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For each of the following production functions calculate the ( MRTS v L,K ) a. Q...

For each of the following production functions calculate the ( MRTS v L,K )

a. Q = L^2/3 K^1/3 when Q=8

b. Q = 3L + K when Q=3

c. Q = min{3L, K} when Q=3

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Answer #1

MRTSL,K = MPL/MPK.

MPL = \deltaQ/\deltaL.

MPK = \deltaQ/\deltaK.

MPL = 2/3*L-1/3 * K1/3.

MPL = 2/3 * (K/L)1/3

MPK = 1/3 * K-2/3 * L2/3

MPK = 1/3 * (L/K)2/3

MRTS = 0.5 * K/L.

b. MPL = 3

MPK = 1.

MRTS = 3/1 = 3.

c. MRTS = 0.

This is so because this production function represents perfect complements, the two inputs are used in fixed proportions. They are used together, and not substituted for each other.

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