Taxation through a Rothbardian Lens



All students of economics will sooner or later be confronted with the standard neoclassical analysis of deadweight loss from taxation. The point of this analysis is not to clarify what the government’s tax revenues should be used for, but rather how and where the government should tax in order to minimize distortions in the market structure—in a sense, in a way that hurts the least. Ideally, the tax should be “neutral.”

Murray Rothbard was a pioneer in analyzing taxation from an Austrian or causal-realist standpoint. He also penned an important critique of the standard analysis of welfare economics. However, he never engaged the standard theory of deadweight loss from taxation, although his insights contain the seed for its refutation. This article draws on Rothbard’s key insights and develops the Austrian analysis of taxation further toward this end.

The conventional analysis in the standard economics textbook is as follows. Both supply and demand in a given market are characterized by a greater or lesser degree of price elasticity. Price elasticity measures how strongly the quantity of a good demanded or offered responds to a change in price.

For example, if demand in a market is inelastic, then consumers buy similar quantities of the good at both low and high prices, i.e., the quantity demanded does not vary very much when prices change. If, on the other hand, demand is elastic, then the quantity demanded collapses relatively sharply when prices increase.

In a normal supply-and-demand diagram, elastic demand is therefore relatively flat and inelastic demand relatively steep, as shown in figure 1.

Figure 1: Market Equilibrium with Inelastic and Elastic Demand

On every market there is a tendency toward equilibrium, i.e., goods tend to be traded for a price (p*) at which the quantities demanded and offered are identical (q*). Thus, market equilibrium lies at the intersection of supply and demand.

A tax on a good drives a wedge between supply and demand. Consumers must now pay a higher price for the good, and producers are left with less of the price paid than would be the case without the tax. Instead of a uniform equilibrium price, there is now a gross price and a net price.

Even with taxation, there is a market equilibrium. From the consumer’s point of view, the gross price to be paid is decisive. From the producer’s point of view, the net price, which is what remains after deduction of taxes, is decisive. In equilibrium, therefore, the quantity demanded at the gross price is exactly equal to the quantity offered at the net price. This equilibrium can only be reached if the quantity of the good exchanged on the market is reduced.

Figure 2: Deadweight Loss from Taxation with Inelastic and Elastic Demand

The deadweight loss is larger the more elastic the demand.

Figure 2 illustrates that the decrease in the quantity exchanged for a given supply schedule depends on the elasticity of demand. The more elastic (flat) the demand schedule, the more the quantity exchanged on the market is reduced due to the tax. The red triangle corresponds to the wedge of taxation driven between supply and demand. The size of the wedge is a measure of the welfare loss from taxation.

This is intuitive: the reduction in the quantity exchanged corresponds to an elimination of transactions that would be mutually beneficial to producers and consumers were it not for the tax. In this sense, there is a welfare loss, normally called a deadweight loss, that must be minimized for the good of all. The deadweight loss corresponds to the size of the wedge of taxation. Using standard neoclassical analysis, it can thus be concluded that the best markets to tax are those characterized by particularly inelastic demand. There the wedge will be smallest and the deadweight loss minimized.

The standard analysis highlights a very important point: there is a welfare loss from taxation. Its conclusion, however, is far from convincing. This becomes clear as soon as we broaden the perspective a bit. It is not enough to consider only the direct effects of taxes on the market in which they are levied. We must also think about the indirect effects of taxation on all other markets, that is, on the economy as a whole.

If demand in the taxed market is inelastic, then the total expenditure of consumers in that market will increase after a price increase such as that caused by taxation. This can be seen quite clearly in figure 2. If demand is inelastic (left), the price that consumers pay per unit of the good increases sharply, but the quantity supplied decreases only slightly. So, with the tax consumers spend more money overall on this good. But where does this extra spending come from?

The increase in spending does not materialize out of nowhere. Consumers, with any given income, can only spend more money on one good if they spend less on one or more other goods. This implies an additional welfare loss from taxation, but one that occurs in a different market. The increase in spending can only be financed if consumers reduce demand in at least one other market. Figure 3 illustrates this scenario.

Figure 3: Total Welfare Loss from a Tax on a Good with Inelastic Demand

There is an additional partial welfare loss on at least one other market, because demand is reduced to finance the increase in total expenditure on the market where the tax has been levied.

Following the same reasoning, we can see that when a tax is levied on a good with an elastic demand, spending in this market decreases. That is, consumers spend less overall on the taxed good after the tax is levied. Spending thus shifts in favor of another market, where demand now increases. This in turn causes a partial welfare gain that compensates for part of the welfare loss that occurs in the market where the tax is levied. This is illustrated in figure 4.

Figure 4: Total Welfare Loss from a Tax on a Good with Elastic Demand

There is a partial welfare gain in at least one other market, where demand is increased, as expenditure decreases on the market where the tax is levied, but this partial welfare gain can never completely overturn the loss from taxation. This is a corollary of the principle of demonstrated preference: the bundle of goods chosen with taxation would have been available without taxation, but buyers preferred another one. Imposing a tax therefore always leads to the consumers being worse off than they would otherwise have been.

Thus, it is evident that the standard analysis of deadweight loss from taxation is misleading. It overestimates total welfare loss when demand is elastic, and it underestimates the loss when it is inelastic. The error arises because the interrelations between goods and markets are left out of standard partial equilibrium analysis. In causal-realist price theory, however, of which Rothbard was a main exponent, these causal relations are clearly understood.

Conclusion

The standard neoclassical analysis of deadweight loss from taxation, familiar from numerous textbooks, falls short. It considers only the direct effects of a tax on the market in which it is levied and overlooks completely the indirect effects of the tax in other markets.

Moreover, the deadweight loss is not necessarily lower if a tax is levied on a good facing an inelastic demand in the market. From a consumer perspective, this is quite easy to see: demand for a good is inelastic precisely when the good satisfies a particularly important need and there are no readily available alternatives, or substitutes, in the terminology of economics. The lack of substitutes means that the consumers cannot avoid the tax very easily. From a government finance point of view, this may be a good argument. From a welfare-economic point of view, it certainly is not.

It remains to be said that every tax distorts the market. The point is that the distortions do not necessarily occur only where the tax is levied, but rather they are spread across the whole economy as acting individuals substitute other beneficial exchanges for the ones prevented by taxation (in the case of elastic demand) or sacrifice exchanges on other markets to keep the reduction in quantity relatively small on the taxed market (in the case of inelastic demand). If one wanted to minimize the overall distortion and thus the welfare loss from taxation, it would make more sense to focus on cutting taxes rather than to look at the elasticity of demand. Murray Rothbard came to this very conclusion in his essay “The Myth of Neutral Taxation.” His radical but logically inescapable conclusion was that:

We are forced, then, to the realization of crucial points from which free-market economists seem to have been fleeing as from the very plague. That neutral taxation is an oxymoron; that the free market and taxation are inherently incompatible; and therefore either the goal of neutrality must be forsaken, or else we must abandon the institution of taxation itself.



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