Suppose that there are competitive firms that produce the final consumption goods by using capital, labor, and land. The production function of firm is given by = ()1(())2(())3

Each firm chooses , , and optimally, taking () as given, where () = ,

and is aggregate capital stock. Under this setting, show that the factor prices, (7) (rental rate of capital), (8) (wage rate), and (9) h (land rent), (10) Derive the aggregate production function.

Hint: First, derive the first-order condition of the firms 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., = = 1) and the land market clearing condition (i.e., = = 1).

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