Question

Meyer Inc produces lampposts using labor (L) and capital (K). Its production function is given by the following expression: Q =min{ 118 L , 186 K} where Q is the output of lampposts. The prices of labor (PL), capital (PK), lamppost (P) and the cost (C) are the following: PL=16, PK=11, P=15 and C=5,889 What is the profit maximizing amount of labor that Meyer Inc should hire?

Answer 1

Answer:

L = 0

K = 535.36

Q = 99,577 units

Explanation:

Q = 118L + 186K  

Budget line: C = L.PL + K.PK

5,889 = 16L + 11K

This is a linear production function, indicating labor and capital are perfect substitutes. Optimal bundle lies on one of the corner points on isoquant.

From budget line,

When L = 0, K = 5,889/11 = 535.36  

Q = 118*0 + 186*535.36 = 0 + 99,576. 96 = 99,577 units

When K = 0, L = 5,889 / 16 = 368.06

Q = 118*368.06 + 11*0 = 45,555.08 + 0 = 45,555 units

So, output is maximized when L = 0 and K = 535.36, since Q = 99,577 units (optimal labor).

Hope this helps!