1. Production function: Q= 2K^2L
a. Find MRTSLK
b. Interpret MRTS(LK) when capital is 12 and labor is 2?
c. Is the firm able to produce more when making this substitution?
Q = 2K2L
(a)
MPL =
Q/
L
= 2K2
MPK =
Q/
K
= 2KL
MRTSLK = MPL/MPK = (2K2) / (2KL) = K / L
(b) When K = 12 and L = 2,
MRTSLK = 12/2 = 6
It means that in order to use 1 more unit of labor in production process, the firm has to give up 6 units of capital.
(c) While making this substitution firm is not able to produce more because MRTS is computed holding the output at a fixed level. This substitution is done by changing the capital-labor input combination while producing the same amount of output.
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