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 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?