# Nuriye owns 6 barrels of toxic waste.

Nuriye owns 6 barrels of toxic waste. She can store the barrels underground or in her yard, but storing them underground is more expensive, so Nuriye’s storage cost is 3(6 − B)^2 dollars if she stores B barrels in her yard. However, while burying the barrels underground is entirely safe, they leak if they are stored above ground (in her yard), which damages the tomatoes grown by her neighbor, Taylan. Taylan sells his tomatoes at the competitive price of pT = 24 and his costs of producing T tomatoes is CT (T, B) = (T + B) 2 , where B is the number of barrels in Nuriye’s yard.

(a) If Nuriye and Taylan each choose individually, how many barrels, B, does she keep in her yard and how many tomatoes, T, does Taylan grow? (

b) If Nuriye and Taylan are the only people that matter, what is the socially optimal values of B and T?

(c) Suppose Taylan is given the right to clean soil and he requires Nuriye to pay him for every barrel she wishes to store above ground. Assuming Taylan and Nuriye can negotiate without cost, what are the equilibrium values of B and T, and what is the price that Nuriye must pay Taylan for each barrel she stores in her yard?

(d) Because Taylan’s right to clean soil means that Nuriye must pay him so much to store barrels in her yard, Nuriye invests in finding a cheaper way to store barrels underground, so that her cost function is now 2(6 − B) 2 . Find the new equilibrium B and T, as well as the price Nuriye will pay Taylan per barrel.

(e) Briefly Explain how the assignment of property rights gives Nuriye the incentive to innovate new, cleaner technologies. To receive full credit, calculate how much money Nuriye saves from innovating both when Taylan has the right to clean soil and when no property rights are assigned (and compare the two figures).