The Cobb-Douglas production function for a beer manufacturer is q=1.52L^0.6K^0.4. Assume that the firm's capital is fixed at 250 units, the rental rate of capital is $5 per unit, and the wage rate is $10 per hour. The amount of labor needed to produce q units of output is A)0.0124q. B)13.832q⁰.6. C)0.0124q¹.67. D)13.832q¹.67.

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Quizplus · Accepted Answer

Given the Cobb-Douglas production function q = 1.52L^0.6K^0.4 and fixed capital (K) at 250 units, we can substitute K = 250 into the production function to find the relationship between labor (L) and output (q). The production function becomes q = 1.52L^0.6(250)^0.4. To find the amount of labor needed to produce q units of output, we solve for L in terms of q. Rearranging the equation and solving for L gives us L as a function of q, which matches the form of choice C, indicating that labor needed is proportional to q raised to the power of 1/0.6, after adjusting for the constants and the fixed capital. This results in a coefficient that reflects the labor needed per unit of output, taking into account the fixed amount of capital and the specific exponents in the production function.

The Cobb-Douglas Production Function for a Beer Manufacturer Is Q=1