A Firm's Production Process Uses Labor $L$ , and Capital $K$ , and Materials

question 23

Multiple Choice

A firm's production process uses labor, $L$ , and capital, $K$ , and materials, $M$ , to produce an output, $Q$ according to the function $Q = K L M$ , where the marginal products of the three inputs are $M P _ { L }$ $= K M , M P _ { K } = L M$ , and $M P _ { M } = K L$ . The wage rate for labor is $w = 2$ , the rental rate of capital is $r$ $= 1$ , and the cost of materials is $m = 4$ per unit. What is the long run cost-minimizing level of capital that the firm must use to produce a target level of output, $Q = 1000$ ?

• A) \(K = 5\)
• B) \(K = 10\)
• C) \(K = 20\)
• D) \(K = 40\)

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