Tuesday, June 21, 2011

The Price of Sex

You’ve heard it said that every man has his price, and no doubt you’ve inferred that so does every woman. It’s easy enough to do research on what the going rate on sex for pay is but that only tells you the prices of those who are currently selling or buying sex. It tells you nothing of the price at which it would be worthwhile for someone outside the market to enter it, and that is after all what we want to know when we talk about everyone having their price. What follows is my attempt to spell out the price distributions of all adult men and women respectively – not just professionals.

The propensity to pay for sex, or have sex for money, must be determined by a large number of relatively independent factors e.g. interest in sex, attractiveness, need for money, availability of alternatives, price, moral qualms, fear of disease, opportunity, the illegality, forgone marriage opportunities, low workload, etc. If that is the case then according to the Central Limit Theorem the disposition will be normally distributed i.e. will fit the famous bell curve. So I can express this behavioral disposition as a trait that is normally distributed.

If there are several groups – like men and women in this case – and the distribution of one group is used as a standard, then the others can be specified in the terms of that standard. The beauty of this approach is that it models supply and demand together i.e. it looks at prices in a situation where women require a certain price knowing what men are willing to pay and men are willing to pay knowing what women require. It doesn’t just ask people what they would charge or pay in isolation.

All we need is stats on the proportion of each group exceeding two or more objective thresholds on prostitution or solicitation. In this case I used the General Social Survey variables - Paidsex and Evpaidsx. These ask if a respondent has paid for (or has been paid for) sex within the last year, and ever since the age of 18, respectively. The first is a higher threshold than the second because it is a subset of it. I also used stats in Steven Levitt and Stephen Dubner’s chapter on prostitution in their book SuperFreakanomics and some prices mentioned in the Governor Eliot Spitzer scandal.

It turns out that 3.4% of men and 0.5% of women exchanged money and sex in the last year, and 1.3% of women and 14.4% of men had done so since turning 18. So from this GSS data I calculated the following normal distributions

Female disposition to have sex for money 0±1
Male disposition to pay for sex -1.739±0.4585

where the female distribution is set as the standard and lower numbers mean a higher propensity. [I give the technical details in the appendix below.]

In other words the average man is more likely to pay for sex than the average woman is to have sex for money, and men are more alike than women when it comes to swapping sex and money. So far there are no surprises.

After mapping these distributions onto prices I put it altogether on the graph you see below. The average woman’s price is therefore $3972.62 but the average man is only willing to pay about one tenth of that - $396.96. Only one in 13423 men is willing to pay the average woman’s price. On the other hand as many as one in 24.3 women are willing to have sex at a price the average man is willing to pay.



You can also see that the asking price at the far right of the graph is $0.72 million. One in 30000 women would require that price. One in a million women would require at least $2 million. This is the roughly the estimated value of life in the US, so one could say that there are women out there that would rather die than have sex for money. On the other hand it’s equally fair to say there are women out there who would pay men for sexual favors. Still most women do price themselves out of the market.

Then there are men. Virtually all men would pay for sex if he had no alternative and his price was accepted. In fact most are willing to pay more than the going rate for street walkers and maybe a third would be willing to pay a high class hooker’s rate of $500.

Where do you think you are on the distribution? If you aren’t in the US then remember to correct for purchasing power parity when translating the prices in the graph.


Appendix

In order to use this information to estimate the distribution of propensity pay for sex, or have sex for money, all we need to do is convert these percentages into normal distribution standard scores – the so called z-scores. All these scores are is the number of standard deviations away from the average one has to be to get that percentage. For women those percentages convert to z-scores of 2.5758 and 2.2262 respectively. In other words a woman who has had sex for money within the last year is at a z-score of 2.5758 on the “propensity to have sex for money” distribution. For men the z-scores are 1.825 and 1.0625 respectively. Now the rest is simple arithmetic.

I took the woman’s distribution as the standard one and set the average at 0 and the standard deviation at 1. You will notice that the difference between the two threshold
z-scores for women (number of standard deviations from the average) is
2.5758-2.2262=0.3496. The difference between the z-scores for the men was 0.7625. Since these differences apply to the same thresholds one can see that the male standard deviation must be smaller than that of the women because more standard deviations fit between the thresholds. The male standard deviation must be 0.3496/0.7625 = 0.4585 or 45.85% the size of the female standard deviation. Now if the female standard deviation was set at 1 then the male standard deviation is 0.4585.

Given that “last year” threshold for men was 1.825 standard deviations away from the average it must be 1.825*0.4585=0.8368 away from the average on the female standard and since this must correspond to the 2.5758 z-score for women on the same standard distribution the male average must be 2.5758-0.8368=1.739 standard deviations away from the female average.

So now we have the female distribution set at 0±1 the male distribution on the same scale is 1.739±0.4585. It should really be expressed as the reverse of this because we want price to go from low to high as we go from left to right so I’ll rephrase the above as

Female disposition to have sex for money 0±1
Male disposition to pay for sex -1.739±0.4585

To convert these to money values I needed two more anchors – two prices for sex that I can link to particular z-scores. From SuperFreakanomics I found that 1 in 3300 women in Chicago are streetwalkers charging $42 on average. This proportion of women corresponds to a z-score of -3.4289. That was one anchor.

Another anchor is afforded by the Governor Eliot Spitzer scandal. He paid as much as $5000 a time for a hooker. The same agency charges up to $6000 a time. I’m taking this as the top of the market because it was the top price of the most expensive agency. Assuming the girl in question has a dozen or so clients this implies that one in 255000 men are willing to pay this price. This is a z-score of 4.4706 on the male distribution, or 0.3108 on the female distribution.

Finally it’s quite usual for values to map linearly onto the log of prices rather than prices themselves so I mapped the z-scores onto $ prices via logs.

2 comments:

  1. must be determined by a large number of relatively independent factors e.g. interest in sex, attractiveness, need for money, availability of alternatives, price, moral qualms, fear of disease, opportunity, the illegality, forgone marriage opportunities, low workload, etc

    I have a few objections to usign the central limit theorem here.

    1). These are not relatively independent(e.g. Attractiveness and availability of alternatives).

    2). There isn't any particular reason to assume they are identically distributed. Unless I'm missing something.

    3). Why should these factors be additive instead of say multiplicative?

    Not that this means propensity isn't normally distributed but it needs more justification than that. Come to that (and this may be the source of my confusion) what units are you measuring propensity in?

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