3.A firm has production function F(K, L) = 1/4 (K¹/² + L ¹/2). The wage rate is w = 1 and the rental rate of capital is r = 3. (a) How much capital and labor should the firm employ to produce y units of output? (b) Hence find the cost of producing y units of output (the firm's cost function). (c) Differentiate the cost function to find the marginal cost, and verify that it is equal to the value of the Lagrange multiplier
3.A firm has production function F(K, L) = 1/4 (K¹/² + L ¹/2). The wage rate is w = 1 and the rental rate of capital is r = 3. (a) How much capital and labor should the firm employ to produce y units of output? (b) Hence find the cost of producing y units of output (the firm's cost function). (c) Differentiate the cost function to find the marginal cost, and verify that it is equal to the value of the Lagrange multiplier
Chapter11: Profit Maximization
Section: Chapter Questions
Problem 11.9P
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It’s mathematic for economics, and the questions should solve by the one of these
partial derivatives, Lagrange multipliers, first order differential equations.
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