Suppose a firm that produces one good under perfect competition has a production Q(L, K) = L/2 + K/4 %3D p is the price of output, w is the wage rate andr the cost of capital (rental). a) Find an expression for total profit as a function of L and K. b) Find the critical point of this function. c) Show that this critical point is a unique global maximum. Hint: Remember that the domain of the production function is defined fo quadrant R?, i.e. L and K must be greater than zero.

Suppose a firm that produces one good under perfect competition has a production Q(L, K) = L/2 + K/4 %3D p is the price of output, w is the wage rate andr the cost of capital (rental). a) Find an expression for total profit as a function of L and K. b) Find the critical point of this function. c) Show that this critical point is a unique global maximum. Hint: Remember that the domain of the production function is defined fo quadrant R?, i.e. L and K must be greater than zero.

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)

14th Edition

ISBN:9781305506381

Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

ChapterB: Differential Calculus Techniques In Management

Section: Chapter Questions

Problem 5E

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