The Calculus of Prostitution

By Mark Trodden | March 17, 2007 8:11 pm

Here’s a question for our highly mathematically talented readership: what does the following condition describe?

[(δU/δL) / (δU/δC) | Sp=0] ≤ w – [(δU/δr) / (δU/δC) | S = 0]

If you said

“An individual will start to sell prostitution if the price for selling the first amount of prostitution, minus the costs of a worsened reputation for doing so, exceeds the shadow price of leisure evaluated at zero prostitution sold.”

you were spot on. That’s right; according to Marc Abrahams’ Improbable Research column in The Guardian, this is the equation to describe when a prostitute finds it worthwhile to sell (typically) her services.

The story is a little unclear, but the very least you’ll need to make sense of the equation is a definition of the variables:

  • U is the “utility”
  • L is the amount of leisure you have.
  • C is the amount of goods and services you, as a consumer, consume.
  • S is the amount of prostitution you, as a prostitute, sell to your customers.
  • W is the going price for prostitutes.
  • R is a measure of your reputation.

And here I am working on particle cosmology when there are these huge open problems in other fields!


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Cosmic Variance

Random samplings from a universe of ideas.

About Mark Trodden

Mark Trodden holds the Fay R. and Eugene L. Langberg Endowed Chair in Physics and is co-director of the Center for Particle Cosmology at the University of Pennsylvania. He is a theoretical physicist working on particle physics and gravity— in particular on the roles they play in the evolution and structure of the universe. When asked for a short phrase to describe his research area, he says he is a particle cosmologist.


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