6. (15 %)

Consider a two-good (X,Y), two-factor (L,K) general equilibrium economy. Production technologies are X = F^X(LX, KX) and Y = F^Y(LY, KY), where both F^X and F^Y exhibit constant returns to scale and are strictly concave. Factor endowments satisfy LX + LY = L̄ and KX + KY = K̄. Consumer preferences are represented by standard Cobb-Douglas functions.

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