Suppose that labor is the only variable input in the production process for a competitive profit-maximizing firm that produces coffee mugs. The firm's production function is shown below.

a. Fill out columns three and four of the table above (the marginal product of labor and the value of the marginal product of labor when the price of output equals $3 per mug).

b. Suppose that the competitive wage for workers who can make coffee mugs is $19 per hour. How many workers should this firm hire? Why?

c. Suppose that schools that teach pottery skills increase the supply of workers that can make coffee mugs and that this event lowers the competitive wage for coffee mug workers to $13 per hour. How many workers should this firm hire? Why? Does this represent a shift in the firm's demand for labor or a movement along the firm's demand for labor? Explain.

d. Suppose there is an increase in the demand for coffee mugs and that the price of coffee mugs rises to $5 per mug. Fill out the last column of the table above to show the value of the marginal product of labor when the price of mugs is $5 per mug.

e. Suppose that the competitive wage for coffee mug workers remains at $13 per hour and the price of mugs is $5 per mug. How many workers should this firm now hire? Why? Does this represent a shift in the firm's demand for labor or a movement along the firm's demand for labor? Explain.