Question

Miguel and Jake run a paper company. Each week they need to produce 1,000 reams of paper to ship to their customers. The paper plant's long-run production function is Q=4K⁰.⁷⁵L ⁰.²⁵, where Q is the number of reams produced, K is the quantity of capital rented, and L is the quantity of labor hired. For this production function, the MPL=K⁰.⁷⁵/L⁰.⁷⁵and the MPK =3L⁰.²⁵/K⁰.²⁵. The weekly cost function for the paper plant is C=10K+2L, where C is the total weekly cost. 1. What ratio of capital to labor minimizes Miguel and Jake's total costs?

Answer 1

To minimize total costs, Miguel and Jake should use equal amounts of capital and labor, that is 1:1.

Step-by-step explanation:

To minimize total costs, Miguel and Jake need to find the ratio of capital to labor that maximizes their production function's marginal product of labor divided by its marginal product of capital, also known as the MPL/MPK ratio.

In this case, the MPL/MPK ratio is (K^0.75/L^0.75)/(3L^0.25/K^0.25).

Simplifying the ratio, we get K^1/L^1, which means that the ratio of capital to labor that minimizes total costs is 1:1. This means that Miguel and Jake should use equal amounts of capital and labor to achieve their production goal of 1,000 reams of paper per week.