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Assume that the production function is Cobb-Douglas: Y = AKα1 -α L where α is the parameter that satisfies 0 < α < 1
a) Formulate a profit maximization problem for a perfectly competitive firm that takes nominal wage rate W; rental price of capital R; and the price of final good P; as given.
b) Derive the first order conditions that characterize the firm's optimal decisions with respect to capital and labor inputs.
c) Show that the marginal product of capital (MPK) is an increasing function of labor L; and a decreasing function of capital K.
d) Using the firm's optimality conditions, show that average labor productivity (Y/ L) is proportionate to real wage (W/P)
e) Using the optimality conditions show that in equilibrium the firm earns zero economic profits.
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