Let P., P. represent output prices and W the wage rate . Labor demand in each sector comes from profit maximiziation - which entails equating the marginal value product of labor to the wage : Given output prices , show graphically how the equilibrium wage rate and the allocation of labor between the two sectors is determined . Using the production functions , show mathematically how the equilibrium wage rate and the supply curve for each good (C, F) is determined (as a function of output prices ). Also , discuss how the returns to land and capital are determined iii Using your result in part ii, given output prices , show how an increase in the amount of capital (K ) available for production affects : (1) the quantity supplied of each good ; (2 ) the real return to capital ; (3)the real return to land ; and (4) the real wage rate . IV Given output prices , show how an increase in food productivity (" 8 ") affects the supply (output ) of each good and the real return to each input . V Given output prices , what happens to the supply of each good , and the real return to each factor , if productivity in both sectors (i.e., 1 and @ ) doubles