The production function for a firm is f (x, y) = 64x 3/4 y 1/4 , where
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The production function for a firm is f (x, y) = 64x3/4y1/4, where x and y are the number of units of labor and capital utilized. Suppose that labor costs $96 per unit and capital costs $162 per unit and that the firm decides to produce 3456 units of goods.
(a) Determine the amounts of labor and capital that should be utilized in order to minimize the cost. That is, find the values of x, y that minimize 96x + 162y, subject to the constraint 3456 - 64x3/4y1/4 = 0.
(b) Find the value of l at the optimal level of production.
(c) Show that, at the optimal level of production, we have
Transcribed Image Text:
[marginal productivity of labor] [marginal productivity of capital] [unit price of labor] [unit price of capital]
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a b c Fx y A 96x162y 345664x3414 Note that 3456 6...View the full answer
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Related Book For
Calculus And Its Applications
ISBN: 9780134437774
14th Edition
Authors: Larry Goldstein, David Lay, David Schneider, Nakhle Asmar
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