Question
Suppose there are two consumers, A and B. The utility functions of each consumer are given by: U A (X,Y) = X 2 *Y U
Suppose there are two consumers, A and B. The utility functions of each consumer are given by:
UA(X,Y) = X2*Y
UB(X,Y) = X*Y2
Therefore:
- For consumer A: MUX = 2XY; MUY = X2
- For consumer B: MUX = Y2; MUY = 2XY
The initial endowments are:
A: X = 20; Y = 95
B: X = 15; Y = 60
a) (16 points) Suppose the price of Y, PY = 1. Calculate the price of X (PX) that will lead to a competitive equilibrium. Put this equilibrium price of X in the blank below.
PX =
b) (8 points) How much of each good does each consumer demand in equilibrium? Consumer A's demand for X is Consumer A's demand for Y is Consumer B's demand for X is Consumer B's demand for Y is
c) (4 points) What is the marginal rate of substitution (MRS) for consumer A at the competitive equilibrium? MRS =
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