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Given the production function Q=K2L2 and the price of capital and labor as r=4 and w=8,...

Given the production function Q=K2L2 and the price of capital and labor as r=4 and w=8, respectively, if the goal is Q=2500 find the level of capital (K) and labor (L) to minimize cost.

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Answer #1

Method used in order to find result

Here In order to find level of K and K we have to :
Minimize : Total Cost(TC) = wL + rK = 8L + 4K
subject to L2K2 = Q = 2500

For that we have used Legrange multiplier, differentiation and First order condition and find the value of L and K that will minimize cost.

Level of L and K that will minimize Total Cost is L = 5 and K = 10

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