Question

Explain the relationship between a firm’s short-run production function and its shortrun cost function. Focus on the marginal product of an input and the marginal cost of production.

b) A U.S. electronics firm is considering moving its production to a plant in Mexico. Its estimated production function is q=L 0.5 K 0. 5 . The U.S. factor prices are In Mexico, the wage is half that in the United States, but the firm faces the same cost of capital: ? and ? What are L and K What is the cost of producing units in both countries?

Answer 1

A). There is a strong relationship between a firm's short-run production and its short-run cost function. Marginal product can be defined as the number of output that results from one additional unit of a factor of production. On the other contrary, the marginal cost refers to the added cost in producing an additional unit of output. It is clear and obvious that a change in the amount of money invested in manufacturing would also lead to a change in the number of output and vice versa.

In the short-run production function when the firm employs two inputs, labor and capital" and as the firm is operating in a short-run production period, the relationship can be seen through the fact that both production function and cost function assume that the firm uses a certain level of technology. More clearly and specifically, in the short-run production function it is assumed that firm utilize state-of-the-art technology in the production process. Another important assumption is that the production function is impacted by the law of diminishing. Therefore it implies that, when a firm decides to invest more money to employ more workers, then after some time at some point the marginal product starts to diminish. To summarize, the relation between short-run production and cost function can help a firm to make suitable adjustments in its production approach to achieve the cost efficiency.

B). At the Pareto optimal point,

MPL/MPK = w/r

MPL = dq/dL = 0.5L^-0.5K^0.5

MPK = dq/dK = 0.5L^0.5K^-0.5

w/r = 5/10

So, at the optimal point, (0.5L^-0.5K^0.5)/( 0.5L^0.5K^-0.5) = 5/10

Or, K/L = 0.5

Or, L = 2K

Substitute this in production constraint:

Q = L^0.5K^0.5

100 = (2K)^0.5K^0.5

K = 70.72

L = 141.44

TC = wL+rK = 5(70.72)+10(141.44) = $1768