For a firm, assume the following: Production function is: Q = min(L, 4 K) Wage rate...

Question

Question

For a firm, assume the following: Production function is: Q = min(L, 4 K) Wage rate...

For a firm, assume the following:

Production function is: Q = min(L, 4 K)

Wage rate = 30

Rent = 100

Cost Outlay = 9,000

(Take all calculations to 2 decimal places)

Part 1: What is the optimal amount of labour hired?

Part 2: What is the optimal amount of capital employed?

Part 3: What is the optimal amount of output produced?

business economics

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Answer 1

Answer #1

Solution:-

Q = min (L, 4K)

Implies L = 4K

Cost constraint = Wage rate * Labor + Rent * Capital = Cost Outlay

30L + 100K = 9000

Put value of L in above equation:-

30(4K) + 100K = 9000

120K + 100K = 9000

220K = 9000

K = 9000 / 220

K = 40.91

L = 4 x 40.91

L = 163.64

Q = min (163.64, 4 x 40.91) = min (163.64, 163.64)

Q = 163.64

Part 1; L = 163.64

Part 2; K = 40.91

Part 3; Q = 163.64

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Answer 2

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