The Manager of a National Retailing Outlet Recently Hired an Economist

Essay

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?