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 8 units of good Y. Consumer B is given an initial endowment of 3 units of good X and 4 units of good Y.
Consumer A’s utility function is given by: UA(X,Y) = X4*Y,
And consumer B’s utility function is given by UB(X,Y) = X*Y.
Therefore, consumer A’s marginal utilities for each good are given by:
MUX = 4X3Y
MUY = X4
Also, consumer B’s marginal utilities for each good are given by:
MUX = Y
MUY = X
Suppose the price of good Y is equal to one. Calculate the price of good X that will lead to a competitive equilibrium.