Answer to Question #41062 in Microeconomics for Anthony

Question

Assume that a firm hires only labour and capital to produce bicycles.

a. Explain the cost minimization rule for this firm and why this rule is logical…

b. Suppose that the firm hires 100 units of capital and 500 units of labour and
that the MPl is 20 while MPk is 25. If a unit of labour costs $4.00 and a unit of
capital costs $5.00, is the firm minimizing costs? Explain.

c. If the price of capital falls to $4.00 what should the firm do to minimize cost?
Explain why your answer is consistent with the cost minimization rule.

Answer 1

a. Сost is minimized at the levels of capital and labor such that the marginal product of labor divided by the wage (w) is equal to the marginal product of capital divided by the rental price of capital (r) (MPl/w = MPk/r). More intuitively, you can think of cost being minimized (and, by extension, production being most efficient) when the additional output per dollar spent on each of the inputs is the same (or, in less formal terms, you get the same "bang for your buck" from each input). This formula can even be extended to apply to production processes that have more than two inputs.
b. K = 100 units, L = 500 units, MPl = 20, MPk = 25, w = $4.00, r = $5.00.
If the firm is minimizing costs, MPl/w = MPk/r, and in our case:
20/4 = 25/5 = 5, so the firm is minimizing costs.
c. If the price of capital falls to $4.00, the firm should increase the use of capital and decrease the use of labor to minimize cost.