Question

For a firm, assume the following: Production function is: Q = min(L, 2 K) Wage rate = 50 Rent = 90 Cost Outlay = 4,000 (Take all calculations to 2 decimal places) Part 1: What is the optimal amount of labour hired?Number Part 2: What is the optimal amount of capital employed? Number Part 3: What is the optimal amount of output produced?

Answer 1

Q = min(L, 2K)

Implies L = 2K

Cost constraint: Wage rate x Labor + Rent x Capital = Cost Outlay

50L + 90K = 4000

Put value of L in above equation;

50(2K) + 90K = 4000

100K + 90K = 4000

K = 4000/190

K = 21.05

L = 2 x 21.05

L = 42.10

Q = min(42.10, 2 x 21.05) = min(42.10, 42.10)

Q = 42.10

Part 1; L = 42.10

Part 2; K = 21.05

Part 3; Q = 42.10