0
$\begingroup$

Question:

A firm produces chairs using labor and capital. The price of labor is \$50 dollar per unit, and the price of capital is $100 per unit. At current output, the marginal product of labor is 10 chairs, and the marginal product of capital is 15 chairs. To reduce the total cost of producing the current quantity of chairs, how should the firm change its spending on labor and capital?

Answer:

Increase labor; Decrease capital. In order to reduce the total cost of producing the current quantity of chairs, one of the inputs to production must increase and the other must decrease. If neither changed, the cost would not be reduced. If one increased or decreased and the other did not change, the firm wouldn’t be producing the current quantity of chairs – it would be producing more or less, respectively. While the marginal product of labor (MPL = 10) is less than the marginal product of capital (MPK = 15), the RATIO of the MPL to the price of labor (10 / 50 = 0.2) is greater than the RATIO of the MPK to the price of capital (15 / 100 = 0.15). To reduce the total cost, the firm should increase spending on labor, which increases output by 0.2 chairs for every dollar spent, and decrease spending on capital, which only increases output by 0.15 chairs for every dollar spent.

$\endgroup$
2
$\begingroup$

You can do both. Effectively you say "let me move one dollar from labor to capital expenditure and see what happens". By doing so you have reduced labor by 0.01 and thus reduced production by 0.15 chairs, but increased capital by 0.02 and thus production by 0.2 chairs. Net effect is 0.05 chairs more at the same cost.

Equivalently, MPL/MPK = 1.5< w/r =2, or MPL/w= 0.15 < MPK/ r = 2. Second is just rearrangement of the first, but with both you answer where the dollar of you cost is more efficient.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.