3. Ocean City is a vacation beach community one mile long, with all of its 1,000 daily vacationers evenly distributed along the beach and boardwalk. At each end of the boardwalk is an urgent care clinic specializing in the treatment of jellyfish stings. The clinic on the south end of the boardwalk is Clinic S and the one on the north end of the boardwalk is Clinic N. On any given day, there is a 10% chance of being stung by a jellyfish. Due to the hot sand and the congested boardwalk, each vacationer's travel cost of going to a clinic after a jellyfish sting is $20 per mile. However, this is preferable to the excruciating pain of non-treatment, so all who are stung go to one clinic or another for treatment. (Assume that, once stung, a person does not go back into the water, so that each person can only be stung once at most.) Finally, assume that each clinic's marginal cost of treating each sting is a constant $8 per sting.

3.A (10) What is the expected demand for each clinic as a function of its price and the other clinic's price? (Make sure to show all of your work in deriving these demands.)

3.B (15) One morning, the owner of Clinic S decides to set a price of $60 for each jellyfish-sting treatment and tells the Ocean City sign maker to make a sign that he can post outside advertising this price. The owner of Clinic N overhears the sign maker talk about Clinic S's sign (advertising the $60 price) before she puts in her order for a sign. She quickly figures out her profit-maximizing price given this information and orders a sign with that on it. What price did she request the sign maker put on Clinic N's sign? At the end of the day, do you think the owner of Clinic S will regret his decision to set a price of $60? Explain.

3.C (15) Some enterprising entrepreneurs decide that they would like to offer jellyfish-sting insurance to the vacationers each day when they arrive at the beach. They would like to sell the insurance to the vacationers as they enter Ocean City, before they pick out their spot on the beach. However, the government of Ocean City is considering a law that would require that all sales of jellyfish insurance occur on the beach, after vacationers pick out their spot in the sand, and, to be fair, the same price must be charged to all vacationers. How would you advise the government of Ocean City? What is a potential risk or unintended consequence if this law is passed?