The followings are short run production functions for two firms operating in different industries with different capital

structures.

F(L)1=K1AL

F(L)2=Min{G,AK2}+L

K1, represents the sector-specific capital employed by the firm 1, K2, represents the sector-specific capital, employed by the firm 2, while L represents the labor employed by the firm. Use r1 ,r2 to represent the rental price of capital structures. w to represent the wage of labor, P1 is the price of the good produced in the first industry and P2 is the price of the good produced in the second industry. Assume that all markets (commodities and factor markets) are competitive, and labor are mobile across industries. G represents public infrastructure investment by the government and A represents the technology level. (Hint: G is fixed in the short run).

a) Write down the profit maximization problem and derive labor demand curves for each firm? What is the employment (for labor) level for firm 1 and firm 2 ?