A firm is employing capital and labor such that the marginal product of capital is 30 and the marginal product of labor is 10
If the price of a unit of capital is $50 and the price of a unit of labor is $10, is the firm minimizing its costs? If not, can you recommend a change for the firm to make in its relative amounts of labor and capital used? Explain.
No, the firm is not minimizing costs. The slope of its isoquant is -10/30 (-1/3) and the slope of its isocost line is -10/50 (-1/5). In order to minimize costs, the firm needs to produce where these slopes would be equal. In other words, the firm needs to produce where the slope of its isoquant is equal to -1/5 . If the firm was to increase its use of labor or decrease its use of capital, the slope of the isoquant will fall.
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