Question

Question 24 6 pts Clearly type out your answer to parts (A), (B) and (C) in the space provided. Retain all of your handwritten work for this question to be uploaded separately after you have completed the exam. Given the following long run production and cost functions: 9 = 1362 C = 15L +3K (A) What input has diminishing marginal returns? (B) Does this production function display increasing, decreasing or constant returns to scale? (C) What is this firm's expansion path assuming input prices do not change?

Answer 1

A) labor exhibits Diminishing Marginal returns

MPL = dQ/dL = (1/3)*K^2* L^(-2/3)

dMPL/dL = (-2/9)*K^2* L^(-5/3) < 0, exhibits Diminishing Returns

.

but dMPK/dK > 0 , so increasing returns to K

B) for all t > 1

q(tL, tK)= ( tL)^(1/3) * (tK)^2

= t^(7/3)*q(L,K)

thus it exhibits Increasing Returns to scale

c) at cost minimization

MRTS = w/r

MRTS = MPL/MPK = K/6L

so, K/6L = w/r

Expansion path : K = (6w/r)*L