A village has six residents, each of whom has $1000. Each resident may either invest his money in a government bond, which pays 11 percent/yr, or use it to buy a year-old steer, which will graze on the village commons. Year-old steers and government bonds each cost exactly $1000. Steers require no effort to tend and can be sold for a price that depends on the amount of weight they gain during the year. Yearly weight gain, in turn, depends on the number of steers that graze on the commons. The prices of 2-yr-old steers are given in the table as a function of the total number of steers.

Number of steers . Price per 2-year- old steer

1 ............... $ 1200

2 ................ 1175

3 ................ 1150

4 ................. 1125

5 ................. 1100

6 ................. 1075

a. If village residents make their investment decisions independently, how many steers will graze on the commons?

b. How many steers would graze on the commons if investment decisions were made collectively?

c. What grazing fee per steer would result in the socially optimal number of steers?