The Corona Brewery uses water from a river to produce yellow water in bottles. Recently, a cooperative of 19 vitamin drink makers (also called Covid19) have opened a factory upstream from the Corona bewery. Covid19's manufacturing operations pollute the river water: let x denote the number of gallons of pollutant that Covid19 dumps into the river each day. Corona's profits are reduced by x ² dollars per day, because that's how much it costs Corona to clean the pollutants from the water it uses. Covid19's profit-maximizing level of operation involves daily dumping of 30 gallons of pollutant into the river. Altering its operations to dump less pollutant reduces Covid19's profit: specifically, Covid19's daily profit is reduced by the amount (1/2)(30 x) ² if it dumps x gallons of pollutant per day. There are no laws restricting the amount that Covid19 may pollute the water, and no laws requiring that Covid19 compensate Corona for the costs imposed by Covid19's pollution.

Coase's argument holds that the two firms will reach a bargain in which the Pareto efficient level of pollution will be dumped. Determine the efficient level of pollution.

(a)If efficiency requires that x < 30, then determine the range of the bargains the two firms could be expected to reach i.e., the maximum and minimum dollar amounts that Corona could be expected to pay to Covid19 in return for Covid19's agreeing to dump only x (less than 30) gallons per day.

(b)Now suppose a law is passed that requires anyone who pollutes the river to fully compensate any downstream firm for the damages caused by the polluter's actions. How does this change the Pareto efficient level of pollution? How does this change the pollution level that Covid19 and Corona will agree to? How does it change the payments that one of the firms will make to the other?

(c)Now suppose that Corona is not the only firm harmed by Covid19's pollution: there are more than one hundred firms whose profits are reduced by the pollution. How would this affect your answers in (a) and (b)? (You will not be able to give a precise quantitative answer here, because you do not know exactly how much each firm is damaged by the pollution. But describe qualitatively how the answers to (a) and (b) will change.)