Suppose a firm's technology is represented by the Cobb-Douglas production function F(L, K) = 5LK. The wage rate is $50 and the rental rate of capital is $10. What is the least-cost combination to produce 100 units of output?

What will be an ideal response?


The tangency condition requires that MRTSLK = K/L = W/R = ($50/$10) = 5. This means that there should be 5 times more capital than labor, so the production function can be written F(L, 5L) = 5L(5L) = 25L2. Therefore, to produce 100 units of output requires 100 = 25L2 which implies that L = 2 and K = 10.

Economics

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