Yester-day, I posted a problem to Facebook:

Assume that the market for CEOs of large corporations is very tight, with directors competing ferociously for candidates. How will the burden of a tax on compensation to CEOs be distributed between the CEOs and the stockholders? If a heavily progressive tax is placed on the incomes of CEOs, what will happen to the pre-tax income levels of these CEOs?

So far, for whatever reasons, no one has offered answers, though the answers should be obvious. What makes the exercise interesting is the inversion of the answer to the second question. A great many people who could correctly and quickly answer the question itself would almost surely miss the inversion if not asked the question.

In the entry in which I previously discussed tax incidence, I made the point that (setting aside transactions costs) the distributed burden of a per-unit tax is the same regardless of whether the tax is formally imposed upon the buyer or upon the seller or upon both. I didn't, though, explain who then actually bears the burden, because that was irrelevant to where I was going with the entry. But it has preyed upon my mind that I didn't explain that bit.

The answer is that the burden falls most heavily on whichever party is least flexible in response to the monetary price.

Imagine, for example, that buyers, driven by some internal compulsion, must always buy (or try to buy) the same quantity of something, regardless of its price. Price won't necessarily rise without limit, because of competition amongst sellers. If a per-unit tax is formally imposed upon buyers, well, they'd buy that same quantity and then pay the tax on top of what they'd been paying the sellers. Setting aside feelings of pity, or somesuch, the sellers would just shrug. If a per-unit tax is formally imposed upon sellers, then they can otherwise pass along the full cost to their buyers, and competition isn't going to help buyers because the sellers all face the same increase in their costs, so that their calculated optimal prices just increase by the amount of the tax.

On the other hand, if sellers somehow always had to sell the same amount while buyers were flexible, then the shoes would be on the other feet. If the tax is formally imposed upon sellers, then they'd just sell the same amount at the price where quantity demanded absorbed that amount. If the tax is formally imposed upon buyers, well, then buyers are at least going to slightly reduce their consumption unless the sellers cut their prices to fully-offset the tax, so the sellers do this if they must sell that same amount.

When the tax isn't actually per unit, the mathematics and the results can be somewhat messier, but the same underlying dynamics will decide the distribution of the burden.

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In that earlier entry, I said The next time that you hear or read of a politician arguing for employer-provided benefits, such as for health-care, consider the incidence. My primary point at that time was that there may be little or no difference in ultimate burden between a tax formally imposed upon employers and one formally imposed upon employees. But let's pursue the question.

Supposèd advocates of the interests of employees often call for requiring various sorts of employee benefits. At the same time, these alleged advocates tend to model the labor market as if workers have very little choice in their terms of employment. But if, indeed, workers don't have much flexibility, then it will be they who bear most of the cost of the mandated benefits — implicitly they are forced to buy the benefits, rather than spend their wages or salaries on other things.

The accuracy of that characterization of inflexibility will vary across regions, times, and employee-types. All else being equal, it will be less true in times when employers are competing heavily for workers, and more true in times when employees are struggling to find or to keep jobs. Thus, for example, in a recession, employees tend to bear more of the cost of benefits supposedly funded by employers.

In economics, when we write or speak of the incidence of a cost or of a benefit, we refer to the ultimate distribution.

Most people get the idea that, often, costs or benefits can be passed along, so that the party upon whom they formally fall isn't necessarily the final recipient. This is certainly true of taxes.

There's a standard result of microëconomics that, if one sets aside the effects of transactions cost (dat ol' debbil), then the incidence of a per-unit tax is same, regardless of whether it is formally placed on the seller or formally placed upon the buyer. Almost every first-term microëconomics course demostrates this result, although they usually dumb-it-down by failing to note that transactions costs can somewhat undermine the equivalence.

The argument goes as follows: Imagine that the quantity offered for sale fits some function S(P_s) where P_s is the price received by the seller, and that quantity that buyers seek fits some function D(P_b) where P_b is the price that buyers must pay. If the pre-tax price is just P, and sellers have to pay additional tax and tax-related costs of t_s, and buyers have to pay tax and tax-related costs of t_b, then

P_s = P - t_s

(tax-related cost subtracted because it is a reduction in the price that what the seller receives) and

P_b = P + t_b

(tax-related cost added because it is an increase in how much the buyer must pay). Algebraïcally,

P_b = P_s + t_s + t_b

and

P_s = P_b - t_b - t_s

And the market would equilibrate where

S(P_s) = D(P_b)

(At a lower P, D would be greater than S, and it would be in the interest of sellers to increase their prices or of buyers to offer a little more per unit; and, a higher P, S would be greater than D, and it would be in the interest of sellers to cut their prices a bit, or for potential buyers to cut the amount that they offered.) Which is to say that the equilibrium is

S(P_s) = D(P_s + t_s + t_b)

as if the buyer formally paid all the tax on the seller's received price, and

S(P_b - t_b - t_s) = D(P_b)

as if the seller formally paid all the tax on the buyer's paid price.

(The next time that you hear or read of a politician arguing for employer-provided benefits, such as for health-care, consider the incidence.)

Now, let's consider the incidence of a tax on carbon emissions (ignoring the question of whether there should be such a tax), in the absense of transactions costs, the incidence would be the same whether the state formally taxed the producer of the emissions, or taxed the consumer of each product associated with the emissions, based upon the amount of the emission associated with that product. But it is plainly less costly to place the formal tax on the producer than to have separate filings for each consumer.

Which brings me to this story:

Whatever measures are imposed to curtail carbon emissions, they can be conceptualized as a tax. And it's really, folks, not that the Chinese officials don't understand that the incidence would be the same (or very nearly the same) in the absence of transactions costs, nor that they don't recognize that the transactions costs would be lower if the tax were formally imposed upon producers. Rather, it's that the Chinese state

• knows that some consuming nations would avoid or evade the tax, lowering the incidence upon China,
• would be able to disguise some of its emissions for domestically consumed production as emissions for exported product, and
• would like to misdirect blame for any failure to reach agreement.