[MUSIC] If you ask, how can you find the top of the hill, most people answer by saying you should look for the highest point or keep walking upward until there's nowhere else to go. But an economist might say, look for the place that's flat. At least with regard to smooth and convex curves, the maximum point will be at that place where the slope of the curve is zero. This simple attribute of hills lies behind the idea of Marginalism in economics. To maximize or minimize some outcome with respect to some underlying input or variable means that you're going to wanna look at the margin. At the marginal effect that changing the input has on the outcome. Assessing the marginal effects is also the core idea when you want to maximize or minimize the difference between two curves. Again, assuming smoothness and certain convexity. Thus monopolists, in choosing the profit maximizing output, will classically want to produce the quantity at which the marginal revenue, the revenue from the last unit produced, equals the marginal cost, the incremental cost of producing that last unit. Consider these two graphs. In the left-hand graph, Marginal Benefit, MB of one or more unit of some activity Q decreases as Q goes up. As it might if Q was the time spent studying for an exam. As you study more and more, the marginal benefit of the last hour decreases while the marginal cost of studying or of some activity goes up. It becomes more tiresome, the last hour after spending eight hours becomes more annoying. And the total benefit is the area between these two curves. Up to this point, Q star, the total benefit curve is increasing because up to that point the marginal benefit is at every point, is above the marginal cost. But after Q star, the marginal benefit, the total benefit, excuse me, is decreasing, because beyond that point, the marginal cost is above the marginal benefit. A law student might stop studying when you think the annoyance of the next minute outweighs the incremental expected increase in the exam score that minute might provide. That's the essence of marginalism that you maximize things at the flat point or that total benefit will be maximized when the marginal benefit is equal to the marginal cost. This is the point where the slope of the total benefit curve is zero. Thinking on the margin has huge payoffs for both law and regulation. Imagine that the BP oil well has just dumped a billion barrels of oil into the Chesapeake Bay. The government can clean up the spilled oil for a cost of $100 million and thereby avert a social cost of $500 million. Should the government undertake the cleanup or force BP Oil to do so? Most people would think this is a no brainer. The benefits are five times greater than the costs. So, doing the clean up clearly passes cost benefit analysis. But an economist would wanna ask whether the last bit of clean up was cost effective. The economist would want to think on the margin. It's possible that for merely $20 million, $450 million of the pollution, social costs can be averted. That means that spending the final $80 million only saves an additional 50 million in social costs. On the margin, society might be better off not cleaning up the last bit of pollution. But BP might still be liable for 500 million. Can you see why optimal deterrence might still be 500 million if the government pays for the clean up? Or consider this, when I was on a Disney cruise with my kids, I accidentally dropped a tissue overboard. Should we turn the boat around and search for the quickly disintegrating tissue? Thinking on the margin also suggests an improvement in the famous learned hand rule. That was first announced by Judge Hand in United States versus Carroll Towing. A case in which a barge broke free of its mooring and damaged other vessels. Judge Hand had the temerity in this startling opinion to propose a formula to assess whether liability should be found. Now I've already mentioned this formula before in the lecture on risk and uncertainty, but this is how Judge Hann's opinion describe the formula with slightly different letters than is used today. Judge Han said, since there are occasions when every vessel will break from her moorings and since if she does, she becomes a menace to those about her. The owner's duty as in other similar situations, to provide against resulting injuries is a function of three variables. The probability that she will break away, the gravity of the resulting loss, injury if she does, and the burden of adequate precautions. Possibly it serves to bring the notion into relief to state it in algebraic terms. And again I'm still reading from Learn at Hands Opinion. If the probability be called P, the injury L and the burden B, liability depends upon whether B is less than L multiplied by P. That is, IE whether B is less than PL, unquote. Hands reasoning has great power for all or nothing precautions that completely eliminate the probability of loss. But a more general version of the hand formula would think about the marginal burden of precaution for example of tying down the barge with an additional cable. And the marginal impact of that precaution in reducing the probability of loss. Restated in marginal terms, the law should ask for a potential defendants to take precaution, should call upon potential defendants to take precaution up to the point at which the marginal benefit is equal to the marginal reduction in probability times the loss. Try to think, and now as homework, try to think of another legal rule or regulation where the law should turn on a consideration of marginal cost and marginal benefits. [MUSIC]
