A village has six residents, each of whom has accumulated savings of $100. Each villager can use this money either to buy a government bond that pays 15 percent interest per year or to buy a year-old llama, send it onto the commons to graze, and sell it after 1 year. The price the villager gets for the 2-year-old llama depends on the quality of the fleece it grows while grazing on the commons. That in turn depends on the animal's access to grazing, which depends on the number of llamas sent to the commons, as shown in the following table: Number of llamas on the common Price per 2-year-old llama ($)
1 122
2 118
3 116
4 114
5 112
6 109

The villagers make their investment decisions one after another, and their decisions are public.

a. If each villager decides individually how to invest, how many llamas will be sent onto the commons, and what will be the resulting net village income?
b. What is the socially optimal number of llamas for this village? Why is that different from the actual number? What would net village income be if the socially optimal number of llamas were sent onto the commons?
c. The village committee votes to auction the right to graze llamas on the commons to the highest bidder. Assuming villagers can both borrow and lend at 15 percent annual interest, how much will the right sell for at auction? How will the new owner use the right, and what will be the resulting village income?