There are a large number of chicken farms of varying sizes on the Delmarva peninsula and together they produce huge quantities of fecal waste. Some of that waste washes into the Chesapeake Bay creating pollution that threatens the viability of the Chesapeake ecosystem. You are part of a team that is working to reduce this pollution, with a target of cutting Chesapeake Bay chicken waste runoff by 50%. For purposes of this problem, assume that the runoff from each farm into the bay can be measured at negligible cost. (In the real world, measurement costs are a significant impediment to creating effective pollution controls for farms but don't worry about that here.) Your team does a survey and concludes that 50% of the chickens are currently raised on farms that adjoin Delmarva rivers or the bay itself while the other 50% of chickens are raised on farms further away from the water. Waterside farms have runoff into the bay of 100 tons per thousand tons of chicken produced while inland farms have runoff into the bay of 50 tons per thousand tons of chicken produced. The total cost to farmers of reducing waste runoff is TC = x2 (with a corresponding marginal cost given by MC = 2x) where x is the number of tons of waste reduced per thousand tons of chicken produced. [Please note that in the problem set different plants had different marginal cost functions. In this case, all farms have the same marginal cost function but because that function is increasing and the farms begin with different amounts of relevant waste, they will have different marginal costs for the last ton of waste reduction if both types of farms are required to make a 50% reduction in their runoff.] Your team is evaluating the economic effects of imposing a 50% runoff reduction on each current farm or creating a tradeable permit system. You recognize that given the conditions above, you can simplify the analysis by focusing on two representative farms (one that produces 1000 tons of chicken waterside and one that produces 1000 tons of chicken inland) while recognizing that there are many farms so that a competitive market would exist in pollution permits. Assume that the runoff controls do not change the distribution of where chickens are grown. [That distribution probably would change in the real world but taking account of it would make the problem more complex.]
a. Suppose that a system of tradeable permits is created in which each permit authorizes one ton of waste runoff into the bay. Each farm is initially given permits without charge equal to half of that farm’s current runoff (50 permits to the representative waterside farm and 25 permits to the representative inland farm). Find the equilibrium price of permits, assuming there are no impediments to a competitive market in permits.?
b. Suppose that instead of either direct controls or tradeable permits, a system of waste taxes is imposed. That is, any farm is entitled to create any amount of waste that they choose, but the waste is accurately measured and assessed a fee of $60. per ton of waste. How much will a waterside farm reduce waste per thousand tons of chicken produced (in comparison to the initial situation with no controls at all)? ?
c. With a tax of $60. per ton as in the previous question, how much will an inland farm reduce waste per thousand tons of chicken produced (in comparison to the initial situation with no controls at all)?