Zowie! Surfboards has the following production function.

If surfboards sell for $30 and the nominal wage rate is $200,how many workers should the firm employ?

Question

Zowie! Surfboards has the following production function.

If surfboards sell for $30 and the nominal wage rate is $200,how many workers should the firm employ?

Quizplus · Accepted Answer

To determine the optimal number of workers, we need to find the level of output where the marginal product of labor (MPL) equals the wage rate (W/P). From the production function, we can find that MPL = 30L - 2L^2. Setting this equal to W/P = 200/30 = 6.67, we get 30L - 2L^2 = 6.67. Rearranging this equation, we get 2L^2 - 30L + 6.67 = 0. Solving for L, we get L = 1.66 or L = 9.99. Since we cannot have fractional workers, the optimal number of workers is 4 (since 3 workers gives an output of 87.6 and 4 workers gives an output of 88, which is the maximum). Therefore, the answer is C) 4.

Zowie! Surfboards Has the Following Production Function