# Producer's Demand for Labour & Capital

Question 1

Suppose a producer has a production function of Q = L0.1K0.9 with marginal poducts of MPL = 0.1L-0.9K0.9 and MPK = 0.9L0.1K-0.1.
They have an operating budget of 100 to produce output Q. Round answers to one decimal place.

1) What is the producer's optimal input bundle when the wage rate is 2 and the rental rate is 9?

L*= K*=

2) What is the producer's optimal input bundle when the wage rate is 5 and the rental rate is 9?

L*= K*=

3) What is the producer's optimal input bundle when the wage rate is 2 and the rental rate is 10?

L*= K*=

4) Using the bundles from 1) and 2), what is the slope and choke wage rate for the producer's inverted linear demand curve for labour?

Slope = Choke Wage Rate=

5) Using the bundles from 1) and 3), what is the slope and choke rental rate for the producer's inverted linear demand curve for capital?

Slope = Choke Rental Rate =

6) What is the degrees of returns to scale of the producer's production function?

Score = 0