Suppose that Patty’s Pool has the demand data given in Table 2 in the chapter. Further, suppose that Patty has just two types of costs: (1) rent of $25 per day and (2) towel service costs equal to 50 cents per swimmer. Over the short run, rent is a fixed cost (Patty has a lease she can’t get out of), but towel service is a variable cost (it varies with the number of swimmers). Patty’s marginal cost is therefore constant at 50 cents.

a. Under these cost conditions, what are Patty’s short-run profit-maximizing output and price? What is her profit or loss per day?

b. Now suppose that, in addition to the costs just described, the town imposes a “swimming excise tax” on Patty’s Pool equal to $2 per swimmer. What are Patty’s new short-run profit maximizing output and price? What is her new profit per day? (Hint: First decide whether or not the excise tax affects Patty’s marginal cost.)

c. In addition to the costs just described (including the swimming excise tax of $2 per swimmer), suppose the town imposes a “fixed swimming tax” requiring Patty to pay $2 per day for operating her pool, regardless of the number of swimmers. What are Patty’s new short-run profit-maximizing output and price? What is her new profit per day? (Hint: First decide whether or not this new fixed swimming tax affects Patty’s marginal cost.)

d. Now suppose that costs are as in (c), except that the fixed swimming tax is $5 per day instead of $2 per day. What are Patty’s new short-run profit-maximizing output and price? What is her new profit per day?

e. With the $5 per day fixed swimming tax, what should Patty do in the short run? If Patty’s long run costs are the same as her short-run costs, what should she do in the long run? (Hint: Think about shutdown for short run; exit for long run.)

f. Based on your answers to b, c, d, and e, assess the following statement: “When an excise (variable) tax is imposed on a monopoly, it will pass part, but not all, of the tax on to consumers in the form of a higher price. But a fixed tax has no effect on monopoly behavior over any time horizon.” Are both of these sentences true? Explain briefly.