The Economics of Spongeworthiness

July 7th, 2010
This is awesome. From Freakanomics:

In a recent paper, Avinash explores a decision problem drawn from Seinfeld. When the contraceptive sponge that Elaine favors is taken off the market, she scours the city buying up as many sponges as she can; but with finite supply, she faces a difficult decision as to which men are worthy of her precious sponges.

Avinash uses the tools of stochastic dynamic programming to help Elaine solve her problem.

Download the paper here. Here is a snippet:
But when she has a fi nite stock and cannot buy any more, her optimal decision will be based on a “sponge worthiness threshold” of quality, Qm, such that her decision will be yes if Q > Qm. The threshold depends on the number m of sponges she has: the fewer sponges left, the higher the threshold needed to justify using up one of them.
Let Vm denote Elaine’s expected present value of utility when she has a stock of m sponges. She meets a man and observes his quality Q. If she decides to use one of her sponges, she gets the immediate payo Q and has continuation value Vm-1 on the second day,which has present value Vm-1. If she decides not to, there is no immediate payo , only the present value of continuation with m sponges, namely Vm. Therefore her decision rule is:
Spongeworthy if Q + Vm-1 > Vm
that is, if Q > Qm  (Vm – Vm-1) ; (1)
And the abstract of this article is hilarious:
This is a paper about nothing.
That should be the abstract for more academic pieces.