Philosophers on the efficiency of Taxes and Welfare

This is the fifth article on the theories defended by Murphy and Nagel in the book The Myth of Ownership


Progressive taxes as a matter of efficiency

Murphy and Nagel believe that their ill defined notion of reserve price can be used for another purpose: to prove that if we do not want to disappoint the rich, we have to tax them more. That involves not merely a matter of fairness to the poor –they insist– but of efficiency in regard to rich people’s interests. The argument is this: rich people would pay large amounts of money to have, say, a reliable defense against attacks from other countries. However, it might well happen that poor people cannot afford to pay as much. Therefore, if people were taxed equally, there would be less defense than that for which the rich are willing to pay.

This argument for progressive taxes does not imply a comparison between different scales of utility, though there is always a temptation to engage in it –maybe implicitly– to “reinforce” the point. Certainly, it is one thing to say that the government is right in taking a dollar from a rich man who would like it to be spent on defense rather than on any other thing, and quite another to say that the government is right in taking the dollar from a rich man because a poor one would use that dollar for a good higher on his scale. In the first case we compare values for the same individual; in the second we conflate two scales of values.

As said, if we try to justify progressive taxes using the first comparison, we must avoid sliding inadvertently into the second (always, unless we want to deceive ourselves). Nothing in the first comparison implies that defense is more valuable to the rich. History provides many examples of poor people that have given everything they had to defend their small farms; we know that poor fishermen have died defending their huts; we know that poor people –as anyone else– do not like to see soldiers taking away their goods and abusing their daughters.

That first comparison alone (i.e. among the priorities of the same individual) might allow Murphy and Nagel to deduce that progressive taxes are more efficient from a rich taxpayer’s point of view. However, we must bear in mind the conditions that would make it true –and realize that without them, the conclusion is false.

As the conditions are not taken into account by Murphy and Nagel, we would do well in having a look at them: if there are some services that are in a bad situation according to the views of rich taxpayers, and if higher taxes were to be used to improve the services that the rich want to see improved (as distinct from redistribution, etc.), and if the poor were uninterested in it (or interested but unable to pay more), then it would be a matter of efficiency, from rich taxpayers’ point of view, to make them pay more. However, even then, this would not prove that the tax has to be more than slightly higher for the rich, or strictly proportional, or progressive. It would only discard (under those conditions) a tax that would take the same amount of money from each individual, regardless of income.

The whole argument about the efficiency of higher taxes reminds me of a humorous Brazilian saying: “you have proved your point, but it is only a small point, and then only a meaningless point”. Efficiency could be an issue if we suspected that rich people want to be taxed more heavily. If there are rich people who think that taxes are too low and would like to pay more, they have been very quiet.

We may add more meaning to the argument if we make a shift and start comparing the choices of different people. Of course, it would require dropping the claim that we are talking of efficiency from the point of view of rich taxpayers. Murphy and Nagel slide occasionally into this second strategy, but the change in the meaning of “efficiency” is not always clearly indicated to the reader. This second strategy is in fact the same that gave something resembling a justification to the notion of a surplus value: we would compare different people’s preferences. Of course, when we say “we would compare…” we must understand that the government will do it for us.

Murphy and Nagel write “The more money you have, the less a marginal dollar is worth to you”.[1] That seems to imply –and must imply if the assertion is meant to justify their theses–  that an extra dollar is less useful to a rich man than to a poor man. But all we can sensibly say is that both the rich and the poor man would use an extra dollar for the item that is one step lower than the last item that is already covered in their list of priorities. The poor man’s list may be shorter and that would mean that his last item is closer to the top.

Now, if being higher in anyone’s list were an objective reason for the claim that it is more efficient to use an extra dollar for that purpose, then we could say that higher taxes for the rich are a matter of efficiency.[2] In that case, we would have demonstrated that there is a fundamental dilemma between efficiency and respect for ownership. Perfect efficiency would be reached when all earn the same. And if authorities cannot achieve that ideal, then they might try to approach it by using taxes, cash transfers, subsidies, etc. But the argument is wrong: it would prove that another glass of beer provides a more efficient opportunity for spending than another street map for an expensive mobile phone. Why? Because the extra glass is the last unattended priority in some poor man’s scale.

So this is the second strategy to prove that higher taxes for the rich are more efficient –interpersonal comparison of utility–, and it fails. The poor man would have to drink a lot of beer before he starts calling an extra glass “mere efficiency”.

Minimum wages and welfare payments as a matter of efficiency

After dealing with progressive taxes and concluding that they are efficient from the rich taxpayer’s point of view, Murphy and Nagel try to convince us that a government that imposes minimum wages and social welfare is not really redistributing wealth but only being efficient, even from the rich taxpayer’s point of view. They write: “Such programs are usually regarded as redistributive, but the alternative to a decent social minimum is a society with real poverty, which often results in higher rates of crime, drug addiction, and single motherhood, all of which impose their own costs not only on the poor but on everyone. To be grim about it, the cost of subsidizing wages for unskilled labor to make them sufficient to support a family might well be balanced by savings in the costs of prisons and law enforcement that such a change would produce, not to mention the value for everyone of the change in social environment”.[3]

The alternative between government provided welfare and poverty is misleading: most countries on Earth have both. They have minimum wages and rising crime; welfare payments and single motherhood; redistribution and drug addiction. They have had them for half a century –at the very least. It is already very difficult to claim that this system is in the interest of poor people; it is impossible to claim that it is efficient from a rich taxpayer's point of view.
In a very well known book about welfare Losing ground, Charles Murray has shown that the assumption that welfare expenditure improves the condition of the poor is not necessarily true. Moreover, examining long series of statistics he has argued that the assumption is often wrong, and that welfare often worsens poverty.
Murphy and Nagel deal with these objections as they do with all others that might contradict their theses. They avoid all reference to them.

But even if we disregard the experience we have about the inefficacy of redistribution to prevent crime, single motherhood, and drug abuse, and if we decide that the expectations governments had in the sixties and seventies were right but failed for some unknown reason, we could not deny that we are redistributing wealth, i.e. benefiting some people at the expense of others. Nevertheless, that is exactly what Murphy and Nagel deny: “The reduction of social and economic inequality is in this way seen as a public good, paid for according to its monetary value to different individual taxpayers. This case differs from that of national defense, for example, in that it makes no sense to tax the poor for some of the costs of raising their spendable income. But it is still driven by efficiency, not fairness –a direct appeal to the interests of each, with no sacrifice being imposed on anyone. There are obvious political advantages in portraying social welfare policies in this way, but that doesn’t mean there is nothing in it”.[4]

Actually, there is nothing in it, apart from the political and rhetorical advantages. If redistribution is good, if it prevents social problems, it is still redistribution. If the government taxes some people to give money to other people, we have already a loss for those who pay, and an advantage to those who receive. Therefore, even if we assume with Murphy and Nagel that redistribution has the effect of reducing crime, etc. a reduction that equally benefits both sides on the redistribution scheme, then we still have the original loss and advantage involved in it.

There would be a balance if we assumed that only –or mostly– the rich get advantages from the prevention of crime, single motherhood, and drug abuse. Of course, that is not true; more than that, it is rather the opposite. Poor people are the first victims of crime,[5] a thing that many law scholars tend to forget when they treat crime as if it were a war of the poor against the rich. Stories do not replace statistics, but they may show things statistics cannot tell. I remember the case of a poor woman living in a shanty town in Argentina. She complained in this way: I have saved money to buy a TV set. Only, I cannot get it into my house. No bus enters the shantytown where I live. I could afford a taxi this once, but no driver would run the risk, he would leave me outside the shantytown. I am a strong woman, I could carry the TV set myself for some blocks. But I know I wouldn’t reach my house with it in my hands.

The limitations imposed by crime, the daily fear, the petty harassments, the exactions, all of that beats poor people everyday. They might not actually benefit from redistribution, but they surely benefit from the prevention of crime.

Murphy and Nagel must have a surmise that efficiency is not a good argument for redistribution. Just in case rich people do no like their arguments, they have others: “if, for whatever reason, the well off are not unhappy to live in a society full of poor people (it solves the servant problem) then we have to consider the question of distribution independently”.[6] As always, when they say “we have to consider…” they do not refer to unconvinced rich taxpayers, but the government.

If efficiency fails as an argument, our philosophers would base redistribution on some moral standards and public duties that we (that is, the government) think can be reasonably imposed on people. There we have more choices than with efficiency, so we might think that “appropriate foreign aid”[7] for poor countries is one of the duties we can impose on people. We the government, of course.

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[1] P. 82.

[2] Even then, we are leaving aside the question: who earned it? But the argument does not hold water even if we evade that essential question.

[3] P. 87.

[4] Same page.

[5] The robbery rate for persons in households with annual incomes of less than $7,500 is 7 times higher than for those with incomes of more than that amount. US Bureau of Justice Statistics http://bjs.ojp.usdoj.gov/index.cfm?ty=tp&tid=92..

[6] P. 88.

[7] P. 94.

Murphy, Nagel, and Marx on surplus value

This is the fourth article on the theories defended by Murphy and Nagel in their book, The Myth of Ownership


A new theory of the “surplus value”

So far, we have examined three arguments presented to sustain the claim that ownership is a myth: 1) that (most) governments create conditions that make industry and commerce possible –or at least safer; 2) that it is the market that generates differences in wealth; and 3) Ronald Dworkin’s attempt to portray the creation of wealth as accidental possession or accidental delay. The first one results in a non-sequitur; the second is –at best–  an inaccurate way of speaking. The third one…it is difficult to say anything about the third one.

Murphy and Nagel present another way to justify the main thesis of their book. They use for this purpose the notion of a “surplus value”[1], which sounds similar to Marx’s theory, but is quite different. However, there is a link between the two: both are part of efforts to prove that, in some odd way, the rich do not pay fully for what they get. According to Marx, they get work without paying the full value they get from it. According to Murphy and Nagel, the rich buy goods without paying the full value they get from them. Both theories share another characteristic: they are wrong.

The theory of surplus value was the cornerstone of Marx’s description of the relation between capitalists and workers. It provided also the motive for Marx’s prediction of capitalism’s doom. Marx believed that value is only determined by work, not by capital; therefore, what capitalists gain is actually taken from the workers, who receive enough to survive and reproduce, leaving the rest, the “surplus value”, to the capitalist. There, said Marx, lies the inner weakness of capitalism: competition leads capitalists to use more and more capital (machines and such) and less labor. But then their profit will diminish, because labor –and not capital– is the source from which they take their surplus. More machines and fewer workers mean a smaller surplus value for the capitalist. Certainly, Marx himself was aware that his theses were against the facts everyone knows to be true, and spent most of his life trying to fill this enormous hole below the waterline of his theory. Anyway, the whole explanation was proved wrong by Eugene Böhm-Bawerk, already in 1886.[2]

Murphy and Nagel do not attempt to revive Marx's “surplus value” theory, but they come up with something that would also (if true) show that the rich do not really pay (in some way) for what they get. They call this pernicious characteristic of capitalism, a “surplus” collected by the rich, and they conclude that it is only fair that the government pares it off. They explain that the market “automatically creates a large surplus –the difference between actual price and reserve price– for people who have lots of money. Poor people benefit from this surplus only with very cheap private goods like salt an digital watches. To them, most things do not feel cheap or costless, because most purchases are close to their reserve price”.[3]

In this explanation, our philosophers compare two prices: the actual market price people pay for a good –say a computer– which is the same for rich and for poor; the other is the highest price each individual buyer would be disposed to pay for that good: this is the reserve price. Of course, that highest price is different for each person. It varies according to his means, his views about the utility he expects from the good, his opinion about future prices, etc. There is also a minimum price for each seller, below which he will not sell: that is the reserve price of the seller, and it also varies according from person to person. And, for the same person, it may change several times following his changing views and needs.

Murphy and Nagel’s assumption that the reserve price is always higher for those with higher income is absolutely unwarranted. In auctions, the highest bidder is not always the richest person in the room. People who are always disposed to pay the highest price are not likely to remain rich –or become rich. Of course, if we leave the realm of real life and build instead imaginary situations (a favorite method in modern philosophy known in older times as “Jesuitism”), we may puzzle the reader for a while, and even convince him that what he knows to be false might be true –at least true in untrue situations. Let's tailor a very odd situation (maybe even impossible) to prove our thesis on it, and pretend that we may extend our conclusions to the real world.

Say we are in a lifeboat, and there is a shortage of water. Never mind that in such a case there would be rationing. We can always imagine things if it helps to prove our theses, and we can postulate that there is no rationing. Water is sold to the highest bidder. In such situation, a billionaire would be willing to pay billions for a single glass of water. Nevertheless, in every modern city we may see that the same rich man pays only cents for the same glass. Is that fair? If we take the price he would have been disposed to pay in an extreme situation as his reserve price, we might say that his gain is enormous. Now let’s compare that with the situation of a poor man in a lifeboat. At most he could offer some hundreds of dollars for the glass of water, but not millions. Therefore his reserve price is lower, and his gain is lower when he buys water for a few cents.

See, rich people get a surplus all the time. The richest of them get billions of surplus every single minute of their lives. Governments can dig in that immense heap of utility and give part of it to those whose surplus is smaller.

As common sense would lead us to suspect, there is a fundamental mistake in the above reasoning. If there is one fallacy in economics that is worse than all the others, it is that in which the utility of goods is assigned in the abstract to a genera ("water", "gold", "corn") and not to a concrete piece of it, for a concrete individual, in concrete circumstances. If we think in terms of the value of nourishment as compared to that of ornament, then we would conclude that people should pay more for bread and water than for gold and for the most beautiful pieces of art. But that is only true if we are starving, and it would be unsound to exchange a Rembrandt for a bar of chocolate –except in very unusual circumstances. 

For sure, practical men rarely disregard the circumstances in which they make their choices; nevertheless, theoreticians have been often deluded by paying attention only to the abstract utility of a good, the utility of the whole genera. Böhm-Bawerk called it a wrong turn in economic theory.[4] It misled economists for a long time, but it has been corrected more than a century ago. Today we know that it is nonsensical to ask whether iron is more useful than gold and water more useful than iron, all taken as genera. Of course we can live –though miserably– without iron tools but not without water. It does not prove that I do right in paying more for a glass of water than for any tool made of iron. And, unless we live in starving conditions, or labor without tools, I may do right in buying a gold ring for the woman I love. These are basic notions that should be explained and learned in the first lesson of economics.

Now we can return to Murphy and Nagel and their claim that, for the same price and article, rich people collect a larger surplus than the poor. To prove that, they must assume that the price a man would pay in an extreme situation is his reserve price in any other situation, which is wrong. If instead what they claim is that in normal circumstances the more money a man has the higher would be the price he is willing to pay for the same good, that is plainly false. On the other hand, if their claim is that a rich man would pay millions for the last glass of water on a lifeboat, then the only thing that they are saying is that a rich man is able to spend more money than others in those goods he considers more important in each circumstance. But they are not saying (let alone proving) that all rich men –in all circumstances– consider a glass of water of immense value. That is true only on the lifeboat. It is hardly a proof that the rich man gets a larger utility –more for the same money– than the poor one when both buy a glass of water in a restaurant.

Murphy and Nagel write that “With a public good [from roads and defense to subsidies to the arts] individuals can’t obtain different amounts of it and there is no need to charge everyone the same, so there is no automatic radically unequal allocation of surplus. The question for the state then becomes what single amount of the good to provide to everybody, and to what separate price for each?” They think that governments acting in this way can be compared to monopolies: “The government must operate more like a price-discriminating monopoly. It needs to figure out how much the public good is worth to each individual and charge each of them accordingly”[5] (I have added the bold italics for reasons that will be clear in the next paragraph).

All this is wrong: merely a page before these words, the authors had acknowledged that public goods (say defense against foreign attacks) are worth the same for the rich and for the poor. They admit that “The main reason for this difference in value is not that some people care more about the dangers of military invasion than others, but that some people have more money than others, so that a dollar more taken from them to be spent on defense, does not mean a dollar less for basic necessities, but only for something less important”.[6] If we think about the consequences of this caveat, we must realize that what the authors call “reserve price” does not show or say that a good is always more valuable to the rich buyer; it only says that he can afford it. Unfortunately, Murphy and Nagel create the impression that the good is worth more for those who could afford it. The authors themselves seem to be convinced of that in one page –but also of the opposite in another page. Public goods are worth more for the rich and they are not worth more for the rich.

As in the automatic “generation” of differences among individuals by the market, in the theory of the surplus we find again what we may call the fallacy of the “forgotten caveat”. Of course, caveats are legitimate defensive weapons in theoretical warfare, but only if what is acknowledged in them has a real role in the theory. If not, they are better called “contradictions”.

Shifting between cardinal and ordinal numbers

The notion of a “reserve price” is very apt to lead to confusion, and that can be seen in Murphy and Nagel’s use of it. Of course, a reserve price is not a price. It is not paid or offered by anyone. It is just a way of saying that we –or a bureaucrat– think that someone would have been disposed to pay a higher price –either in real life or in a lifeboat. It is a loose way of referring to someone’s valuation of a good, his expectations of future prices, and a host of other things, but not to a price. Unfortunately, the notion makes the shift between cardinal numbers and ordinal numbers seem natural and unobjectionable.

Here it may be useful to make a short comment about the difference between ordinal and cardinal numbers as they are used in economics. Individuals may put their priorities in a list and assign numbers to them, but these are ordinal numbers. They express priorities: this first, that second, etc. It makes no sense to add, multiply, or do any arithmetic with them, other than saying: first of all I must have the roof repaired, and then buy a new pair of shoes, etc. If a new pair of shoes is in the second place in my list of priorities, then two new pairs do not equal the utility I expect from the roof that is first in my list. Furthermore, ordinal numbers have meaning only within the choices of an individual: I cannot say that the item that is topmost in my buying list is for that reason more important than the item that is second in yours –more important to whom?

Prices are cardinal numbers. It makes sense to add prices, to multiply them, etc. And I can compare prices offered and paid by different people. When I say that this computer’s price is twice as much as that other one, I am using cardinal numbers. I know that ten hammers will cost me ten times the price of a single hammer. But when I say that a computer is of more value to me than to you I am engaging in comparisons between choices of different people. I am using (or rather misusing) ordinal numbers.

Apart from wrongly assuming that a reserve price must be “automatically” higher for rich people, Murphy and Nagel misuse the notion of the “reserve price” to implicitly engage in comparisons between scales of utility for different people, which is wrong and radically different from comparing real prices. As we have seen, they suggest that governments have to establish how much a good is worth for different people –i.e. according to the “reserve prices” they would pay, as established or guessed by some government’s bureaucrat. However, it is one thing to compare the price of computers offered in two stores, and quite another to compare the utility that a computer has in your scale of priorities as against the priority it has in the scale of your rich neighbor. To say that the eleventh element in my scale should be considered more valuable than the twentieth in yours is nonsense. To acknowledge that truth we do not need to endorse relativism: it is enough to realize that value is always value for an individual. Most readers of this article do not plan to buy a pneumatic hammer, and that does not mean that they deny that it may be useful to those who buy it.

 We often hear that one dollar more is of less marginal value for a rich taxpayer than to a poor one. That assertion is at the base of many arguments in The Myth of Ownership. It is a confusing way of saying that, if that dollar is taken from him, the rich taxpayer would have to give up the satisfaction of an item that is many steps down on his present scale of utility. It would be the last one, say one more drill bit to be used in one of the hundreds of bench drills in his mill. If a dollar is taken from a poor taxpayer –say a plumber– he too will be forced to give up his last item, which actually might be a similar drill bit. Our plumber would have used it with his only hand drill. We must understand that nothing of that means that we are justified in saying that one more bit is more valuable for the plumber than for the industrialist (more valuable to whom?). We cannot build an “impersonal” scale from all the others and assume that there is any meaning in it. Relative positions have meaning within an individual’s scale.[7] If we forget it, we would be led to think that it is wise to say that the good at the 21st place in Smith's scale of utility (a new subscription to a science magazine) is of less value than the good at the 20th place in Johnson's scale (a new subscription to a porn magazine).

In short: it does not seem that the notion of a “surplus” value collected automatically by all the rich is anything more than another rhetoric device of the kind Murphy and Nagel so justly condemn. And the notion of a “reserve price” does not improve their justification of higher taxes, unless we take the price of goods in lifeboat situations to be the reserve price in normal times. Furthermore, we should not be led to forget for a minute that conflating individual scales of utility is meaningless.

As an aside, it is useful to remember that at the first steps of the production of new goods, they are usually sold to the rich and that they often pay exorbitant sums for that privilege. The first books, cars, and computers were very expensive, and only the rich –sometimes with a love for novelty and experiments could pay for them. In a way, and contrary to the suggestion that the rich get a surplus that is denied to the poor, the rich finance the development of products that initially could not be made for the mass market. Of course, no rich person would think it sensible to say that the poor owe him anything for it. And that is fair. We do not have to pay for all the consequences that have been made possible by rich people –or by governments.

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[1] Pages 82-83.

[2] Böhm-Bawerk, E: Marx and the close of his system. The essay can be downloaded freely from www.mises.org/books/karlmarx.pdf. Concerning Marxism, as with many other issues, the Internet removes the excuse of ignorance.

[3] P. 83.

[4] Positive Theory of Capital. Libertarian Press, p. 138

[5] P. 83.

[6] P. 82.

[7] And we must also bear in mind that individual preferences and choices are not fixed for life but change daily, not necessarily because of whim, but because we have to face different conditions.