Question

For a firm, assume the following:

Production function is: Q = min(L, 3 K)

Wage rate = 25

Rent = 80

Cost Outlay = 5,000

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?

Answer 1

Solution:-

Q = min (L, 3K)

Implies L = 3K

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

25L + 80K = 5000

Put value of L in above equation:-

25(3K) + 80K = 5000

75K + 80K = 5000

155K = 5000

K = 5000 / 155

K = 32.26

L = 3 x 32.26

L = 96.78

Q = min (96.78, 4 x 32.26) = min (96.78, 96.78)

Q = 96.78

Part 1; L = 96.78

Part 2; K = 32.26

Part 3; Q = 96.78