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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.

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

"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.

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.

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.

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.

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.

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.

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

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.

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.

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.


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.

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


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


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