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 pays15 percent interest per year or to buy a year-old llama, send it onto the commonsto 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 onthe commons. That in turn depends on the animal’s access to grazing, whichdepends on the number of llamas sent to the commons, as shown in the followingtable:

Number of llamas on the commons 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 decisionsare public.

 

a. If each villager decides individually how to invest, how many llamas will besent 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 thatdifferent from the actual number? What would net village income be if thesocially optimal number of llamas were sent onto the commons?

c. The village committee votes to auction the right to graze llamas on the commonsto the highest bidder. Assuming villagers can both borrow and lend at15 percent annual interest, how much will the right sell for at auction? Howwill the new owner use the right, and what will be the resulting village income?