Consider a firm that is operating in a perfectly competitive environment

4. Consider a firm that is operating in a perfectly competitive environment in the output and input market. The firm’s production function is given by Q = A*K^(α)*L^(β), where Q is the level of output, K is level of capital, L is the level of working hours, and A is a productivity parameter. The output price is given by P; and the input prices for capital and labor are r and w, respectively. (You can normalize P to be 1).(a) Write down carefully the firm’s problem in the long run. Solve for the optimal firm’s demand for inputs.(b) What is the labor share in this economy? Show it!

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