There are fifty farmers in a valley. Each year the valley floods, destroying all crops. A dam can be built at $2,000 for each foot in height (this cost is an annualized cost). The first foot saves each farmer $100 per year in damages, the second foot saves each farmer an additional $90 in damages, the third, $80; and so on.

a. Suppose the dam is three feet high. What is the social benefit of one more foot?

b. What is the socially optimal height of the dam?

c. Suppose forty of the farmers get together and agree to share costs:

How high will their dam be? Why are the remaining ten farmers

“free riders”?