題組內容

6. (15 %)
Consider a two-good (X,Y), two-factor (L,K) general equilibrium economy. Production technologies are \( X = F^X(L_X, K_X) \) and \( Y = F^Y(L_Y, K_Y) \), where both \( F^X \) and \( F^Y \) exhibit constant returns to scale and are strictly concave. Factor endowments satisfy \( L_X + L_Y = \bar{L} \) and \( K_X + K_Y = \bar{K} \). Consumer preferences are represented by standard Cobb-Douglas functions.

(a) Show that any competitive equilibrium allocation must satisfy production efficiency. (7%)