Suppose there are two consumers, A and B.
The utility functions of each consumer are given by:
UA = X2Y
UB = X*Y
Therefore:
- Consumer A: MUX = 2XY; MUY = X2
- Consumer B: MUX = Y; MUY = X
The initial endowments are:
A: X = 80; Y = 14
B: X = 70; Y = 6
a) ) Suppose the price of good Y is equal to one. Calculate the price of good X that will lead to a competitive equilibrium.
b) How much of each good does each consumer demand in equilibrium?
Consumer A's Demand for X:
Consumer A's Demand for Y:
Consumer B's demand for X:
Consumer B's demand for Y:
c) What is the marginal rate of substitution for consumer A at the competitive equilibrium?
d) ( Illustrate the situation in an Edgeworth Box. Be sure to label your box carefully and accurately. Identify the initial endowment and label it W. Identify the competitive equilibrium and label it D. Draw the budget constraint that each consumer faces and identify the values where it intercepts the perimeter of the Edgeworth Box (there are two different intercepts to identify).