Saturday 4 July 2009

A final word on rationality

I have already briefly addressed BERL's argument that Matt and I assume strict rationality: we don't. Since they keep raising the argument, I'll try to kill it a bit deader this time (given my apparent murderous proclivities).

The left hand graph shows a rational consumer's decision. The consumer picks the consumption point where the marginal cost curve cuts the marginal benefit curve. The costs curve here includes price (constant) and health costs: I've set health costs as negative over the initial part of the range, then increasing in the later part. The consumer enjoys gross benefits equal to the green area plus the blue area, but incurs costs equal to the blue area. We then call the green area consumer surplus: net benefits for the consumer.

The right hand graph moves us into Slack's preferred world. Specify that the consumer's perceived marginal cost curve is the lower one, but the actual marginal cost curve is higher: there are no health benefits in the lower range and health costs mount more quickly. The consumer still chooses the consumption point that he had chosen in the graph at left, but he's chosen incorrectly. I have assumed that the consumer is irrational: he cannot tell that the true MC curve lies above the perceived MC curve. Or, you could equally assume that he's rational but has incorrect information about the true costs curve. But, does this mean that the consumer gets zero benefits from drinking? Of course not. In fact, the consumer's gross benefits have not changed at all: only his net benefits. Gross benefits remain the area under the marginal benefit curve: here, green plus purple plus blue plus yellow. However, costs are higher than he had thought: blue plus purple plus yellow plus red. Net benefits are then the green area minus the red area. The red area counts as "excess costs" of irrational behaviour.

So, has anything in our critique of the BERL report required strict rationality? No. All we need is that, on average across all of the consumers that BERL defines as "harmful", including the folks drinking 1.8 pints of beer per day, the green area approximately matches the red area. It can be the case that for some consumers the green area is smaller than the red area, so long as there are enough others for whom the green area is larger that they balance out in aggregate. So long as that's the case, worrying only about external costs of harmful alcohol use is just fine. Whether I believe the left graph or the right graph to be the correct one is utterly beside the point. We only require that green roughly matches red on average across all of BERL's "harmful" consumers.

BERL assumes "that it is irrational to drink alcohol to a harmful level and that harmful alcohol use has zero private benefit." Our approach is flexible enough to allow irrational behaviour and doesn't require the somewhat restrictive assumption that private benefits are zero.


  1. After the financial crisis I'm not sure how anyone could believe the left graph, but as you say its beside the point...My question is do you have any information about the shapes of these curves? Is it unreasonable to suggest for example that at a certain consumption level the MB curve is vertical and thus MB is zero for all consumption above this level?

  2. Financial crisis: macroeconomics. Very different.

    The standard default assumption is that demand curves are downward sloping. The massive onus is on anyone suggesting different to prove otherwise. It's the entire foundation of our discipline: demand curves slope down.

    A vertical MB curve doesn't mean that marginal benefit is zero; it means that it is indeterminate. If you want a zero marginal benefit, you want it to be horizontal and to conincide with the x-axis. You can throw kinks into the MB curve if you like, or have it asymptote to 0 as consumption gets large, but you need somehow to make the integral under the early part of the curve disappear. And that's why I've asked whether it's even possible to run BERL's model in a standard framework.