Suppose that there are competitive firms that produce the final consumption goods by using capital, labor, and land. As in the lecture note, the production function of firm j is given by ytj=(ktj)1(A(Kt)ntj)2(A(Kt)ltj)3 As in the lecture, each iirm chooses ktj,ntj, and ltj optimally, taking A(Kt) as given, where A(Kt)=aKt, and Kt is aggregate capital stock. Under this setting, show that the factor prices, (7) Rt (rental rate of capital), (8) wt (wage rate), and (9) ht (land rent), (10) Derive the aggregate production function. Hint: First, derive the first-order condition of the firm's profit maximization problem, and then exploit the fact that the production function exhibits constant returns to scale. Also, Use the labor market clearing condition (i.e., Nt=N=1 ) and the land market clearing condition (i.e., Xt= Lt=1) Suppose that there are competitive firms that produce the final consumption goods by using capital, labor, and land. As in the lecture note, the production function of firm j is given by ytj=(ktj)1(A(Kt)ntj)2(A(Kt)ltj)3 As in the lecture, each iirm chooses ktj,ntj, and ltj optimally, taking A(Kt) as given, where A(Kt)=aKt, and Kt is aggregate capital stock. Under this setting, show that the factor prices, (7) Rt (rental rate of capital), (8) wt (wage rate), and (9) ht (land rent), (10) Derive the aggregate production function. Hint: First, derive the first-order condition of the firm's profit maximization problem, and then exploit the fact that the production function exhibits constant returns to scale. Also, Use the labor market clearing condition (i.e., Nt=N=1 ) and the land market clearing condition (i.e., Xt= Lt=1)