1. On a tropical island there are 100 potential boat builders, numbered 1 through 100. Each can build up to 16 boats a year, but anyone who goes into the boatbuilding business has to pay a fixed cost of $15. Marginal costs differ from person to person. Whereydenotes the number of boats built per year, boat builder 1 has a total cost functionc(y) = 15+y. Boat builder 2 has a total cost functionc(y) = 15+2y, and more generally, for eachi, from 1 to 100, boat builderihas a cost functionc(y) = 15+(iy).

a. Derive the market supply curve.

b. Suppose the market demand function isy(p) = 698p. Find the equilibrium price and number of boats built in a year.