Pareto's Republic and the New Science of Peace

by Filip Palda

  Taxes, no matter what their level, should minimize disruptions to Pareto efficiency for that level. In practical terms this means devising taxes that minimize the deadweight loss for each “crop” of tax revenue harvested, or more technically, to minimize the deadweight loss per unit of tax. To minimize the deadweight loss per unit of tax, government first needs to build a catalogue of these losses and get an idea of how they react to taxes, much as a farmer would need to know the costs of various fertilizers and equipment available for the planting of the crop.

  Yet before we can understand the list of deadweight losses economists have compiled, we need the stark example of the effects of theft on the victim to give us a feel for deadweight loss. Theft is a very crude form of taxation, levied not by the government but by a private individual. Anyone who has had a wallet or purse stolen knows that the loss of cash is usually the smallest cause of their suffering. The real drama arises from the loss of irreplaceable pictures, billets doux, and from the hours spent on replacing identity documents and credit cards. These hours are lost to the individual and to society. The value of what he or she could have been doing otherwise cannot be recuperated and as such is a form of deadweight loss. Surprisingly, the money stolen is not a deadweight loss, but rather a transfer. The dollars have not disappeared from the economy. They remain ready to pass from the thief’s hands to those of unwary merchants.

  Modern states emulate the thief by using force, if necessary, to relieve us of our earnings. The taxpayer considers his transfer of sums to government to be a personal loss, but as in the case of the thief, the transfer is not a loss to society because it goes into state coffers from which it may be spent. The difference between theft and taxation lies in the degree to which each generates a deadweight loss. With impersonal government taxation, one does not suffer the administrative running around and expense that accompany the pickpocket’s highly personalized levy. Yet deadweight losses are not completely absent.

  Taxes discourage people from entering into profitable exchanges with each other. The value of these discouraged exchanges is a deadweight loss. For instance, studies show that when government raises the income tax, some people who are not in salaried positions, such as self-employed carpenters, sign makers, and consultants, to list a few, start to work in the underground economy where they pay no tax. A deadweight loss can arise because not every consumer is willing to pay for their services without asking for a receipt for purposes of tax deduction. By limiting the pool of consumers they serve, tax evading producers cut themselves from serving potentially high-paying clients. To the carpenter this is of no concern because the evaded tax more than compensates for the extra payment he or she would receive in the legitimate market. Yet the economy is poorer because the carpenter now works for a client in the underground economy who values his or her work less than a potential client in the legitimate economy. For example, a hotel would be willing to pay the carpenter $30 an hour to improve its façade but at a fifty percent income tax the carpenter would only make $15, and so prefers to work off the books for a client willing to pay at most $20. The income tax has “re-slotted” or “displaced” people from high-yield to lower-yielding activities. The worker who evades the tax does not see things this way, because the tax has created a wedge between what the $30-an-hour employer is willing to pay and what the worker perceives to be his gain of $15 for working.

  This is the manner in which taxes can blind people to the best opportunities the economy offers. Government is richer, but the economy is poorer. Even employees on a payroll may produce deadweight losses in the face of high income taxes by increasing their absenteeism. “You pretend to pay us and we pretend to work” was the slogan often used in communist countries where governments implicitly taxed their workers to excess by paying them salaries far below their productivity.

  There are as many types of deadweight loss as there are taxes. The list of deadweight losses from taxation includes the lost benefits to consumers and producers from discouraged exchanges, reduced productivity due to discouraged investment in machines, the loss to society from having thousands of clever lawyers and accountants plan ways around taxes, the flow of resources away from places that produce true riches to places that produce tax rebates, and the money and effort devoted to hiding what one has from the taxperson.

  No one knows for sure how many types of deadweight losses there are and spotting new problem areas is an ongoing field of research for economists. Yet what almost all known deadweight losses have in common is a property called non-linearity, and it is this property that gives rise to the theory of efficient taxation. I say “almost” because there is a curious creature economists call a lump-sum tax, more popularly known as a head-tax or poll-tax that in principle should have no deadweight loss. A lump-sum tax is one you have to pay no matter what you choose to consume, or whether you work or not. As such, it does not influence a person’s calculations about whether some deal is good or not. People of course have less money to play with because of the tax, but it does not stop them from playing well with it. They will still seek out the best possible exchanges and no opportunities for exchange will go unexploited. In practice, the head tax has rarely been used, and when it has been, it has almost invariably led to popular revolt. We shall not discuss it further here.

  The non-linearity of deadweight loss

  An efficient tax system should minimize deadweight losses for each dollar of revenue the government collects. The premise here is that the deadweight loss from a dollar of tax depends on some feature of the tax that is within government’s control. Formula One race car designers shape their car frames to minimize drag and turbulence from air currents. Similarly, government can “shape” taxes to minimize their drag on the economy.

  The drag in question arises from a property of deadweight loss known as non-linearity. Non-linearity is a concept imported from mathematics. Applied to taxation it states that each unit increase in tax creates a more than proportional increase in the deadweight loss. It is solely because of this non-linearity that the discussion of efficient taxes has any meaning. Let us first try to understand what non-linearity means and then we will see how so many prescriptions for government radiate from this property of deadweight losses. Non-linearity is an important topic in physics and biology where it is the idea that drives chaos theory and theories about the origins of order in the universe. Closer to home, non-linearity is well understood by anyone who has fretted about the costs of driving a car. Doubling one’s speed more than doubles the use of gasoline. Doubling the speed again more than doubles the use of gasoline above the previous increase. People who like to drive fast have non-linearity to curse for the significant increase in gasoline consumption that comes from accelerating to higher speeds. Our bodies also feel the effects of non-linearity. Walking slowly up the stairs is far less tiring than walking slightly faster. In all physical endeavours doubling one’s performance calls for more than double the effort to achieve that result. From the business world you will no doubt have heard the expression “diminishing returns” to indicate that throwing more resources at a problem brings progressively less impressive results. These shifting results and demands are all members of the family of non-linear effects.

  Why should the deadweight loss from a tax be non-linear? The reason is that taxes kill increasingly productive activities for every additional dollar raised. As you tax corporations, at first only the least efficient ones will go out of business. These are the ones with outdated machinery and bad labour relations. Not much is lost by their disappearance. Every subsequent increase of equal increments in the tax knocks out ever more efficient and profitable firms. Each dollar of additional tax becomes a burden that can break the backs of even the most efficient companies. Non-linearity is at play because the first dollar of tax raised costs less than the last dollar when costs are counted in deadweight loss.

  The theoretical rule for efficient taxation

  Armed with the concept of non-lineari
ty we are ready to understand why the question of an optimal tax arises solely from non-linear increases in deadweight loss. Consider two different methods of raising a hundred dollars of tax from two people. The government could ask each to pay fifty dollars, or it could place the full burden on one and ask nothing of the other. Non-linearity means that the deadweight loss from a hundred dollar tax paid in equal halves by each of two identical people is less than the loss from having one person pay the entire tax. The reason is that if you tax each person equally, then the deadweight loss from the fiftieth dollar each pays is identical. If one person had to pay the whole sum, the deadweight loss from the first fifty dollars he or she paid would be the same as that felt by the first taxpayer in the case of equal sharing. But the deadweight loss associated with the next fifty dollars he or she paid would be higher per dollar than the highest deadweight loss felt by the second person in the case of equal sharing due to non-linearity. So the sum of deadweight loss for the first fifty and last fifty paid by one person would exceed the sum of the deadweight losses paid by two people each paying fifty dollars.

  The Brazilian government learned this lesson to its detriment in the early 2000s when Shell Brazil decided to close several hundreds of its gas stations in reaction to excessively high taxes. The government had felt obliged to target Shell and other high profile producers with high taxes because it was unable to tax independent gas stations that were good at concealing their earnings. The economic consequence of this was that Shell shut down not only inefficient stations that were earning little profit, but was driven also to shut down ordinarily high-yielding stations that were performing an important service to the public. Had the tax been evenly divided among Shell and the independents, then certainly inefficient independent stations would also have closed, but because the burden would have been spread evenly, the lower tax that resulted would have spared Shell from closing its most efficient stations. The Shell Brazil example illustrates why an efficient tax system is one in which each citizen carries some reasonable fiscal backpack, rather than one that piles spine-bending loads on just a few. This is the principle of efficient taxation at its simplest. There are deviations, but as we shall see, an even spreading of the load remains at the heart of all recipes for efficient taxation.

  The competitive advantage of countries that tax efficiently

  Economists have worked diligently to devise efficient systems of taxation because such systems allow government to invest in public goods at the lowest possible deadweight cost. Public goods such as infrastructure (like bridges and roads) are vital to economic development. We can appreciate the importance of public goods purchased through efficient tax systems by looking at poor countries. They offer an extreme example of the manner in which inefficient tax systems can put a brake on development. One of the almost universal features of poor countries is that they suffer from high rates of tax evasion compared to rich countries. A high rate of evasion means that these governments have relatively few evident targets upon which they can levy taxes. Foreign corporations wishing to exploit natural resources for a fee are often the only reliable source of government revenue. In extreme cases, taxes take the form of stolen lives. People either have their time and effort stolen by forced military service where the government “rents” them out as labourers, or it sets them directly to building roads or working in mines.

  As we saw in the previous section, when you focus taxes disproportionately on a narrow segment of the economy, excessive deadweight losses result. In the case of poor countries, corporations stop investing, young men stop working and defect to fight for rebel groups, and the consumer hides his or her savings under the bed. The national income that is lost when foreign companies are discouraged from investing and the mayhem created by private militias are among the deadweight losses produced by these inefficient systems of taxation.

  The logic behind foreign aid is that it should enable poor countries to overcome the tyranny of high deadweight losses per dollar of tax levied. In rich countries, most people pay taxes without question. Their deadweight loss from taxation is lower than that of poor countries because the burden is more evenly spread. By lending money to poor countries, rich countries are lending their ability to generate funds at low deadweight losses. The road that would cost a poor country a million dollars in cash plus another million in deadweight losses that would come from raising the money through taxes will cost it a million plus perhaps a hundred thousand dollars in interest if borrowed from a rich country. The theory is that once it has built its infrastructure and protected its property rights, the poor country will have developed a broad tax base from which it can repay its loans at a now reduced domestic deadweight loss.

  Getting everyone to pay their taxes is not a question of fairness for poor countries. It is a question of survival and is one part of the puzzle to attaining prosperity. As more people pay the taxes they owe, the burden on those already paying can fall, and the deadweight loss per unit of tax can also fall. One can understand this point best by reading the works of Richard Abel Musgrave, a tireless exponent of efficient taxation in less developed countries.

  Refinements to the idea of efficient taxes

  The example of poor countries suggests that the first step towards efficient taxation is the conquest of tax evasion. Countries that have been successful in taming, if not eliminating evasion, followed a three-pronged approach. First, they developed sophisticated means of measuring the value of property and the incomes people earn. Second, they managed to gradually eliminate legally entrenched evasion, such as official exemptions from tax. Concerning these first two points, economic historian Carlo Cipolla explains in his book Before the Industrial Revolution that the

  preindustrial state did not have at its disposal the techniques and the means of investigation available to the industrial state… Moreover, the nobles and the clergy normally enjoyed fiscal immunity… In the course of time both the Church and the nobility lost ground in their effort to evade taxes… Still, over most of Europe for most of time fiscal privileges were a reality that created delays, reduced receipts, and complicated the tax raising process. (page 40)

  Finally and perhaps most importantly, countries that are now rich managed to convince people that it was in their interests to voluntarily pay taxes. What economists Bruno Frey and his collaborator Benno Torgler have dubbed “tax morale” depends in great part on the public’s belief that government is working on their behalf and that the money they are paying for public services is being well spent. Such beliefs are found in countries where government has corruption and inefficiency under control.

  One must be aware of this historical context to appreciate that the fundamental principle of efficient taxation, which is to spread the burden evenly, is not one that can be clinically prescribed. It emerges at the confluence of many reinforcing social and technological currents. From the perspective of economics, tax evasion is a source of deadweight losses. From the sociological perspective it is a display by the citizen who evades of profound disrespect for the citizen who pays his or her taxes. Whatever perspective one takes, taming tax evasion remains a vexing struggle.

  Countries that had sought to reduce evasion to acceptable levels could then allow themselves to consider refinements to the even spreading of the tax burden. Saying that efficient taxes are spread evenly has some meaning, but is imprecise. The first serious effort at greater precision came from Cambridge mathematician Frank Ramsey in the 1920s. Ramsey was a friend of John Maynard Keynes, Bertrand Russell, and Ludwig Wittgenstein. He was someone who would have joined the pantheon of the world’s great minds had he not died at a very young age. Food poisoning claimed his life at the age of 26, but before then, he managed to found the modern theory of optimal taxation. His prescription was to tax all goods at the same rate in some circumstances, and to tax most heavily those goods that did not respond much to changes in price in other circumstances. If you absolutely need to buy cigarettes, then a tax will not discourage you
from your purchase. This makes you a promising target for Ramsey tax commissars. Your inflexibility means that the tax will not discourage you from entering into profitable exchanges.

  If everyone is similar and works a fixed number of hours, Ramsey suggested it made sense to tax all goods at the same rate. This turns out to be exactly the same thing as a flat or “linear” tax on income. Problems arise with this simple view once we admit that some goods are hard to tax. In such cases, Ramsey’s prescription was to tax most heavily goods that people keep consuming even when prices rise steeply. The idea is that in a world where taxes distort relative prices, we want taxes to create the smallest possible disruptions to consumption patterns because any deviation from these patterns will push us further away from the point where all gains from trade are exploited. This rather complicated analysis was just the first wrinkle of many that would appear on the face of efficient tax theory.

  In 1957, Richard Lipsey and Kelvin Lancaster came up with a “second-best theory” of government intervention that had applications to efficient taxation. The deadweight loss from a tax in one sector of the economy might be not be so bad if this tax somehow reduced activity in another part of the economy where deadweight losses were high due to another tax. For example, a tax on cigarettes could cause a deadweight loss to smokers, but the resulting decrease in disposable income might cause a reduction in the consumption of highly taxed and harmful alcohols. Further twists in the theory of efficient taxation came with Arnold Harberger’s 1964 analysis of the effect of taxes on investment, and with insights by British economists in the 1970s who sought to favour the poor over the rich by attaching “distributional weights” to the deadweight losses from different economic classes.