Can evolution save the elephant?

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?

Assume the value of a pound of ivory is independent of tusk size, so ten ten-pound tusks are equivalent to one 100-pound tusk. Assume also that the elephant population is constant, as is the per-elephant cost of poaching elephants and smuggling ivory. Under these assumptions, what is the impact of a reduction in average elephant tusk size?

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.

 

A "big tusker"

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.

Comments

[Ben J]

Frances,

This is a really great example of price elasticity of demand, and how important it is when discussing the effects of a change in price. It's much clearer than what I've seen in the past.

On a related noted, the current microeconomics theory course for second year undergraduates at my university uses a petrol subsidy example. In my home state in Australia, a petrol subsidy of 8 cents per litre was applied to petrol to ease the ever terrifying 'cost of living' pressures. Of course, the full amount was not passed onto consumers. This predictably triggered outrage and - I don't joke - a special commission to investigate why the full amount hadn't been passed on.

Next time I'm trying to explain why, I'll just send people to this post.

[Frances Woolley]

Ben - thanks so much for that comment, appreciate it.

[James]

"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."

Are you using revenue generating and profitability interchangeably? Clearly in the case with the smaller tusks, costs are also higher. While you can make a statement about revenue, it seems profit is ambiguous without knowing the average total cost.

Also, you *can* unambiguously say that producers would prefer the scenario with the larger tusks, producer surplus is larger.

Your argument does not appear cogent to me. The elasticity of demand affects revenue in the face of change quantity, but we are talking about a change in quantity *with a simultaneous increase in costs*, which seems to me, leaves profitability ambiguous.

[Frances Woolley]

James "Clearly in the case with the smaller tusks, costs are also higher"

That's right. The argument assumes costs are constant on a per elephant basis, that is, the only cost of ivory is the cost of killing an elephant. Hence if tusks shrink by 50%, the cost of supplying a pound of ivory will exactly double.

When demand is inelastic, a 50% decrease in the quantity available will *more than* double the price of ivory. Hence profits will unambiguously increase.

When other costs are introduced into the analysis, the results will not be quite so clean, but it will still be the case that with a sufficiently inelastic demand for ivory, smaller tusks could make poaching more profitable.

"Also, you *can* unambiguously say that producers would prefer the scenario with the larger tusks, producer surplus is larger."

Well spotted. That's because I haven't drawn the curves quite right - I should have shown the supply curve rotating upwards, rather than shifting upwards. Good point. I'll fix that.

[Alex Godofsky]

Really, the elephants don't care that poaching is more profitable. If demand is perfectly inelastic then the competition to reduce tusk size actually causes their extinction. Example: you have 100 elephants each with 100-pound tusks, and demand/quantity demanded is 1000 pounds of ivory. Demand could be satisfied by killing 10% of the elephants. The elephants evolve to have 10-pound tusks (but there are still 100 of them); now demand can only be satisfied by killing 100% of the elephants.

[reason]

Why don't poachers (or gamekeepers) just anaethetise the elephants and saw off the tusks. Maybe then evolution will select for regrowing tusks and everybody will win.

[Frances Woolley]

reason "Why don't poachers (or gamekeepers) just anaethetise the elephants and saw off the tusks"

The problem is that tusks are living teeth. Imagine waking up in the morning and finding that someone had sawn off your incisors, and all you had left were the stumps. It makes my fingers hurt just typing it.

[Frances Woolley]

Alex "If demand is perfectly inelastic then the competition to reduce tusk size actually causes their extinction. "

Yup. The only hope is that demand for poached African elephant ivory isn't perfect inelastic, or that one of the other assumptions of the model e.g. constant per elephant costs of poaching and anti-poaching will give way. There is an alternative source of ivory: tusks from domesticated Asian elephants. It tends not to be used to the same extent because the ivory is of lower quality, in part because the tusks are smaller, and I think they might also be less dense (though I'm not sure of that), and also because Asian elephants have non-tusk value in their domestic work. But if African elephant tusks became small enough, Asian tusks might start to become more attractive.

See this current TED conversation http://www.ted.com/conversations/16713/how_do_we_save_african_elephan.html for a discussion of some of the issues.

[jb]

On a brighter note:

In thailand a british man dragged a piano up a mountain to play beethoven to blind elephants. Elephants loved it, they were all ears. And the reason he played to blind elephants, if you're gonna play to elephants you're gonna play to blind elephants ; cause you don't want them to recognize their mothers teeths on the piano keys

[James]

Not yet convinced.
"The argument assumes costs are constant on a per elephant basis, that is, the only cost of ivory is the cost of killing an elephant."
While assuming costs are constant, your analysis is correct - **the graph does not support constant costs**. The supply curves are marginal cost curves, the shift shows that at each quantity level marginal cost has gone *up*. We *know* that at each level the costs are higher, we also know that the average total costs must be higher - it's just not clear by how much. Hence, ambiguous effect on profit since the change in costs are unknown.

[Frances Woolley]

James, "costs are constant on a per elephant basis"

By which I mean that the only costs are the costs of killing an elephant and removing its tusks, and these are independent of the size of the tusks. Some elephants are protected by lions and wardens with infrared lights and serious firepower, some elephants live on islands in rivers infested with crocodiles and hippos, and some elephants are easier to get at. Hence some elephants cost less or more to kill than others - that's what generates the upwards sloping marginal cost curve.

Think about it. If you have 1000 tusks, average weight 100 pounds, average cost per tusk $500 (average cost per elephant $1000). You have 1000 tusks, average weight 50 pounds, average cost per tusk $500 (average cost per elephant $1000). How do the costs in those two situations compare? How do the revenues in those two situations compare? What happens to profits when tusk sizes decrease? The answer isn't in the least bit ambiguous (in fact, it would make quite a good, though slightly tough, exam question).

Fixed costs have no impact on the analysis. If average cost per tusk or average cost per elephant changes, yes, then the analysis changes - that's why I assumed away that situation.

[Min]

I doubt if evolution can save the elephant, any more than it saved the saber toothed tiger and giant sloth. As large mammals, elephants live too long and have too few children. The pace of evolution is too slow.

[Giovanni]

Frances,

I think another useful way to approach this issue is through the derived demand for poaching activity, measured as the number of elephants killed in a given period. Let n = the number of elephants killed, z = the number of kills needed to get a ton of ivory, c = cost per kill, p = the price per ton of ivory. Suppose the global demand for ivory is given by D(p,a), where a = some exogenous factor that affects ivory demand. The market-clearing condition for ivory is: n/z = D(p,a). The zero-profit condition for poaching is: p = cz. Together these conditions give the derived demand for poaching: n = zD(cz,a).

This equation describes a curve in (c,n)-space whose position depends on z and a. A little calculus shows an increase in z shifts this curve to the right if and only if e > -1, where e = the price elasticity of ivory demand. That is, if ivory demand is price-inelastic declining tusk size will cause more elephants to be killed at any given level of per-kill cost, as your analysis concludes.

The derived demand equation implies growth in poaching will follow: (1/n) dn/dt = (1 + e) (1/z) dz/dt + e (1/c) dc/dt + v (1/a) da/dt, where v = elasticity of ivory demand with respect to a. This relationship gives some cause for hope, for exactly the reason you’ve suggested. If the per-kill cost of poaching rises in coming years, and assuming ivory demand is reasonably price-elastic, then n may stabilize at a value low enough to prevent extinction even if z continues to rise.

But suppose ivory demand is perfectly price-inelastic. Poaching will now grow according to: (1/n) dn/dt = (1/z) dz/dt + v (1/a) da/dt. Note that c does not appear in this relationship. In this case derived demand becomes: n = zD(a), a vertical line the position of which entirely determines the amount of poaching. Now even dramatic increases in per-kill cost will not save the elephant. Only successive declines in world ivory demand can do this, and these will have to be sufficiently large to offset the effect of declining tusk size in encouraging poachers to kill ever more elephants.

[Frances Woolley]

Giovanni - that's so elegant, lovely! Thank you.

[James]

Frances,

Your original statement, and argument, are correct. ("The argument assumes costs are constant on a per elephant basis")

:)