Homework Answers
1. q = 100KL
MPL = 100K
MPK = 100L
w = $320
r = $80
At cost minimizing combination of inputs: MRTS= MPL/MPK = w/r
100K/100L = 320/80
K = 4L
Put , K = 4L and q = 5000 in the production function , we get :
5000 = 100(4L)(L)
5000 = 400L2
12.5 = L2
L = 3.535
K = 4(L) = 4(3.535) =14.14
Cost : C= wL + rK
= (320)(3.535)+ (80)(14.14)
= 1131.2 + 1131.2
= $ 2262.4
The minimum cost of producing 5000 units of output is $2262.4.
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