One of the points taught in a great many introductory courses on microeconomics is that a tax-cut can be expected to have the same effect on schedules of supply and of demand, and thence on the resulting equilibrium, as would a subsidy. In this sense, economics shows that a tax-cut is equivalent to a subsidy. And, ignoring differences in administrative costs, the resources possessed by the state given a tax-cut are equivalent to those after dispensation of a subsidy. But it is only in these effects that microeconomics shows an equivalence; and, even if we confine ourselves to the considerations of non-normative microeconomic theory, we would be speaking or writing rather loosely if we simply said that a tax-cut were the same as subsidy.

In the sphere of normative discourse, whether a party's refraining from taking is equivalent to giving is determined by whether that person or group of people is entitled to take. A person who forgives a debt may be said to give;[1] but the person who does not steal that which is yours does not in this way donate to you. The invaders or other thugs who declared themselves to be lords did not give what they merely did not confiscate from the farmers whom they conquered.

To treat a tax-cut as morally equivalent to a subsidy, or to do as so many progressives and left-wing populists — to insist that a failure to increase some tax on some party to a prior or even new level simply is a subsidy — is to insist that the state is morally entitled to tax at the greater level, that the state owns those resources.

This moral claim is certainly not a principle of economics nor a consequence of bringing economic principles to bear on moral theory, and should not be allowed to pass as such nor by insinuation.

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[1] A creditor who forgives a debt has given her rights as surely as if she had assigned them to a third party.

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 my field of awareness, there has recently been more discussion than usual about deductibility of constituent-state taxes and of municipal taxes from income computed for purposed of Federal taxation. I think that most of the discussion has been fundamentally wrong-headed.

In the textbooks of middle-schools, of high-schools, and of introductory courses in college on civics, on politics, or on economics, there are discussions of various proposed guidelines for taxation, based on ostensible or insinuated theories of justice. One commonly offered theory is that people should be compelled to pay based upon supposed ability; another is that they should be compelled to pay based upon the amount of services that they receive from the state.[1] I've yet to see such a discussion in such a textbook that could withstanding much critical examination.

In any case, these homilies don't serve to explain how-and-why taxation is effected in the real world, except in-so-far as some of their prescriptions are invoked to argue for a tax of one sort, even as conflicting rationalizations are offered (often by the very same people) to argue for taxes of other sorts. Historically and to the present day, taxation has been fundamentally opportunistic. That which has been taxed is whatever seemed to be most readily taxable. Targets of convenience have been wealth or income that has been thought to be easily tracked and measured, difficult to relocate outside of the jurisdiction, or for the taxation of which there is wide-spread acquiescence if not support within the community. (It is with respect to that last aspect that textbook theories have their real relevance.)

The state is not satiated by some steady extraction of wealth from the community. When extractions are greater than were expected, the state will not return the surplus to the taxpayer as such, except under extraordinary pressure; and, here-to-fore, states have always moved towards attempting to extract as much tax from their communities as the communities will suffer. This tendency is natural, as the people who make-up the state generally see their positions within society improve as they have increasing command over resources; mechanisms that exist in sectors whose rewards are determined by markets which cause participants to identify and pursue efficiencies simply have no correspondents within the state; the state is able to cultivate dependencies in the wider population; and many people imagine a very extensive rôle for the state within society (especially those people who lose sight of the distinction between the state and its subjects). The state grows ever larger and becomes ever worse at the allocation of resources, and so seeks ever greater extractions.

When, within the jurisdiction of a constituent state or within a municipality, there is greater community resistance than elsewhere to taxation, there is less taxation than there otherwise might be. That difference is a target of opportunity for a federal state, whose jurisdiction encompasses a wider community. There is a mechanism for obtaining the acquiescence of that wider community without typically triggering a significantly intensified resistance on the part of the communities subjected to a federal surtax in the face of lower taxes by other entities. That mechanism involves allowing taxpayers to deduct what taxes they pay to those other entities from the calculated worth of something that the federal state taxes; because, in the face of those deductions, parts of the wider community become less resistant to rate increases.

Let's say that people in jurisdictions A, B, and C, which are all of roughly the same size, face a federal tax of 30% on income, and that people in jurisdictions A and B face a more local 10% tax on pre-tax income, while people in jurisdiction C face a no such tax. If the federal tax is increased to 1/3 on taxable income, but local income taxes are made fully deductible, then the people of jurisdictions A and B face no net increase in income tax, and so may acquiesce; the people in jurisdiction C may thus find themselves out-voted and their taxes increased by about 3%.

A great many people imagine what thus happens is that, given deductibility of more local taxes, people in jurisdictions with lower local taxes are force to subsidize those in jurisdictions with higher local taxes; but that conclusion is spurious. It would in some sense follow if the quantity or quality of goods and services delivered by the state were well correlated with the amount of resources that it extracts from the community, but there is no such correlation, except in transitory cases in which the state deliberately impairs performance to provoke acquiescence to greater extractions. The people paying lower taxes than they otherwise might are not getting something from those paying higher taxes than would be tolerated without the mechanism of deductibility. They are simply less victimized. One would be no less mistaken in claiming that people who live in other nations with lower income taxes are ipso facto subsidized by American taxpayers.

(For purposes of economic analysis of some sorts, tax-cuts and subsidies are equivalent, but those in the jurisdictions that are less taxed by the federal state have not received a tax cut, they have instead not been subjected to tax increases imposed elsewhere. And the aforementioned equivalence holds only if either there is no prior property in resources, or the state has a prior claim on whatever resources are involved. If no one has a claim prior to taxation and subsidization, then no one is paying taxes; they are being extracted from resources that are un-owned. If the state has a prior claim, then there are again no tax-payers; there are people who are granted more or less wealth or income belonging to the state. And, if there are no tax-payers, then the tax-payers subsidize no one.)

Eliminating the deductibility of other taxes would create greater resistance to federal taxes, as some who had previously not been subjected to higher levels then would be. But not everyone thus penalized would previously have been a supporter of imposing those levels on others. Innocent by-standers would be dragged into a fight; there could not be justice in that.

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[1] When I say state, I don't necessarily mean one of the constituent states of a federation such as the United States. I certainly don't mean the jurisdicational area of one of those states, nor the inhabitants of such an area. A state is an organization that successfully claims an effective monopoly of some sort in the control of violence.

The state of California has introduced a raft of new taxes associated with motor vehicles. These include an increase of the tax on gasoline (which increase alone is expected to cost the typical driver an additional $280 per year), a general increase in vehicle registration fees, and a new tax of $100 per annum on ULEVs. That last tax is advocated on a theory that, since they travel more miles per gallon of gasoline, ULEVs put more wear-and-tear on the roads with each gallon consumed. I very much doubt that, even on average, the difference comes to about $100; and of course drivers with ULEVs who do very little driving will be disproportionately taxed.

I drive a 2012 Honda CR-Z. It is a hybrid whose design alludes to that of the Honda Civic CR-X (aka CRX) much as the modern Volkswagen Beetle, Cooper S Mini, and Fiat 500 allude to models of the past. (Honda was well-advised not to name this successor CRY.)

The first- and second-generations of CR-X came in three basic varieties: the HF, which was designed for fuel economy; the DX, which offered a bit more performance; and the Si, which was a genuine sports car. (The CR-X originated in an effort to design a vehicle with superior fuel economy, but this naturally led to a streamlined body and limited seating, as with a sports car.) The CR-Z combines three analogous varieties into one, by having three operating modes: an Econ mode, a Normal mode, and a Sport mode. (There is also a special hill-climbing mode.)

I had no desire for the Normal or Sport mode. I'm never in the latter, and only in the former when a mechanic switches modes and I travel a few yards before realizing what has happened. (I've used the hill-climbing mode briefly just a very few times, to deal with especially steep inclines).

In the Econ mode, the CR-Z functions as a ULEV, but the model has not been classified as a ULEV, because there is no politically practical way of ensuring that CR-Z drivers are operating them in that mode. Here-to-fore, the implication for me has been that I cannot legally use car-pool lanes without having a passenger, whereäs those with recognized ULEVs can. But now, unless the state engages in hypocrisy (which is quite plausible), I will dodge that $100 tax.

I don't do a great deal of driving; I've had the car since the start of summer in 2012, but my odometer only recently passed 9000 miles (14484 km). And a significant part of what little driving I do is to visit my family in another state jurisdiction. Most of my recent driving has been primarily to ensure that the twelve-volt battery stays charged and that gaskets don't dry-out. My insurance company has repeatedly demanded to know why I drive so little. On the first few occasions, I explained that driving has become expensive; more recently I've just told them to shut-up and simply be happy that I drive far fewer miles than my policy covers.

[Every now-and-then, I'm provoked or otherwise prompted to explain the false economy of conscription. What prompts me to do so now is the ill health of James Earl Carter, since, after all, that alleged champion of human rights restarted registration for the military draft.]

There is a wide-spread belief that the burden of taxation is somehow reduced by conscripting service. Usually the service under consideration is military. The notion is that, with a conscripted force, one only has to pay an average soldier some amount M_C, whereas with a volunteer force, one has to pay an average soldier some greater amount M_V. So people think that there's a per-soldier savings of M_V - M_C This thinking is utterly wrong.

First of all, conscription involves its own peculiar costs of administration and of enforcement. Those are far more substantial than most people imagine, and even if we use an accountant's notion of cost, the difference between the annual cost of a volunteer army and that of a conscripted army would come to less than $30 per soldier.

But an accountant's notion of costs really misses the Big Picture here.

Imagine that the state got people into the service (army or whatever) by promising them M_V, but then, once they were enlisted, declared a surprise tax (peculiar to their pay) T = M_V - M_C That would be a tax exactly equal to the supposed savings. Defrauding them in this manner wouldn't have reduced the tax burden; rather, it would have enabled it.

If the state had used more overt force to get those same people to enlist — threatening them with imprisonment if they did not — the tax wouldn't be reduced; it would merely be disguised. Their financial loss would be just the same, M_V - M_C exactly that amount of tax that people mistakenly believe would be saved by using conscription. The supposed savings was no savings at all, just a tax that people failed to recognize as a tax.

However, in the real world, the draft doesn't end up getting the same people who would have been tricked by promising pay and then taxing some of it away. It draws from a larger population, some of whom might be making less money than they would in the service, but a great share of whom are making more even than M_V (the pay at which enough volunteers would be found). If someone is indifferent between her job in the private sector and the job that she has as a conscript, except for the pay, then the implicit tax that she pays is M_J - M_C where M_J was her private-sector pay. For example, if M_J was $60K and M_C is $15K, then she is paying an implicit tax of $45K.

Because of this sort of situation, even if we ignore the peculiar costs of administration and of enforcement that I mentioned earlier, the tax burden of conscription is greater than that of paying recruits enough for an all-volunteer service.

However, in the real world, people are not indifferent between jobs (except for pay). Some people are willing to take a pay cut to defend their country; and, obviously, those people might pay a lower implicit tax (if conscripted).[1] But other people wouldn't choose to go into certain lines of work — such as soldiering — for all the wealth in the world. The only thing that gets them into the conscript force is the fact that the certainty of being punished by their state is an even worse fate in their eyes. So let M_W be the wealth of the whole world; the tax paid by each of these conscripts is something greater than M_W - M_C In some cases, it can be summarized thus ∞ And that, folks, is the actual tax cost of conscription.

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Registration for military service was reïntroduced by James Earl Carter in an attempt to seem efficacious after the Soviet Union invaded Afghanistan. Early in his campaign, Ronald Wilson Reagan was saying that he would end that registration; but, as it became plain that he could win the election without maintaining that promise, he walked away from it. William Jefferson Clinton, who had dodged the draft as a young man, decided that young men during his Administration should none-the-less be required to register.

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[1] I say might because a revulsion towards the conscription itself could subvert that willingness.

Imagine that, under some law passed long ago, some group of persons was able to take $10 000 from you, without your consent. Further imagine that they spent this money on a statue of your beloved dog, Earl, and presented it to you.

The statue is actually rather nice. The artist truly managed to convey Earl's personality! Setting aside what it cost you, you'd like it a great deal. And, if you'd tried to have one made like it, it would perhaps have cost you $20 000, rather than $10 000. (They have many statues made, and get each at significant discount.)

None-the-less, you don't like it as much as you'd like $20 000; you don't like it as much as you'd like to have kept your $10 000. And no one else is willing to pay $10 000 for a statue of your dog.

Most of us would say that you're entitled to feel yourself worse-off, not-withstanding that, by some accounting, you've got a $20 000 return on a $10 000 cost.

Yet officials and other citizens who complain about Federal tax burdens (or about intervention in general from the Federal government) are often mocked as supposed hypocrites if they come from jurisdictions in which the Federal government spends more than it takes in revenue. The principle may be exactly the same. Even if the Federal government delivers money (rather than commodities) to the constituent state, if it requires that the money be spent in a particular way, then this is like compelling someone to buy a statue of Earl. And the constituent states were not themselves the taxpayers, so giving those states money without mandates still leaves people with reason to feel aggrieved, even when the money is more than that taken from taxpayer. (It is not as if each constituent state has just one taxpayer who is also its one voter, able then to direct how the money be spent.)

A financial bond or note is a promise to pay some fixed amount at some given date. Two things, beyond the promised amount of payment, determine the price of a such an instrument.

First, there is the associated danger of a default. A possibility of default turns the bond or note into a sort of lottery, in which the actual pay-off could be the full, promised value, or nothing, or anything in-between (at least, anything reaizable in terms of the minimum division of the payment), or even some new pledge, promising a later payment of some sort. Each of these outcomes has some associated plausibility, and the lottery is valued accordingly.

Second, there is also the fact that the instrument is a promise of future payment; since pay-off cannot itself be put to immediate use (as consumption or as investment), its price is discounted to reflect time-preference and the forgone productivity of assets used to buy it.

Just to get the gist of that clearly, imagine that the value of a lottery were simply that of the mathematical expectation of its pay-off. The price of a bond would then be discounted expected pay-off.

So far, the causality here is just flowing one way. Possible-pay-offs and their probabilities determine an expectation or something like that, and then time-preference and productivity determine the present value of that expectation or expectation-like value, and that's the price of the instrument. And if the pledge were issued by a private institution, that would generally be it.

On the other hand, when such instruments are issued by a state, politics can make things interesting.

The Greek state is going to default on repayment of its borrowing. Its citizens are simply not willing to accept the costs to them of full repayment. In fact, they're not willing to fully repay what remains after politically possible subsidies from other states. Those who have lent money to Greece will receive less than they were promised.

The price of bonds issued by the Greek state already reflects the expectation of default. This reduced price is going to be used against bond-holders, both against those who are paying it now, and against those who paid a higher price and have held onto their bonds even as value dropped (as they gambled that the Greek state would not default or at least not default as much as some expect). What will happen is that populists, anti-rentiers, and opportunists will argue as if all bond-holders had paid that steeply discounted price, and as if those who paid that price lose nothing if they only recover the nominal purchase price.

And what makes that interesting is that it means that causality should now be flowing cyclically, where present price pronouncèdly affects the relative plausibilities of possible pay-offs, even as these continue to affect present price.

I've not sat down to work-out a formal model. But, while I don't expect that the equilibrium price of a Greek bond would be zero, I don't know that one can rule that out. (On the other hand, while economic equilibria are useful in understanding and approximating, the world is never in equilibrium.)

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I do think that something might be said here about the ethics of sovereign debt.

It isn't heads of state or of government, or treasurers, or legislators as such who repay this debt. It isn't voters as such who pay-off this debt. It is tax-payers as such who pay-off sovereign debt (except where it is paid by selling assets such as territory and state enterprises). Sometimes the tax-payers weren't even born when the state went into debt. Moral claims against them for repayment are thin at best. I once read buying sovereign debt compared to buying shares in pirate ships (which one could at one time do openly in some places, and can still do quietly in some places), and I think that comparison quite apt.

On the other hand, it is plain that most of the Greeks protesting against austerity measures are signally unconcerned about the welfare of the Greek tax-payer; they just want any resources drawn from him or her to be directed to them.

In 1988, George Herbert Walker Bush ran for President, and expressed his central campaign promise

Read my lips: No New Taxes.

After he took office, a repeated, emphatic message from the main-stream media was that he was stupid for holding to this promise and resisting any increase in taxes. Ultimately, he folded, and supported a tax increase, at which point, the main-stream media turned on a dime, and one of its repeated, emphatic messages was that he had dishonorably broken his promise.

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.