Draw the budget constraint that each consumer faces and identify the values where it intersects the perimeter of the Edgeworth Box (there are 2 different intercepts to identify for each consumer).

Answer 1