A village has six residents, each of whom has accumulated savings of $100. Each villager can use this money either to buy a government bond that pays 10 percent interest per year or to buy a 1-year-old goat, set it onto the commons to graze, and sell it after a year. The price the villager gets for a 2-year-old goat depends on the amount of weight it gains while grazing on the commons, which in turn, depends on the number of goats sent onto the commons, as shown in the following table:

Number of goats on the commons	Price of 2-year-old goat ($)
1	125
2	117
3	114
4	111
5	108
6	105

a. If each villager decides individually how to invest, then how many goats will be sent onto the commons and how many villagers will buy a bond?

What will be the resulting village income?

b. What is the socially optimal number of goats for this village to send onto the commons?

What would village income be if the socially optimal number of goats were sent onto the commons?

c. The village committee votes to auction the right to graze goats on the commons to the highest bidder. Assuming the villagers can both borrow and lend at 10 percent annual interest, how much will the right to sell for at auction? $  

How many goats will the new owner send onto the commons, and what will be the resulting village income?

goat(s) will be sent out onto the commons and the resulting village income will be $.