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.
Or, to put it in a nutshell, as over at Cosmic Variance:
[(δU/δL) / (δU/δC) | Sp=0] ≤ w - [(δU/δr) / (δU/δC) | S = 0]
This calculation describes when a prostitute finds it worthwhile to sell (typically) her services, where:
* 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.
When discussing prostitution in the ancient world, I think we can leave 'R' out of the equation. Most of the women attested in the sources were slaves [who had no 'L'], ex-slaves (freedom for the slave prostitute did not necessarily mean freedom from prostitution -- a cold fact that makes the connection between slavery and sold sex even closer) or lived in social conditions that were close to slavery [very little 'C']: we know that poor women and children were promised clothing and shoes in return for prostituting themselves.
Prostitution in Roman times was, on any estimate, widespread: a Roman male would encounter prostitutes in bars, inns, outside circuses and amphitheatres, and at festivals and fairs, almost anywhere in the city. For the customer, sex was readily available and inexpensive -- a win-win situation both for the client and the brothel-owner. Slave traders, too, had a flourishing business. Clement of Alexandria tells us that slave wholesalers transported prostitutes as if they were grain or wine, while retailers acquired them as if they were bread or sauce. Such brisk, prosperous trade attracted upper-class investors who, through judicious use of middle-men, largely escaped the social opprobrium associated with it. The jurist Ulpian (I'll talk more about him when we finally return to Julia Mamaea!) coolly declared that "rents which are derived from the lease of urban properties will be included in an estate even though they are derived from prostitution: for brothels are operated even on the properties of many honourable men."
The state, too, could not resist the profits to be made from the sale of sex. Beginning with the Emperor Caligula in 40 AD, a tax was collected at a maximum rate of 1 denarius per prostitute per day -- or so much as she earned with one man [or 'W' -- which ranged from the unfortunately-named fraction of a denarius, the as, earning an estimated 2 - 16 asses per man (16 asses = 1 denarius)]. The best guess for 'S' is that the ladies brought in 2.5 - 3 denarii per day for high-priced and 2 - 2.5 for lower-priced prostitutes (admittedly, two or three times higher than the wages of unskilled male labourers, but, then again, the men could keep their wages). The prostitute tax was a handy source of revenue and was not rescinded until well into Christian times.
The Palmyran connection
In the year 137 AD, the Senate in the city of Palmyra published the tariff and regulations fixing the taxes levied on goods brought into and exported from the city and services provided within it. The 'laws' were inscribed on those huge stones illustrated above in both Palmyrene and Greek
Since in the past most of the dues were not included in the tax law but were only exacted by custom -- because it had been written into the contract that the person collecting the tax should do so according to the law and the custom -- and since it frequently happened in this matter that quarrels arose between the merchants and the tax collectors, it has been decreed that... the dues should be written down, along with the original law, on the stone stele which is opposite the temple called Rabaseire [a god of the underworld; location unknown].
Since you absolutely want to know: the tax on prostitutes thus displayed was 6, 8, or 16 asses per day, the price, presumably here too, of one client encounter. This suggests that the cheaper street walkers caught in the Roman tax trap (the 2 asses types) were either untaxed or non-existent in Palmyra. The law tariff also informs us that a tax of 22 denarii was charged for an imported slave, which makes it quite clear that the import of slave-prostitutes would have been a one-way bet and big money-spinner for the city.
But what the devil is 'U'?
[My remarks on the economics of Roman prostitution are owed to Thomas McGinn's fascinating and learned study, The Economy of Prostitution in the Roman World: A Study of Social History and the Brothel]
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