Posted: March 24th, 2017
Consider a single-product firm under monopoly. The firm’s profit function is given by ? = PQ-wL-rK, where P=price, Q=output, L=labor, K=capital, w=wage, and r=rent. Let the market demand function and the firm’s production function be Q=PQ=P-2 and Q=K raised to the power (4/5)*L raised to the power (4/5), respectively. (a) Is the production function homogeneous? If so, of what degree? Discuss the returns to scale for this function. (b) Is the production concave? Is it quasiconcave? Show your work. (c) Rewrite the profit function as a function of L and K. Is it homogeneous with respect to L & K? If so, of what degree? (d) Is the profit function concave in L &K? Is it quasiconcave? Show your work. (e) What would happen if this function pertained to a perfect competition instead of a monopoly?
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