4. Demand curve

Derive the short-run labor demand curve associated with the production functions below. The level of output is denoted by q. The two inputs are E (labor) and K (capital). Let's normalize the price of output to one, p = 1. In the short run, the capital stock is fixed at K0 and the rental rate of capital is r. Derive the amount of labor demanded by the firm as a function of wage w. Plot the labor demand curve, with labor on the x-axis.

Question 4.1 q = E0.5K0.5

Question 4.2 q = min {2E, 3K}. HINT: You will not need to take first order conditions here.