Suppose there are two consumers, A and B, and two goods, X and Y. Consumer A is given an initial endowment of 6 units of good X and 1 units of good Y. Consumer B is given an initial endowment of 2 units of good X and 7 units of good Y. Consumer A’s utility function is given by: UA(X,Y) = X*Y, And consumer B’s utility function is given by UB(X,Y) = X*Y3. Therefore, consumer A’s marginal utilities for each good are given by: MUX = Y MUY = X Also, consumer B’s marginal utilities for each good are given by: MUX = Y3 MUY = 3XY2. Please show your work!!
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?