The not-so-weekly Equation of the Week returns with a formula for determining whether or not a person will engage in prostitution:

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

Where U=utility, L=leisure, C=goods and services consumed, S=quantity of prostitution sold, w=wage for prostitutes, and r=your reputation.

In other words:

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.

Reputation, or more broadly social costs, may be one thing that individuals consider when selecting a profession, but to say it’s the only thing?

The full paper is here, via this Improbable Research Column.

Categories: Business and Economics, Careers, Dating, Equation of the Week, Funny, Incentive Centered Design, Matching Mechanisms