Include correctly labeled diagrams, if useful or required, in explaining your answers. A correctly labeled diagram must have all axes and curves clearly labeled and must show directional changes. If the question prompts you to "Calculate," you must show how you arrived at your final answer.

Quantity of Output Total Cost

0 $12

1 $14

2 $18

3 $24

4 $32

5 $42

6 $54

7 $68

The table above shows the total cost function for a typical firm producing hats in a perfectly competitive market. The market price for hats is $9 per hat.

(a) Calculate the average variable cost of the fifth unit. Show your work.

(b) What is the firm's profit-maximizing quantity of hats? Explain using marginal analysis.

(c) Draw a correctly labeled graph showing the firm's demand and marginal cost curves, and show the profit-maximizing quantity of hats determined in part (b).

(d) If the rent of the building the firm occupies increases, what will happen to the firm's profit-maximizing quantity of output in the short run? Explain.