5. Optimal consumption of a commons Aa Aa A small community is located near a bay. There are five people in the community, each of whom has accumulated savings of $1,000. Each person can either buy a fishing boat and sell the lobsters they catch in the bay (assume the boat does not depreciate over time), or buy a T-bill that pays 13% interest. Thus, someone who chooses not to buy a boat will earn $130 of income each year. Lobsters sell for $10 per pound. The more people who choose to fish in the bay, the fewer lobsters each will catch. The total number of lobsters caught and the total value of the lobsters caught by each person are shown by the following table: Lobsters Caught Income per Boat Number of Boats (Pounds per year) (Dollars per year) 18 $180 AWN 32 $160 42 $140 48 UT $120 50 $100 Suppose that of the five villagers, two (Dante and Antony) say they are definitely going to buy boats and fish, and two (Bethany and Steve) say they are definitely going to buy T-bills. The fifth, Tiffany, is undecided. If Tiffany chooses to buy a boat and fish, she will earn than the $130 she could get from investing her money in a T-bill. Suppose two fishing boats (Dante's and Antony's) are in the bay, while Bethany and Steve purchase T-bills. Fill in the income columns for when Tiffany decides to fish and for when she invests her money in a T-bill. Dante and Bethany and Antony's Steve's Total Lobsters Total Income Income Tiffany's Decision Caught ( Dollars per (Dollars per Tiffany's (Pounds per year) year) Income Total Income year) Invest her money 32 $260 Buy a boat and fish 42 $260 If Tiffany were to buy a boat and fish, the total income earned by all residents of the community wouldSuppose two fishing boats (Dante's and Antony's) are in the bay, while Bethany and Steve purchase T-bills. Fill in the income columns for when Tiffany decides to sh and for when she invests her money in a T-bill. Dante and Bethany and Antony's Steve's Total Lobsters Total Income Income Tiffany's Decision Caught (Dollars per (Dollars per Tiffany's (Pounds per year) year) Income Total Income yea r) Invest her money 32 ':| $260 ':I ':| Buy a boat and sh 42 ':| $260 ':I ':| If Tiffany were to buy a boat and sh, the total income earned by all residents of the community would The socially optimal number of boats can be found by looking at the marginal (community-wide) revenue from each additional boat in the bay and comparing it to the opportunity cost of buying the boat. Recall that the marginal revenue is the additional revenue created from having one more boat in the bay, and the opportunity cost of buying the boat is the income received from investing the money in a T-bill. Total Income from Lobsters Marginal Revenue Lobsters Caught (Dollars per from Lobsters Opportunity Cost of Number of Boats (Pounds per year) year) (Dollars per boat) Buying the Boat 1 18 $180 $180 $130 2 32 $320 $140 $130 3 42 $420 $100 $130 4 48 $480 $60 $130 5 50 $500 $20 $130 The socially efcient number of shing boats is boats. Suppose the bay is on Tiffany's property, so she can legally charge people to sh in it. If Tiffany chooses not to buy a boat, Dante and Antony will be willing to pay at most each to sh in her bay, and she will earn an income of at most . If she does buy a boat and sh, Antony and Dante will be willing to pay at most each to fish in her bay, and she will earn an income of at most If Tiffany is able to charge the highest price Antony and Dante are willing to pay, Tiffany maximizes her income if she buys a and sells shing rights to Antony and Dante. If the bay is held as private property rather than commonly held by all the residents of the community, the socially optimal number of boats be bought