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The Sciences

The Calculus of Prostitution

Cosmic VarianceBy Mark TroddenMarch 18, 2007 5:11 AM

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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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