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Suppose that the firm’s production function is q = 10kl³. The firm’s capital is fixed at k. What amount of labor will the firm hire to solve its short-run cost-minimization problem?

a. l = cube root of (1/10)

b. l = cube root of 10

c. l = 1 over cube root of 10

d. l = 1 over 10

User Alfreddd
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Final answer:

To solve the firm's short-run cost-minimization problem with the production function q = 10kl³ and fixed capital, we would need the desired output level to find the correct amount of labor. However, the question as presented does not provide enough information to give a definitive answer.

Step-by-step explanation:

The student's question deals with a firm's production function in the short run when capital is fixed. Specifically, the function provided is q = 10kl³, where k is capital and l is labor. In the short run, to minimize costs, the firm must decide how much labor to employ when capital remains constant. Due to the nature of the production function and the fixed capital, the amount of labor required isn't directly stated in the question.

However, if we were to solve for labor in a general sense, we would need to set q to the desired level of production and solve the equation for l. Nevertheless, with the information given, there is no way to provide an exact answer for 'l' without additional details on the level of output the firm aims to achieve and the cost associated with each factor of production.

User Thijs D
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