Consider production function Q= L^3 * K^4 - L^2 (a) Determine the MRTS L,K for this...

Consider production function Q= L^3 * K^4 - L^2

(a) Determine the MRTS L,K for this production function

(b) Does this production function have an uneconomic region? If so, describe the region algebraically. (Hint: your answer will be an inequality like this: K<5L)

Solutions

Expert Solution

a) Q = L³ * K⁴ - L²

MRTS(L,K) = MP_L/MP_K

MP_L: Marginal product of labor

MP_K: Marginal product of capital

MP_L = dQ/dL

MP_L = 3L² * K⁴ - 2L

MP_K = dQ/dK

MP_K = 4K³ * L³

MRTS(L,K) = (3L² * K⁴ - 2L)/(4K³ * L³)

MRTS(L,K) = 0.75*K/L - 0.5/(K³*L²)

b) The production function has an uneconomic region where MP_L or MP_K are negative

MP_L < 0

3L² * K⁴ - 2L < 0

3L² * K⁴ < 2L

3L * K⁴ < 2

L < 2/(3K⁴)

Rahul Sunny answered 1 year ago

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