Q = K1/2L1/2 w = $2, r = $2 The firm would like to know the minimum co

Q = K1/2L1/2 w = $2, r = $2 The firm would like to know the minimum cost of producing 2000 units of output. Find the combination of inputs that minimizes the cost of producing 2000 units, the total cost, and identify the expansion path.

What will be an ideal response?

ANSWER

MPL = 1/2 K1/2L-1/2
MPK = 1/2 K-1/2L1/2
Optimization requires:
MPL/w = MPK/r
This results in K=L, which is the equation of the expansion path.
Q = K1/2L1/2 = 2000
Substitute the expansion path relationship to yield:
K* = L* = 2000
Then total cost = TC = 2 ∗ 2000 + 2 ∗2000 = $8,000