Consider a production function that takes the form
y = 10?(LK)?^(1/2), and assume that capital is constant at Ko = 64.
(a) If the real wage is equivalent to the marginal product of labor such that W = aA( ?K/L)?^(1-α)= 10, how much labor will be demanded? What happens to the demand for labor when the real wage declines to w = 8?
(b) Now assume that the capital used in the production process is allowed to vary and increases to K = 100. Holding the real wage constant at w = 8, how much labor will be demanded? How does the increase in capital affect the graph of the demand for labor?
(c) Determine the cross partial derivative of this production function and provide an intuition for the sign on your result.