You are an efficiency expert hired by a manufacturing firm that uses K and E as inputs. The production function for a competitive firm is Q = K1/2 E1/2. The firm sells its output at a price of $32, and can hire labor at a wage of $12.44 per hour. In the short run, capital is fixed at 49 units.
a. What is the short run production function?
b. Compute the Marginal Product of Labor.
c. Compute the Value of the Marginal Product of Labor
d. Compute the Marginal Cost of producing one more unit of output.
e. What is the profit-maximizing quantity of labor?
f. What is the profit-maximizing output level?
g. Graph your results labeling as many points as you can
h. What is the maximum price of capital at which the firm will still make nonnegative profits?