Rhino poaching soaring

According to this article, rhino poaching in South Africa's famous national parks has reached such a level that the government has had to do something about it.

It reports that, because of the high demand for rhinoceros products in Asia, more than eighty rhinos have been killed by poachers, with thirty-three of them near the border with Mozambique. In fact, all the poachers so far arrested have been Mozambican citizens, which suggests that it is poverty that is the primary cause of people engaging in killing rhinos.

Privatisation of rhinos is the favourite suggestion of Robert P. Murphy as the solution, so that if rhinos have value, than private owners will want to make poaching costly enough in terms of access that owners of rhinos will gain enough money to ensure that only a tiny number are ever killed.

The trouble I have always thought is that it is possible that those who deal in rhino horn want rhinos to become extinct because the prestige rhino horn would carry could multiply. If it did, rhino horn could rise to orders of magnitude above its present price of $100 per gram, and it is easy to imagine the wealthy dealers currently existing bargaining on such increases in a legalised market.

Moreover, since the supply of rhino horn, owing to the animals' territorial behaviour and slow growth rate, is necessarily inelastic, prices rises would have to be large to reduce demand. Moreover, is there not a possibility that rhinos could be owned by the very people who make huge profits today from dealing in its horn?