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Q =min{ 98 L , 126 K} where Q is the output of lampposts. The prices...

Q =min{ 98 L , 126 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=11,   PK=5, P=11 and C=5,137

What is the profit maximizing amount of labor that Meyer Inc should hire?

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Answer #1

PL=11,   PK=5, P=11 and C=5,137

Cost function: C = L * PL + K * PK

=> 5137 = 11L + 5K

--------

Q =min{ 98 L , 126 K}

K and L are complementary inputs.

At profit maximizing point in this case; Q = 98L = 126K

=> 98L = 126K

=> K = (98L / 126) ----------- (1)

Put (1) in cost function.

=> 5137 = 11L + 5K

=> 5137 = 11L + 5 (98L / 126)

=> (5137 * 196) = (11L * 126) + 490L

=> 1006852 = 1386L + 490L

=> 1006852 = 1876L

=> L = (1006852 / 1876)

=> L = 536.70

Profit maximizing amount of labor that firm should hire is 536.70

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