The manager of a national retailing outlet recently hired an economist to estimate the firm's production function. Based on the economist's report, the manager now knows that the firm's production function is given by Q=K^(1/2) L^(1/2) and that capital is fixed at 1 unit.
a. Calculate the average product of labor when 9 units of labor are utilized.
b. Calculate the marginal product of labor when 9 units of labor are utilized.
c. Suppose the firm can hire labor at a wage of $10 per hour and output can be sold at a price of $100 per unit. Determine the profit-maximizing levels of labor and output.
d. What is the maximum price of capital at which the firm will still make nonnegative profits?