Microeconomics 6th Edition by Robert Hall, Shirley Kuiper, Marc Lieberman

Exercise 2

Suppose that Patty's Pool has the demand data given in Table 1 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 longrun 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.
Table 1 Demand and Revenue at Patty's Pool