題組內容

4. (20 分)
Consider a pure exchange economy with two goods, X and Y. There are only two individuals in the economy, Individual A and Individual B, whose utility functions are defined as \( U_A = \sqrt{X_A Y_A} \) and \( U_B = \sqrt{X_B Y_B} \), respectively. Individual A's endowment is \( e_A = (\overline{X_A}, \overline{Y_A}) = (40, 40) \), and Individual B's endowment is \( e_B = (\overline{X_B}, \overline{Y_B}) = (60, 10) \).

(2) Find the prices and allocations of X and Y in the competitive equilibrium. (15 分)