3 Question 3 (44 points)
For this problem, round answers to 4 decimal places. Suppose there are two consumers, A and B, and
two goods, X and Y. Consumer A is given an initial endowment of 5 units of good X and 9 units of good
Y. Consumer B is given an initial endowment of 8 units of good X and 6 units of good Y. Consumer
A's utility function is given by: $U_A(X, Y) = X^{\frac{3}{4}}Y^{\frac{1}{4}}$ and Consumer B's utility function is given by
$U_B(X, Y) = X^{\frac{1}{2}}Y^{\frac{1}{2}}$.
a) (12 points) Suppose the price of good Y is equal to 1. Calculate the price of good X that will lead to
a competitive equilibrium.