Steve Levitt links to his paper with Sudhir Venkatesh documenting some stylized facts about street prostitution in Chicago.  It’s definitely worth a read, and one part is fodder for theory:

Prostitutes in their sample report using condoms 90  percent of the time, compared to only 25 percent in our sample for vaginal sex, and 21 percent for anal sex.  Among their Mexican prostitutes, condom use is the default from which customers must bargain away, potentially inducing large increases in prices.  In contrast, in our sample no condom appears to be the default choice, perhaps making it harder for the prostitute to credibly argue for a higher price if no condom is used.  Moreover, in an equilibrium in which condom use is infrequent, infection rates among prostitutes are likely to be extremely high, so that the primary value of condoms to women may be protecting the women from becoming pregnant and hygiene, rather than the spread of disease.  Indeed, one would expect that the johns would likely gain more in disease reduction from condoms than the prostitutes.

SOME DISCUSSION OF HOW CONDOM USE VARIES ACROSS PROSTITUTES IN OUR SAMPLE.  SOME QUOTES ABOUT WHY THEY DON’T USE THEM. SOME FACTS ABOUT AIDS RATES AMONG JOHNS AND PROSTITUTES FROM MEDICAL LITERATURE.

(hmmm, it appears they are not quite done with the paper :) ) They focus on the cost to the prostitute due to increased infection and the like, but there is already some unusual aspects to the demand side.

A John values unprotected sex over protected sex but even moreso if he is the only John, or among very few, who get that privelege.  Holding fixed her frequency of unprotected sex, there is a downward sloping demand for unprotected sex as a function of the price premium over condom-clad.  But that frequency is not verifiable, except insofar as it can be inferred from the price.  Thus, as an equilibrium response the demand curve itself shifts with adjustments to the price.

This means that the prostitute cannot just choose any price.  The price must be such that x% of Johns are willing to pay that price when they assume that x% of other Johns are having unprotected sex.  Typically there will be just a few values of x that satisfy this fixed-point relationship.

So a cross-section of pricing patterns will exhibit a bang-bang (quiet down Beavis) or bi-modal (Beavis!) histogram with high prices and low prices and none in-between.  The high prices correspond to the equlibria in which few Johns have unprotected sex so Johns are willing to pay a lot, and the low prices correspond to the equilibria in which many Johns have unprotected sex and Johns place lower value on it.

It could even happen that the price premium is for protected sex.  In fact it could even be profit maximizing to distort downward the price of unprotected sex in order to signal how risky that would be, enabling the prostitute to raise the price of protected sex.

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