The long-run production function for a rm\'s product is given by q = f(K; L) = 5

Question

The long-run production function for a rm's product is given by q = f(K; L) = 5 K L. The
price of capital is $10 and the price of labor is $15.
a. Suppose the rm wishes to produce output of 500. List 5 combinations of capital and labor that the
rm can transform into 500 output.
b. For each of your 5 combinations from part a, give the cost of using that combination of capital and
labor. Which is the lowest?
c. For your lowest cost combination from part b, calculate the marginal product of capital (MPK) and the
marginal product of labor (MPL).
d. For your answer in parts b-c, is your marginal product per dollar equal across the two inp

Explanation / Answer

a) Q = f(K,L)= 5KL price of capital =$10 ; price of labor = $15 FOR Q=500 ; KL=100 five combination of (K,L) = (10,10) (5,20) (4,25) (2,50) (1,100) b) (10,10) ; COST = 10X10 + 10X15 = 250$ (5,20) ; COST = 350$ (4,25) ; COST = 415 $ (2,50) ; COST = 770$ (1,100); COST= 1560$ (10,10) IS LOWEST c) FOR (10,10) MPK = dQ/dK = 5L =50$ MPL =dQ/dL = 5K = 50$ d) marginal product per dollar is equal across the two inputs.

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