Tax And Indifference Curves

What to Read For How do taxes constrain exchange? How does the elasticity of demand and supply change the way a tax affects output? What happens to the revenue from the tax? What is the deadweight loss from a tax, and how is it calculated in a diagram of supply and demand? What is the "second-best" argument? What is a lump-sum tax? Does a tax stay where it is placed legally?

The earlier chapters have described the workings of supply and demand in the absence of any constraint except for scarcity. Many markets do operate in this unconstrained way and when they do not, the constraints are for many questions unimportant. That the government by taxing cigarettes has added a constraint to the behavior of producers and consumers of cigarettes is no obstacle to predicting how a new report by the Surgeon General or a new cigarette-making machine will change the price and quantity of cigarettes.

Still, governmental constraints are common and they provide useful exercises in the theory of price. The economic choice facing governments is often whether or how to constrain exchange. Much economic thinking, therefore, has grown up around such constraints. The thinking, when fully grown, was found to apply to nongovernmental constraints as well.

Taxation is, aside from death, the most common constraint on exchange. Even in death the tax collector gets his due. It was said in 1820 and could be said today that "the dying Englishman, pouring his medicine, which has paid seven per cent, into a spoon that has paid fifteen percent, flings himself back upon his chintz bed, which has paid twenty-two percent, and expires in the arms of an apothecary who has paid a license of a hundred pounds for the privilege of putting him to death."1 The government intervenes between the

Taxes Add Constraints to Markets

'Sydney Smith, in the Edinburgh Review (1820), review of Seybert's Annals of the United States.

apothecary and his customer, demanding a cut in the gains from their exchange. In the United States at present all levels of government—federal, state, and local—take together a cut of some 40% of national income, and in some other countries, such as Britain and Denmark, their cut is higher. The effects of taxation are important.

A Tax Reduces the The first and obvious effect of a tax on spoons, chintz beds, or, to take a modern Amount of a Good example, gasoline, is that it reduces the amounts of them consumed. A tax of

$0.50 on every gallon of gasoline consumed will reduce the consumption of gasoline below what it would have been. By the operation of the law of demand, a rise in the price will reduce consumption. The government imposing the tax can be viewed as providing an input, namely, the right to operate a gasoline station. In return for this valuable right, the government requires payment of $0.50 on each gallon sold, increasing the cost at each quantity supplied by $0.50. Were the tax imposed on a market for gasoline originally in equilibrium at E0 in Figure 15.1, the immediate effect would be to raise the price to $2.05.

At this high price, however, there would be excess supply—consumers do not wish to consume as much at $2.05 per gallon as they did at $1.55. The new price (including tax) would fall until, by increasing demand and reducing supply, point Ei is reached. In this new equilibrium output is lower. Demanders pay more and suppliers receive less than they did before the tax put a wedge (of $0.50 in width) between the demand price and the supply price.

Figure 15.1

Effect of a Tax on Gasoline

Gasoline Imposing a tax creates an excess supply at Q0. Quantity and price must fall to remove

Price the excess supply.

Figure 15.1

Effect of a Tax on Gasoline

Gasoline Imposing a tax creates an excess supply at Q0. Quantity and price must fall to remove

Price the excess supply.

The First The amount of the fall in output caused by a tax depends on the elasticity of Fundamental the demand and supply curves. The First Fundamental Theorem of Taxation Theorem of is this: A tax has little effect on inelastically supplied or demanded goods. Taxation: A Tax Has Little Effect on Inelastic Goods

TorF: The less elastic is either the demand or the supply A: True, as in apparent in Figure 15.2. In each graph of gasoline, the less will a given tax reduce output. the initial, pretax equilibrium is at the same point, and

Figure 15.2

The Less Elastic Demand or Supply, the Less a Tax Affects Output

The price paid by demanders must rise and the price received by suppliers must fall, so that the tax can be paid. The less elastic the demand or the supply or both, the smaller the fall in quantity caused by these price changes.

The price paid by demanders must rise and the price received by suppliers must fall, so that the tax can be paid. The less elastic the demand or the supply or both, the smaller the fall in quantity caused by these price changes.

in each $0.50 has been added to the height of the supply elasticity of supply and across a row for the effect of curve. Look down a column for the effect of a lower a lower elasticity of demand.

In truth, the result is obvious without the diagrams. Taxes increase prices to demanders and reduce them to suppliers. If neither suppliers nor demanders change the amounts they wish to supply or demand very much when the prices they face change (which is what "less elastic" means), then it is evident that the tax will have little effect on the amounts.

You need information about both elasticities to answer such questions as the following.

T or F: If the elasticity of demand for automobiles is —2.0, an antipollution tax on their sale of 5% of their price will reduce the number of such automobiles consumed by 10%. (Hint: Look at a diagram.)

A: Only if the elasticity of supply of the automobiles were infinite (or, practically speaking, large) would the

But think before you

T or F: A tax on the crops of blue-eyed soybean farmers over 47 years of age in northwest Iowa will fall chiefly on consumers of soybeans if the world demand curve for soybeans is highly inelastic.

A: False. It will fall chiefly on the blue-eyed farmers over 47 years of age in northwest Iowa. The point is that the demand curve facing them is very elastic indeed, full 5% tax appear as a 5% rise in the price consumers face, reducing the quantity demanded by (5)(2) = 10%. Otherwise some of the tax will stick to the auto companies or to owners of secondhand autos. Therefore, false. Inelastic suppliers or demanders pay taxes. The increase or decrease of the price from its pretax equilibrium measures on whom the burden falls.

jump.

regardless of the elasticity of the world's demand curve. This is because it is a residual from the demand of the world and the supply of farmers more popular with the taxing authorities. Not particular types of farmers but all farmers—blue-eyed or otherwise—face the world demand. A tax on the whole soybean crop would have the effect described, not a tax on this one small part of the crop.

How to Sidestep the Question of How the Money from Taxes Is Used

The collecting of taxes, then, hurts somebody. But the collections from a new tax are not usually dumped into the sea. The government uses the command over resources acquired by taxation to redirect the resources toward palace guards, highways, diplomatic receptions, criminal courts, and other useful things. In other words, there is a spending as well as a taxing side to the interventions of governments in the market. And even on the taxing side by itself there are other taxes, which may or may not be changed when a new tax is introduced. These matters, however, are not the subject. For clarity they must be separated from the subject of a new tax. The effect of the tax alone must be separated from the new spending or lowered taxes that the tax would bring.

The way to accomplish the separation is to assume, solely for purposes of clear thinking, that the collections of a new tax on, say, bread are turned back to the public in a neutral way, that is, in a way that has itself no repercussions on the expenditures of government, the level of alternative taxes, or the size and distribution of income. It is not difficult to imagine non neutral methods of turning back the collections of the tax on bread. They could be used to buy ammunition used to shoot half the population; or to eliminate a tax of $10 per gallon on gasoline that had stopped all travel by automobile,- or to subsidize the output of hallucinogens, distributed free to soldiers at guided mis sile installations or to the president and his cabinet; or to increase the income of people with a very high income elasticity of demand for Latin poetry. The decision to do such things with the collections, desirable or undesirable as they may be, is distinct from the decision to impose the bread tax. The tree of possible treatments of a new tax is as shown in Figure 15.3. The rightmost branch of the tree isolates the effect of the tax itself, leaving the examination of combinations of the new tax and changes in total expenditure, in other taxes or subsidies, and in the distribution of income for another day.

Figure 15.3

Possible Repercussions of a New Tax on Bread the effect of the new spending or

Figure 15.3

Possible Repercussions of a New Tax on Bread

Must evaluate the effects of changing the distribution of income

The Second Fundamental Theorem of Taxation: A Tax Causes Deadweight Loss

Looking at a tax on bread this way might seem to assume away all the effects of the tax. What goes out of one pocket of the public in the form of a tax on bread goes back into another pocket in the form of a neutral turning back of the revenues from the tax. This is almost true, but not entirely. The Second Fundamental Theorem of Taxation is that taxes cause additional, net, "deadweight" loss. The fundamental truth about the effect of taxes can be demonstrated with consumers' and producers' surplus:

T or F: The sum of what suppliers and demanders lose from a tax is always larger than the revenue from the tax.

A: True. Consider the tax on bread, taking it to be a specific tax imposed on bakers as illustrated in Figure 15.4. The revenue from the tax is the area A + B, that is, the number of loaves of bread consumed after the tax, Qi, multiplied by the rate of tax per loaf. Recall the notions of consumers' and producers' surplus. As a result of the tax and the reductions in quantities supplied and demanded that it induces, consumers lose consumers' surplus in the amount A + X. Suppliers lose producers' surplus in the amount B + Y. The sum of the two losses to the participants in the market for bread is therefore (A + B) + (X + 7). The revenue portion of the loss, A + B, can be viewed as a transfer that makes someone else better off (whoever it is who gets the proceeds of the tax) even as it makes bread eaters and bakers worse off. Such reshuffling of income results in no net social loss. Alternatively, one could reach down into the lower right-hand corner of the tree of possible repercussions of a tax and suppose that the revenues were in fact turned back to bread eaters and bakers each year, on April 15, say. In either case the portion A 4- B is not socially burdensome. But no matter what the government did with the revenue, there would remain the shaded triangle, X + Y, in the diagram, a loss to bread eaters and bakers that cannot be made up by turning back to them the revenues from

Figure 15.4

The Social Loss from a Tax

Bread

Bread

the tax. The triangle is the social hurt, the fall in national income, the deadweight loss from putting a wedge of taxation between the marginal cost of bread

(the supply price), and its marginal valuation (the demand price).

The General Theory The conclusion is that any disturbance of the competitive output reduces income. of Second Best Any disturbance? Not quite. The assertion is true if the only disturbance to competitive equilibrium in the economy is a tax on, say, food. But if thqre already exist taxes on other goods as well, a tax on food can raise national income. This startling proposition is an example of the logic of second best, so named by the British economist fames Meade and brought to the wide attention of the profession by Kelvin Lancaster and Richard Lipsey.2 Suppose that there is initially a tax on Other Goods but not on Food. The tax on Other Goods reduces national income by lowering the relative price that suppliers perceive and raising it to demanders, persuading them to produce and consume less than the optimal amount. The point to grasp is that the tax raises the price of Other Goods relative to Food. A tax on Other Goods amounts to a subsidy on Food, by virtue of nothing more profound than the arithmetic of relative prices. To write out the arithmetic, if Other Goods sell at 2 tons of Food per dozen of Other Goods before the tax, then Food sells at 0.50 dozen of Other Goods per ton of Food. If the tax increases the price of Other Goods in equilibrium to 3 tons of Food per dozen, then by that very fact Food will sell for 0.33 dozen of Other Goods per ton. Food has essentially been subsidized to the extent of 0.50 — 0.33 = 0.17 dozen Other Goods per ton.

Now suppose that Congress contemplates imposing a tax on Food as well. Will its economic advisors berate it for imposing still further losses of welfare on society? No, they will not, if the tax on Food is enough to offset the tax on Other Goods, namely, a tax of 0.17 dozen Other Goods per ton of Food. This tax will just offset the implicit subsidy on Food provided by the previous tax on Other Goods. It will reestablish the relative price of Food and other goods (that is, 0.50 dozen Other Goods per ton of food) that obtained before any taxes were imposed. The upshot of imposing a tax on Food equal in percentage terms to the existing tax on Other Goods is to eliminate the distorting effects of all taxes. In short, the correct strategy for a society trying to do as well as it can given that it cannot attain the first-best position of no taxes at all is to achieve the second-best position attainable. This may well involve imposing taxes, not eliminating them.

It might seem that we have here a formula for taxes with no costs in efficiency: Impose an equal percentage tax of everything, for this will leave the true marginal costs and valuations of things undisturbed. If "everything" means just that, taxes on commodities that pass through markets and also those that do not (such as home handiwork, sleep, and the contemplation of sunsets), then the formula is correct. If "everything" means, however, only marketed commodities, then it is false. As a practical matter the tax collector cannot reach everything. If he taxes only marketed commodities, then the taxes on vacuum cleaners, supermarket food, and psychoanalysis would amount to subsidies on unpaid housekeeping labor, backyard gardening, and transcendental meditation, and

2 Kelvin Lancaster and R. G. Lipsey, "The General Theory of Second Best," Review of Economic Studies 24 (1956): 11-32.

society would be pushed away from its optimal output of marketed and nonmar-keted commodities.

The Ideal Tax on Aside from taxes on literally everything or taxes on goods inelastically supplied Efficiency Grounds or demanded, the only tax without costs in efficiency is one that alters no Is the Poll Tax incentive to do anything. No margin of substitution in production or consumption is to be disturbed. The only way in which to accomplish this is to make the amount collected by the tax independent of decisions to produce or consume a little more of something. The tax, that is, must be a fixed cost. It's sometimes called a lump-sum tax, which is to say that the tax falls in a lump, a fixed cost.

Q: In the 1370s a poll tax (having nothing to do with elections: pol means "head" in Middle English) of so many shillings per head was imposed by the English king. So irritating did Englishmen find this tax that it contributed to the Peasant Revolt of 1381. True or false: Instead of rioting in the streets, pillaging manor houses, and presenting petitions to the king, Englishmen should have congratulated the king on hitting on a tax with no costs in efficiency.

A: True. Short of emigration or suicide, a head tax cannot be avoided by altering one's behavior. Therefore, it does not change behavior, in particular the behavior of supplying or demanding goods.

The Third Fundamen tal Theorem of Taxation: A Tax Falls Where It Will, Not Where It Is Put

The effect of taxation of gasoline on efficiency (the size of output, because the tax reduces it) and on equity (the distribution of the income between suppliers and demanders, because the tax changes it) depends, in short, on the size of the tax and the elasticities of supply and demand. Further, the effects depend only on these things. In particular, the efficiency and equity of a tax imposed on the exchange of gasoline for other goods does not depend on whether the tax is legally placed on suppliers or demanders. This is the Third (and final) Fundamental Theorem: Taxes fall where they fall, not where lawyers plan to put them.

T or F: A $0.50 tax per gallon of gasoline imposed on consumers at the pump will hurt consumers more than will a $0.50 tax imposed on producers at the refinery, because consumers pay the one, producers the other.

A: The consumer is hurt by a higher price. It does not matter to him whether the gasoline station owner supplies the stuff at $1.90 a gallon (having added the tax of $0.50 to its $1.40 cost) or supplies it at $1.40 cents, inviting the tax agent to swoop down to collect $0.50 more. $1.90 is $1.90 and is higher than the price to the consumer before the tax was imposed, say, $1.55 (which is higher than $1.40 because supply equals demand at a higher price). One can think of the tax as raising the supply price at every quantity by $0.50, because suppliers will want their normal return in addition to the tax. Alternatively, one can think of it as lowering the demand price at every quantity of $0.50, because demanders will value a gallon with a $0.50 tax $0.50 less than one without such a tax. It does not matter. Therefore, false. To put it another way, Figure 15.5 shows two equivalent ways of looking at the question of how a tax affects the market for gasoline. To put it still another way, in the final position the new supply price plus the tax must equal the new demand price. This is the same as saying that the new supply price must equal the new demand price minus the tax.

The proposition that the legal location of a tax does not matter for its economic effect is remarkably powerful. Or perhaps one should say that the proposition is not understood remarkably often.

Figure 15.5

It Does Not Matter Whether a Tax Is Placed on Suppliers (a) or De-manders (b)

A tax can be viewed as shifting supply upward, demand downward, or as placing a wedge between demand price and supply price. In each case the result is the same: Demanders pay $1.90, suppliers get $1.40, the tax collector gets $0.50. Whether the supply or demand curve is shifted does not matter because the economic effect is the same whether the tax collector takes the money from the demander's hand or from the supplier's.

Price

Price

Price

Price

-Quantity

Q: The City of Chicago imposed some time ago an employment tax of so many dollars per month per employee in businesses over a certain size. Alderman Thomas Keane, defending the tax, asserted that the city's lawyers drafting the law had made very sure that it was a tax on employers, not employees. "The City of Chicago will never tax the working man," said Keane. Comment.

A: Well, no matter how skilled the city's lawyers, the tax does tax the working man. The tax increases the cost of employing labor, which one can view indifferently, as a higher supply price for labor or a lower demand price. Like a tax on gasoline or food, the tax on employment will raise the cost of labor, hurting employers (and, by raising costs, hurt their customers). But it will also lower the wage paid, hurting the working man. The legal incidence of the tax—the people presented with the bill for the tax—is not the same as the economic incidence—the people made worse off by the tax.

A somewhat more subtle example of the same point arises in discussions of the corporate income tax. When state governments wish to increase taxes, the choice they face is often described as that between taxing people (with a sales or personal income tax) and taxing corporations. The contrast is imaginary. For one thing, corporations are people (if perhaps out-of-state people), not disembodied entities that taxation does not hurt. For another, the tax on corporate profits, which in the first instance might seem to fall on corporate stockholders, need not stay where it is put. The tax initially drives down the normal return to corporate ownership. This will induce some capital to leave the corporate sector, or at any rate the corporate sector of the state imposing the tax. This in turn raises the relative price of goods produced in the corporate sector and reduces the wage (or employment) of resources employed in the corporate sector. The consumers and employees of General Motors Corporation and General Mills, Inc., pay some of the tax.

The Uses of Entry, This third fundamental principle of taxation, like the first two, is a consequence Revisited of the principle of entry. A tax or subsidy does not stay where it is put if putting it there creates profits above or below normal. The shifting of the incidence of the tax or subsidy does not stop until all profits are normal, which is to say that it does not stop until the marginal suppliers and demanders are back on their supply and demand curves. The argument applies in fact to much more than taxes.

T or F: Renters of apartments close to the University of Iowa get a valuable benefit from performances at the university by champion musicians or by champion basketball players and wrestlers.

A: If a renter did get the benefit the renter would be earning, so to speak, supernormal profits. That is, by comparison with some renter far from the university paying the same price the renter nearby would get extra benefits, free. Such a situation is not an equilibrium. If it existed, people would shift from the sticks to Iowa City (where the university is located), driving up rentals there and lowering them in the places they deserted. In other words, in equilibrium the renter near the university would pay more for che amenity of having the university close by. The amenity looks at first like a subsidy to renters in Iowa City, but in fact they pay for it in higher prices for apartments.

The beneficiaries of any new amenities in Iowa City are in fact the old owners of property, not the people who rent from them. The old property, especially the land itself close to the university, is supplied inelastically. Just as it would bear a tax on property (even if the tax were put legally on the renters instead of the landowners), so too the old property collects whatever element of subsidy to the neighborhood there is in the opening of a new theater or sports arena at the university. Reasoning of this sort is extremely important for all manner of questions of policy.

Q: The city fathers and mothers of Iowa City propose to run a highway through the west side of the city to make it easier for west-siders to get to the downtown. The downtown property owners claim that commuters into town will benefit. The near-west-side property owners over whom the highway will be built claim on the contrary that the only beneficiaries will be property owners, downtown and elsewhere. Who is right?

A: If the commuters into town in fact get any benefit in ease of travel, they will be willing to pay more for their houses and more for the goods they buy in the downtown. The resource that is inelastically supplied— land—benefits. Only to the degree that commuters also happen to be landowners will they benefit. The near-west-siders are right. On such logic are city governments everywhere founded: Landowners are in the long run the only people interested in effective schools, easy roads, and other amenities paid for by the city.

Summary Taxes clog markets A tax puts a wedge, to use another metaphor, between the buying and the selling price, raising one and lowering the other. If the taxed good is elastically demanded or supplied, the resulting change in price has a large effect on quantities. The inelastic supply or demand bears the burden of the tax disproportionately, being unable to move out from under it (to alter the metaphor once again): That is what "inelasticity" means—inflexibility. Society as a whole, however, cannot move out from beneath the burden of a lower-than-optimal output of the taxed good. The area of unsatisfied willingness to pay in excess of willingness to supply is the "deadweight loss." The deadweight loss is indeed the fall in the nation's income caused by the imposition of a tax. But taxes do not always cause a net fall in income. If the tax offsets some implicit subsidy, for example, or if it offsets some other tendency to produce too much of a good, then, by the "theory of second best," the tax may be desirable. The only truly neutral tax is one that affects no incentive to do anything, whether the thing is marketed food or nonmarketed creative leisure. It is nearly impossible to imagine such a tax. No existing income or excise tax approaches it.

The clogging effects of taxes are not felt necessarily where they are placed by law. The notion that taxes and subsidies end up affecting people whom the law did not believe it was affecting is a good example of characteristically economic reasoning. And it is a good example of the principle of entry. Until all incentive to enter or exit is gone, the analysis of a tax or subsidy is not finished. When it is finished, it often turns out that benefit and burden have shifted in the night.

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