Friday, 19 June 2009

A chocolate fish for .......

In this latest blog posting on the BERL study Eric Crampton writes,
But BERL does more than just step outside of the rational addiction model: they drive gross benefits down to zero for all consumption, including all below-the-threshold consumption, the instant your consumption exceeds their epidemiological threshold.
Instead, BERL threw in a step function that I cannot believe is consistent with any plausible utility function: prior to the threshold, benefits at least equal costs; after the threshold, benefits don't just equal zero, they're sufficiently negative to precisely offset all of the gross benefits from any prior consumption. Now, I've conducted an unscientific poll of members of the Department of Economics here at Canterbury. Half of those providing a response say you can't build a utility function that has these characteristics. The other half say that believing any model consistent with those characteristics would itself be evidence of the irrationality of the model's author.
I'm part of the you can't do it half of the survey. Or more correctly I don't think you can write down an utility function with the standard properties which would meet the BERL requirements. In particular I can't see how BERL's function can be continuous. Eric goes on to say,
The best utility function (in my view) of the ones we've come up with has a discontinuity at the harmful threshold that jumps down towards negative infinity for the epsilonth unit after the threshold but then jumps back up to zero for all subsequent units. Or, in discrete terms, benefits are positive and match costs up to the 40th gram of alcohol for men; the 41st gram has very large negative benefits that just offset all of the benefits from the prior 40 grams, and then consumption from the 42nd gram onwards provides zero benefits. Fortunately, I don't believe this model. (Emphasis added.)
The bit I have put in bold above is as far as I can tell, and I may be missing something, what a utility function would have to look like to be consistent with BERL's results. You will note that such a function is not continues, in fact it is discontinues at two points, the 41st gram and the 42 gram of alcohol consumed.

So I'll give a chocolate fish to the first person who can come up with a locally nonsatiated, continuous, concave, monotonic utility function consistent with BERL's results.


Heterosexual middle class white male said...

This is a very good point. Well made.

Richard McGrath said...

Agree with previous comment, re BERL's failure to acknowledge any benefit from drinking beer. I certainly derive enormous benefit from drinking moderate quantities of Epic Pale Ale.