Question is below

[Tragedy of the lCommons] There are n producers, each of Whom must choose a quantity of clean air to consume as part of their production process. {Alter- nativelyj each producer must choose the level of air pollution to emit.) There is initial stock K of clean air. Let la,- 2 0' he the amount clean air consumption of rm i. Then, the amount of clean air remaining is K 2;; kg, and this clean air is enjoyed by all producers. The rms have identical preferences: Riki, 155-3 = 111(ki) +111{K ikj) i=1 1. How much does each rm produce in a {symmetric} Nash equilibrium? How much clean air remains? 2. 1What is the socially efcient output for each rm? How much clean air would remain at the social optimum? 3. Using the rst order conditions, show why each rm will over-produce relative to the social optimum? Tl.'ll'hat canonical game does this strategic scenario remind you of? 4. Suppose the government imposes a tax a! on the consumption of clean air. What is the efcient tax?I