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

question 79

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. Let materials input be fixed now at $M = 2$ . What is the cost minimizing level of capital that the firm must use to produce a target level of output, $Q = 1600$ ?

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

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Definitions:

Mean Time Between Failures

The average time interval between the occurrences of consecutive failures in a system or component.

Inverse

In mathematics, it refers to a function that essentially reverses the effect of another function, often denoted as the reciprocal or opposite in certain contexts.

Preventive Maintenance

A maintenance strategy aimed at preventing machinery, equipment, and systems failures by performing regular, planned maintenance tasks.