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% per year or buy a llama, send it onto the commons to graze and then sell it after one year. The price the villager gets for selling the llama depends on quality of fleece it grows. The quality of fleece depends on how many llamas are grazing.

Number of Llamas Price per Llama

1 122

2 118

3 116

4 114

5 112

6 109

a.If each villager decides individually how to invest, how many llamas will be sent onto the commons and what will be the net village income?

b.What is the socially optimal number of llamas for this village?

c.The village committee votes to auction the right to graze the llamas to the highest bidder. How much will the grazing right sell for? What will be the net village income afterwards?