The profits associated with producing Q for Nash Enterprises are ( = 20Q - Q2, and marginal benefits are MB = 20 - 2Q. Pollution damages (costs) associated with its production are D = 10Q; the marginal damages are MD = 10.
(a) In the absence of any pollution regulation, how much will Nash produce? What will its profits be if it produces that amount? What will be net benefits (that is, profits less damages)?
(b) What is the efficient level of production for Nash Enterprises-that is, the level that leads marginal benefits to equal marginal damages? What will its profits be if Nash Enterprises produces the efficient amount? What will be net benefits (that is, profits less damages)?
(c) Will net benefits be higher under efficient production than under profit-maximizing production? (They should be!)
(d) Describe one policy that, if adequately enforced, will lead to Nash producing the efficient quantity.
(e) The environmental regulator imposes a standard that restricts Nash's production to Q = 5 every year, but, because of the costs of enforcement, it monitors Nash's production only one year out of every two (and Nash knows the monitoring schedule). If it is found in violation of the standard, it must pay $10 for each unit when it exceeds the standard. If Nash is a strict profit maximizer, how much do you expect it to produce in the years when it is not monitored? In the years when it is monitored? What is the 2-year average for how much it will produce? What are the 2-year average profits and average net benefits?
(f) Now, suppose the penalty in (d) is set at $20 for each unit when it exceeds the standard. If Nash is a strict profit maximizer, how much do you expect it to produce in the years when it is not monitored? In the years when it is monitored? What is the two-year average for how much it will produce? What are the two-year average profits and average net benefits?
(g) The regulator has a limited budget for enforcement. Would it get better compliance from Nash if it set a higher penalty (for instance, $40/unit) for noncompliance but monitored once every 4 years, on a known schedule? What is the average over 4 years for how much it will produce? What are the average profits and average net benefits?
(h) Now, suppose that the regulator monitors randomly, so that Nash doesn't know in any year whether it will be penalized or not. The probability of getting monitored is 50 percent, and the payment if found in violation is $20/unit. What is the expected or average penalty that it will pay per unit? How much will it produce if it faces this expected penalty? What are the resulting profits and net benefits?
(i) Is society better off in this case with Nash facing an uncertain monitoring schedule or a certain one, if the penalty is $20/unit and the probability of getting monitored is 50 percent? With which schedule is Nash better off?