cost of producing at any level of output q?

Chapter 7
The Cost of Production 111 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall. To find the marginal product of capital, observe that increasing K by 1 unit increases q by 5L, so MP
K
 5L. Similarly, observe that increasing L by 1 unit increases q by 5K, so MP
L
 5K. Mathematically,
5
K
q
MP
L
K




and
5
L
q
MP
K
L




Using these formulas in the cost-minimization rule, we obtain
5 5
5000 1
10,000 2
L
K
K
w
r
w
L
r




 . The new plant should accommodate a capital to labor ratio of 1 to 2, and this is the same regardless of the number of units produced.

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