For centuries, elephants with large tusks have been targetted by hunters and poachers. The "unnatural selection" in favour of smaller-tusked elephants has resulted in a dramatic decrease in average tusk sizes right across Africa.
Smaller tusks increase an individual elephant's probability of survival, by making him or her a less attractive target for poachers. But what if all elephants' tusks decrease in size? Can evolution save the elephant?
The above figure shows that a reduction in average tusk size has two effects. First, it decreases the size of each individual elephant's tusks, making those tusks smaller and hence less valuable. On the other hand, it leads to a reduction in the overall quantity of ivory available, and thus an increase in the price of ivory. This tends to make tusks more valuable.
Which effect dominates depends upon the elasticity of demand for ivory. If the demand for ivory is inelastic, then a 10 percent reduction in the quantity of ivory available will cause the price of ivory to increase by more than 10 percent. On balance, smaller tusks would make ivory poaching more profitable, by making ivory more scarce and hence more valuable. This is the situation shown in the diagram above. Poaching generates revenue of A+C when tusks are large, revenue of B+C when tusks are small. If the demand for ivory is inelastic, area B will be greater than area A, and smaller tusks enhance the profitability of poaching.
If the demand is elastic, however, there is a limit to the amount people are willing to pay for ivory. When tusks shrink, the price of ivory does not increase enough to compensate for the smaller tusk sizes, and poaching becomes less profitable.
One econometric estimate of the demand for ivory based on 1980s and 1990s time series Japanese data concluded that "income is the major factor determining demand for ivory, and that the coefficient of price is non-significant." That's not good news for elephants - it would be better for them if price had a significant negative effect on quantity demanded. However this more recent analysis basically concluded that little is known about the elasticity of demand for ivory.
100 or 200 years ago a typical African elephant might have looked more like the gentleman on the left above. It's now not unheard of to see a family group with small or even no tusks.
Dramatic as the decline in tusk size is, as measured on evolutionary time span, realistically it probably has less of an impact on the price of ivory than factors such as income levels in ivory-consuming countries, the size of the elephant population, poaching and anti-poaching technology, and the legal status of the ivory trade. Still, it shows how the concept of own-price elasticity of demand can be useful in unexpected places.