The utility functions of each consumer are given by:

U_A(X,Y) = X^*Y

U_B(X,Y) = X*Y³

Therefore:

For consumer A: MU_X = Y; MU_Y = X For consumer B: MU_X = Y³; MU_Y = 3XY²

The initial endowments are:

A: X = 8; Y = 6

B: X = 14; Y = 17

a) (40 points) Suppose the price of Y, P_Y = 1. Calculate the price of X, P_X that will lead to a competitive equilibrium.