02A Holcombe Capitulo 10

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CHAPTER 10 Positive Principles of Taxation 180

CHAPTER 10

Positive Principles of Taxation

The, first nine chapters of the text were concerned primarily with what the government does andwhy. The next several chapters focus on how the government raises revenues to finance itsactivities. The, government has three primary ways of raising revenue: taxation, borrowing, andmoney creation. Borrowing and money creation are discussed in chapter 23. Chapters 10,through 16 cover taxation. Taxation, deserves substantial coverage because the bulk ofgovernment revenues in the United States is raised through taxation. Even with a substantialfederal budget deficit, more than 90 percent of all government revenues are raised throughtaxation.

The principles of taxation can be divided into two general categories. The first categoryis positive principles of taxation, which concerns the effects of taxation. Positive principles of

taxation analyze who bears the burden of taxes and what other economic effects can be expectedto result from the imposition of taxes. The most important positive principles of taxation are taxshifting and the excess burden, or welfare cost, of taxation. Chapter 10 is devoted to these andother positive principles of taxation.

The second category of taxation deals with tax policy. Included in this chapter suchissues as who should bear the burden of taxation and what criteria people might use to determineeach person's fair share of the tax burden. Ultimately, these normative questions revolve aroundhow tax policy can be used to design as desirable a tax system as possible. Of course, whatconstitutes a fair and desirable tax system depends upon the positive effects of particular types oftaxes, so before the non-native issues can be discussed, the, positive issues of taxation must beunderstood.

After looking at the positive and normative aspects of tax policy, the political incentivesinvolved in developing tax policy must be explained to provide a fuller understanding about howtax policy is designed. The positive principles of taxation discussed in this chapter can be usedas a foundation for understanding the effects of different types of taxes and the process by whichtax policy is determined.

TAX SHIFTING

The principles of tax shifting apply to all types of taxes, but, for purposes of simplicity, they willbe examined first within the framework of a unit tax, which is a tax charged per unit of a goodexchanged. For example, cigarette taxes typically are applied as a certain amount per pack of

cigarettes, taxes on beer are set as a fixed amount per can, and gasoline is taxed at a certainamount per gallon. In each case, the amount of tax due is based on the number of units sold. Bycontrast, these taxes could be set as ad valorem taxes, which would be based on the dollar valueof the goods sold. For example, an ad valorem tax might be 12 percent of the value of beer sold,whereas a unit tax might be 10 cents per can of beer sold. A retail sales tax, which is calculatedas a percentage of retail sales, is always a type of ad valorem tax, but excise taxes, which aretaxes placed on particular types of goods, can be either unit or ad valorem taxes.


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A Unit Tax Placed on Suppliers

What will happen if a unit tax is placed on the suppliers of a good produced in a competitivemarket? This situation is illustrated in figure 10.1, which depicts supply curve S, demand curveD, equilibrium price P*, and quantity without a tax Q*. Because suppliers have to pay a unit tax

on every unit of the good they sell, each unit is more costly by the amount of the tax, whichshifts the supply curve up by that amount. The new supply curve is labeled S + Tax, with thearrow between S and S + Tax indicating that the curves differ by the amount of the tax. Giventhe tax and the resulting new supply curve, the price rises to Pd and the quantity produceddeclines to Q', determined by the intersection of the demand curve D with the new supply curveS + Tax. Just as one might expect, when a tax is placed on the supplier in the market, the pricegoes up and demanders end up bearing some of the burden of the tax.

Note, however, that the price does not go up by the full amount of the tax. The tax is thedistance between S and S + Tax, but the distance from P* to Pd is less than the tax. Tracingdown from the intersection of S + Tax and D to the old supply curve S gives the total amount ofthe tax, which means that the revenue per unit left for the supplier after the supplier pays the taxis Ps. That is, Ps is the price per unit that goes to the supplier after the tax is paid. This means

that although the tax is initially placed on the supplier, part of the tax burden is shifted to thedemanders in the form of a higher price and the rest of the tax ends up being paid by suppliers.This phenomenon is known as tax shifting because although the tax is initially placed on thesuppliers, some of the tax is shifted to demanders. The arrow drawn up from P* shows theproportion of the tax home by demanders, while the arrow pointing down from P* shows theproportion of the tax home by suppliers. These proportions will vary depending upon theelasticities of supply and demand, which will be discussed in more detail later in the chapter.


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A Unit Tax Placed on Demanders

Now consider the effect if an excise tax of the same amount per unit is placed on demanders inthe market rather than on suppliers. This is illustrated in figure 10.2. Here, the supply anddemand curves are the same as in figure 10.1, but the excise tax causes the demand curve to shiftdownward to DCTax. When purchasing a good, demanders are concerned with the total pricethey have to pay, so if a tax is placed on a good, their demand will fall by the amount of the tax.Thus, the difference between D and DCTax is the amount of the tax.

With the new demand curve, the equilibrium price is Ps, and the new equilibrium quantityis Q', determined by the intersection of the new supply and demand curves, S and DCTax. Themarket price falls from P* to Ps, which shifts some of the tax originally placed on the demandersto the suppliers. But while demanders pay Ps to suppliers, they must also pay the tax, which isthe difference between DCTax and D. Tracing up from the intersection of S and DCTax to Dshows the amount of the tax, and demanders end up paying Pdfor the good, including both theamount the pay suppliers and the amount they pay in tax. As in figure 10.1, the arrow in figure10.2 drawn up from P* indicates the proportion of the tax paid by demanders and the arrowdrawn from P* indicates the proportion paid by suppliers.

A Tax on Suppliers versus a Tax on Demanders

As figures 10.1 and 10.2 illustrates, a tax placed on suppliers in market can be partially shifted todemanders and a tax placed on demanders can be partially shifted to supplies, so that in eithercase, suppliers and demanders end up sharing the burden of the tax. What difference does itmake, then, if the tax is placed on the suppliers or on the demanders in the market? Thisquestion is addressed in figure 10.3, which uses the S and D curves from figures 10.1 and 10.2, S


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+ Tax curve from figure 10.1, and the DCTax curve from figures 10.2. In effect, figure 10.3 is acomposite of figures 10.1 and 10.2 to see what differences there are in the two cases.

The distance between S and S + Tax is the same as the distance between D and DCTaxbecause both are equal to the amount of the tax. Thus, the heavy arrow in figure 10.3 shows theamount of the tax in both cases. Note that the supply curve shifts up in the first case by the same

amount that the demand curve shifts down in the second case. This means that Pd in figure 10.1is the same as Pdin figure 10.2 and that Psis the same in figure 10.1 as Ps in figure 10.2. In bothcases, the amount paid by the demander, including the tax, is the same regardless of whom thetax is initially placed upon, and the amount received by the supplier after the tax is paid is thesame regardless of the initial placement of the tax.

Thus, it makes no difference whether the tax is placed on the suppliers or the demandersin a particular market. Each ends up bearing the same tax burden no matter who is taxedinitially. However, the tax paid by the suppliers usually will not equal the tax paid by demandersbecause the proportion of the tax paid by each group will depend upon the relative elasticities ofsupply and demand. The group upon whom the tax is initially placed is said to receive the impactof the tax, but, once the tax is implemented, this analysis shows that the burden of the tax can be

shifted to others. The ultimate burden of the tax, after shifting has taken place, is called theincidence of the tax. This analysis shows that the impact of a tax and the incidence of a tax canbe substantially different.

This analysis shows that the actual burden of a tax may be different from the legalassignment of a tax. For example, consumers may be charged a sales tax, but some of this taxmight ultimately be home by suppliers. Likewise, the Social Security payroll tax nominally isshared evenly between employers and employees, but because the employees are suppliers oflabor and the employers are demanders, the actual burden of the tax would be the same whether


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the entire tax was paid by the employees, whether it was paid by employers, or whether it wassplit between them as it is now. Changing the impact of this tax will not change its incidence.Regardless of what the government says, the laws of supply and demand determine whoultimately bears the burden of a tax.

ELASTICITIES AND TAX INCIDENCE

The preceding analysis shows that regardless of which side of the market a tax is initially placedupon, the proportion of the tax ultimately home by suppliers and demanders will remain thesame. What those proportions will be is determined by the relative elasticities of supply anddemand in the taxed market. The effects of elasticities on tax incidence can be summarized asfollows. In general, the more elastic the schedule, all other things held equal, the more theburden of the tax will fall on the other side of the market. For example, the more elastic thedemand curve, the smaller the proportion of the tax paid by demanders and the larger theproportion paid by suppliers. Conversely, the more elastic the supply curve, the greater theproportion of the tax that will be shifted to demanders. In the extreme case of a perfectlyinelastic supply curve, the entire tax will be home by suppliers. For a perfectly elastic supplycurve, the entire tax will be shifted to demanders. These ideas can be illustrated graphically.

Figure 10.4 resembles figure 10.1 in that it shows a tax placed on suppliers in a market.In figure 10.4, DE is a relatively elastic demand curve, and D1 is a relatively inelastic demandcurve. Figure 10.4 compares the effects of an identical tax on suppliers using the two demandcurves to show what difference the elasticity of demand makes. For DE, the burden of taxationcan be found, as in the previous section, by adding the amount of the tax to the supply curve.


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With demand curve DE, the quantity exchanged is reduced to QE, at the intersection of DE and S+ Tax, and the tax is represented by the arrow closest to the P axis. If, instead, the demand in themarket was the more inelastic demand D1, the quantity exchanged will be Ql, where D1intersectsS + Tax, and the tax is represented by the arrow farther away from the P axis. Recall that itwould make no difference if we put the tax on the demanders instead of the suppliers, so the

effects of the elasticity of demand are the same regardless of the initial impact of the tax.A comparison of these two cases shows two things. First, the more elastic the demandcurve, the more the quantity exchanged is reduced. The implications of this will be discussedshortly. Second, the more elastic the demand curve, the greater the share of the tax paid bysuppliers and the smaller the share paid by demanders. This illustrates the general principle thatthe more elastic the schedule, the greater the percentage of the tax that is borne by the other sideof the market. The same thing will be true on the supply side of the market. The reader isinvited to draw a graph like figure 10.4, but with a more elastic and less elastic supply curve, toverify that the more elastic the supply curve, the greater the proportion of the tax that is home bydemanders.

Perfectly Elastic or Perfectly Inelastic Supply

Figures 10.5 and 10.6 show two extreme cases. In figure 10.5, the supply curve is perfectlyinelastic, representing some good for which there will always be a fixed supply on the market.With a perfectly inelastic supply curve, a tax can be put on the demanders, but the entire tax willbe shifted to suppliers. In this case, the market price does not shift as a result of the tax, and P*= Pd. Note also that when the supply curve is perfectly inelastic, the quantity exchanged is notaffected by the tax. The same principle holds for the other side of the market. If the demandcurve is perfectly inelastic, the entire tax will be home by demanders, and the quantityexchanged will not be affected.


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Figure 10.6 illustrates the other extremeCa perfectly elastic supply curve. In this case,the entire tax is home by demanders. With the entire tax shifted to the demand side of themarket, P* = Ps, and the price paid by demanders, including the tax, rises by the full amount ofthe tax. The reader can verify that the same would hold true for a perfectly elastic demand curve.With perfectly elastic demand, suppliers will bear the entire burden of the tax. The case ofperfectly elastic supply is relevant to competitive industries characterized by constant costsbecause the long-run industry supply curve will be perfectly elastic. In this case, whether a tax isput on suppliers or demanders in a competitive constant-cost industry, in the long run demandersend up bearing the entire burden of the tax.

These conclusions make intuitive sense if one thinks about them. An inelastic supply ordemand schedule means that the suppliers or demanders are unwilling to substitute out of thegood in question. If this is so, then the group can do little to avoid a tax on the good because theinelastic schedule implies that it will not alter its quantity much in response to a change in price.Conversely, an elastic supply or demand schedule means that the group is willing to forgosupplying or demanding the good in question if the price changes adversely. In this case, to keepthe elastic suppliers or demanders from leaving the market, the other side of the market has tobear most of the burden of the tax. Simply stated, the more willing the group in question is tosubstitute out of the taxed good, the more able it is to force the other side of the market to bearthe burden of the tax.

Shifts in the Tax Burden

The general principles just depicted graphically can also be illustrated algebraically. In figure10.1 (or any of the other figures), the burden of the tax home by demanders will be Pd- P*, whilethe burden placed on suppliers will be P* - P. Thus, the ratio of the demanders' share of the tax


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to the suppliers will be (Pd - P*)/(P* - Ps), which is the ratio of the change in the demandersprice paid to the change in the suppliers price received after the tax is paid. Both the numeratorand denominator of this expression can be divided by (Q*-Q'), which is the change in thequantity exchanged, without changing the ratio, to yield

(Pd- P*)/(Q* - Q')(P* - Ps)/(Q* - Q')

This expression is the ratio of the slope of the supply curve to the slope of the demand curve,which means that the ratio of the burden of the tax home by demanders to the burden home bysuppliers will be equal to the ratio of the absolute values of the slopes of the demand curve andthe supply curve.

Although no general relationship exists between the slope of a curve and its elasticity,when two curves pass through the same point (as, for example, the demand curves in figure10.4), the flatter curve is the more elastic. Thus, the more elastic the curve is, the greater theshare of the burden home by the other side of the market. Furthermore, at the point ofintersection, the ratio of the slopes will be equal to the ratio of the elasticities, so that for small

changes, the ratio of the burden home by suppliers to the burden home by demanders will be theratio of the elasticity of supply to the elasticity of demand. Economists often prefer to think interms of elasticities rather than slopes, but we should note that the precise relationship is betweenthe ratio of the slopes of the curves and the share, of the tax ultimately home by each side of themarket.1

To summarize, taxes placed on one group in an economy can be shifted through themarket to other groups so that the individuals on whom a tax is initially placed will notnecessarily be the ones who ultimately bear the burden of the tax. More specifically, the moreelastic a supply or demand schedule is, the greater will be the proportion of the tax that can beshifted to the other side of the market. But the proportion of the tax home by demanders will bethe same regardless of whether the tax is initially levied on suppliers or demanders, and the same

will be true of suppliers. Finally, the ratio of the demanders burden to the suppliers' burden willbe equal to the ratio of the slopes of the supply and demand curves.

These principles of taxation were illustrated in a simple framework, but the basicprinciples apply to conditions in a more complex world. For example, workers supply be labor tofirms, and firms also buy inputs from other firms. Thus, if a tax is placed on away a firm, that taxcan be shifted backward to the firm's suppliers, including its workers, whom and forward to thefirms demanders-its customers. Thus, it is very unlikely that the party on whom a tax is initiallylevied will bear the entire burden of the tax, and it may even be able to shift the entire burden ofthe tax to other parties. The principles just discussed will be very useful in future chapters whenthe effects of specific taxes are analyzed.

THE WELFARE COST OF TAXATION

The welfare cost of taxation is sometimes referred to as the excess burden of taxation or thedeadweight loss of taxation. All three terms mean the same thing. The welfare cost of taxationarises because the taxpayers not only must pay the tax to the government but also will alter theirbehavior in response to a tax to avoid the tax to some degree. The cost involved in behavingdifferently to try to avoid the tax results in a burden on the taxpayer over and above the dollaramount of the tax paid, so it is referred to as an excess burden. There is an excess burden because


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taxpayers would have been better off if they simply could have paid the same amount in taxeswithout having to alter their behavior than they are when the tax also pushes them to behavedifferently.

For example, suppose that the government decides to raise more revenue by placing a taxon gasoline. Taxpayers will be worse off for two reasons. First, they must pay the tax every

time they purchase gasoline. Second, the tax will cause the price of gasoline to rise, whichcauses consumers to reduce their consumption of gasoline. This means that the tax not onlycollects revenue, but it also alters consumers consumption bundles away from what they thoughtwere optimal to consume without the tax. The change in consumption imposes the excessburden on consumers because it gives them an incentive to consume a less-preferred mix ofgoods, lowering their utility in the process. Recall that when a tax is levied in a market, thequantity exchanged in that market declines, and the substitution out of the taxed good isresponsible for the welfare cost of taxation.

This concept is illustrated graphically in figure 10.7, which closely resembles the otherfigures in the chapter. The tax per unit is Pd - Ps, as in the earlier examples. The quantityexchanged is Q' after the tax is imposed, so the amount of tax collected is (Pd - Ps) X Q', the area

of the shaded rectangle in figure 10.7. For example, if there is a 10 cent per gallon tax ongasoline, and 1,000 gallons are sold, then the total tax collected would be the 10 cent tax pergallon times the 1,000 gallons sold, or $100. The tax per unit in figure 10.7 is (Pd- Ps,), whichcorresponds to the 10 cent per gallon tax, and Q' is the quantity sold. The area of a rectangle isits base times height, and the base of the shaded rectangle is the quantity sold while its height isthe tax per unit, making the shaded area a graphical representation of the amount of tax revenuecollected from the tax.


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The excess burden of the tax results from the decline in consumption of the taxed good fromQ* to Q'. The tax prevents those units from being exchanged, so the net benefits to buyers andsellers from those lost exchanges will not be realized. The welfare cost of the reduction in outputfrom Q* to Q' can be calculated by taking the value to buyers that would have been realized fromconsuming additional units and subtracting the opportunity cost to sellers from producing the

additional units. Using the demand curve as a measure of the marginal gain to consumers fromconsuming additional units of the good and the supply curve as a measure of the opportunity costof producing the good, the net gain that could have been produced from the units between Q' andQ* is the area in the shaded triangle between the demand and supply curves. This trianglerepresents the dollar value of the burden of taxation resulting from the altered behavior becauseof the tax, in the same way that the shaded rectangle represents the dollar value of the taxrevenues collected. Considering the payment of taxes as a burden, this welfare loss is an excessburden of taxation. That excess burden exists because the tax alters peoples behavior inaddition to collecting revenue from them.

Within this framework, consider the costs of taxation to taxpayers. The shaded areamarked Tax in figure 10.7 represents the amount of taxes paid by the taxpayers in this market.

This is a cost to the taxpayers, but the revenues from this tax are then used to pay for publicsector goods and services. The more darkly shaded area marked Excess Burden of Taxrepresents the cost to taxpayers in terms of foregone output in this market. Output level Q*would have been produced without the tax, but the tax alters peoples behavior in the market andcauses Q' to be produced. This is a cost to the taxpayers just as much as the dollar amount of thetaxes they pay, but whereas the revenues from the tax can be used to pay for public sector output,the cost of the excess burden is simply lost. Thus, the government produces output thatpresumably has some social value in exchange for the revenues it collects, but the total tax costof government output is the dollar expenditure plus the excess burden associated with the raisingof the tax revenue.

The Excess Burden as a Cost of Taxation

Because the excess burden represents one of the costs of taxation, it should be taken into accountwhen calculating the total cost of taxation to finance activities in the public sector. The tax withthe minimum excess burden is most desirable from an efficiency standpoint because it producesthe least social cost for the revenues it raises. To minimize the social cost of taxation, one of thegoals of tax policy is to minimize the excess burden of the tax system.

A look back at figure 10.4 can help illustrate how this might be done. Note that when atax is placed on a good with a more elastic demand, the quantity exchanged falls more than whenthe tax is placed on the good with the less elastic demand. Thus, placing, a given tax on a goodwith a more inelastic demand tends to minimize the excess burden of the tax. This becomes evenmore obvious in the extreme case depicted in figure 10.5. In that case, when the supply curve is

perfectly inelastic, the quantity exchanged is not affected by the tax, so the tax causes no excessburden. In general, the excess burden of a tax can be minimized by placing larger taxes on goodswith very inelastic demand or supply schedules. When supply or demand is inelastic, the groupwith the inelastic schedule will not alter its behavior appreciably no matter what happens to theprice of the good. If the tax does not affect individuals behavior, there will not be an excessburden.


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Lump Sum Taxes

A tax that completely eliminates the excess burden of taxation is called a lump sum tax. Theamount of a lump sum tax would not vary no matter what an individual does, so there would beno way taxpayers could alter their behavior to avoid the tax. The simplest example of a lump

sum tax is a levy of a certain amount that would have to be paid by every individual at the timethat the tax was announced. For example, the government could announce that as of today,everyone owes the government a tax payment of $1,000, with no exceptions permitted. Becausethere would be no way to avoid paying the tax, the tax would have no effect on the behavior ofpeople (except that they would have to come up with the money to pay the tax), which meansthat it would have no excess burden. If there is no action people could take to reduce their taxburden, then the tax has no excess burden. A lump sum tax is ideal from an efficiency standpointbecause it minimizes the excess burden of taxation.

A lump sum tax might be held as a theoretical ideal of an efficient tax, but it is difficult toconceive of how lump sum taxes could be applied in the real world. For example, if thehypothetical $1,000 tax were extended so that from now on everyone had to pay a tax of $1,000

every year in the future, it would be in effect a tax on having children because children could notbe expected to earn their own money to pay the tax. An income tax gives people an incentive toearn less income and take more leisure, and a property tax gives people an incentive to minimizeimprovements to the value of their property. Indeed, it is difficult to think of a tax that will notcause people to alter their behavior in some way to avoid the tax.

A tax in a market with a completely inelastic supply or demand could act like a lump sumtax if it signified that people would never alter the quantity supplied or demanded of the good-inother words, if the good really were of fixed supply or if demanders would always demand aconstant amount under any circumstances. Although a tax on such a good might qualify as alump sum tax, no such fixed supply or demand for a good actually exists. And for many goodsthat have relatively inelastic demands, there is frequently a reluctance to tax them for reasons of

equity. Medical care is often cited as a good with relatively inelastic demand, yet medicalservices and drugs tend not to be taxed at all so as not to place an additional burden on those whoneed the care. Food is another category of goods that have a relatively inelastic demand, yet inmany states there is no sales tax on food, again for equity reasons.

In general, goods we think of as necessities have relatively inelastic demands, yet it isargued that necessities should not be taxed for reasons of fairness. Conversely, luxury goodshave relatively elastic demands, yet they are typically taxed at higher rates, again for reasons offairness. Thus, in the attempt to minimize the excess burden of taxation, equity issues oftenconflict with efficiency issues. From an efficiency standpoint, the best tax is one with theminimum excess burden because the tax imposes the lowest total cost on an economy for a givenamount of revenue raised.

EXCESS BURDEN AND INDIVIDUAL CHOICE

The principle of the welfare cost of taxation can also be illustrated with indifference curves toshow how the excess burden of taxation makes individuals worse off than if a lump sum is used.Consider the individual whose utility function is depicted in figure 10.8. The individual is facedwith the budget constraint X1Y1, without a tax and chooses to consume the combination of X andY given by point A. When a tax is placed on good Y, the budget constraint rotates inward to


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budget constraint X1Y1N. At this new budget constraint, the individual can consume the sameamount of X as before the tax on Y if the individual consumes only good X. However, theamount of Y that the individual can consume if he consumes only Y will fall as a result of thetax. By considering the tax in this way, it is easy to see how the budget constraint would rotateto illustrate a tax on one of the goods. With the tax placed on good Y, the slope of the budget

constraint has changed, and because the slope of the budget constraint depicts relative prices, thenew slope illustrates that with the tax on good Y, the price of Y relative to X has risen.

With this tax placed on good Y, the individual will now consume the combination of Xand Y given by point B, where the individual's indifference curve is tangent to budget constraintX1Y1'. By being on a lower indifference curve, the individual is worse off at point B than atpoint A for two reasons. First, the individual is worse off because of the amount of the tax paidand, second, because the tax causes the individuals behavior to change to try to avoid payingsome of the tax. To avoid paying the tax associated with good Y, the individual consumes lessof Y. From the consumer's standpoint, the excess burden arises because the tax increases therelative price of the taxed good, Y.

If instead of levying a tax on good Y, a lump sum tax is applied, the same amount of taxcan be collected without the excess burden. The amount of the tax collected can be measured interms of either good X or good Y, but in either case it is the distance from point B to the originalbudget constraint. A new budget constraint, X2Y2, can be drawn running through point B butparallel to the original budget constraint. Along this new budget constraint the same amount oftax can be collected as at point B, but relative prices remain the same as along the originalbudget constraint.


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The new budget constraint depicts the effect of a lump sum tax on the individual thatraises the same amount of revenue as the tax on good Y. The utility-maximizing point for theindividual point is C. Because point C is on a higher indifference curve than point B, theindividual is better off with the lump sum tax than with the tax on good Y. The difference in theindividuals well-being is the difference in utility between the indifference curve at point B and

the higher indifference curve at point C. Note that at point C, the individual consumes more Ythan at point B, where Y is taxed. This illustrates that the individual substitutes out of the taxedgood because its price is higher. The difference in the individual's utility at point C whencompared with point B is the excess burden of the tax on Y, because it is the utility loss theindividual suffers because the tax pushes the individual to change his behavior to avoid the tax.

The excess burden exists because a tax, in addition to taking tax revenue away from thetaxpayer, discourages the consumption of the taxed good. The taxpayer is better off if the taxsimply extracts the revenue without altering the relative prices facing the individual. Comparethe individuals situation at point B and point C. The tax revenue is the same in both cases, butthe relative price of good Y is increased on budget constraint X1Y1'. This makes the individualworse off because the tax gives the individual the incentive to substitute out of the consumption

of good Y, creating the excess burden. At point C, the lump sum tax allows the individual topurchase X and Y at their original relative prices, so the individual consumes more of good Y.The individual is better off because the consumption choices are not distorted by the lump sumtax. The efficiency characteristics of a lump sum tax are so attractive that it is too bad lump sumtaxation is not more feasible in the real world.

Inelastic Labor Supply and the Welfare Cost of an Income Tax

In considering the excess burden of a tax, we have argued that if either the supply or demandcurve for a good is completely inelastic, there will be no excess burden from a tax in that market.This is true because individuals in the market will not alter their supply or demand quantity

under any circumstances. In other words, they will not substitute out of the taxed market. Thissection considers that idea in more detail to show that the unwillingness to substitute is thecrucial element in the argument. A perfectly inelastic schedule might result from offsettingincome and substitution effects, however, and it is the substitution effect that is the keycomponent in minimizing the excess burden. If there are offsetting income and substitutioneffects, the substitution effect still creates an excess burden. If there is no substitution effect, thenthere is no excess burden.

This can be illustrated by viewing the effect of an income tax on labor supply. Considerthe reaction of an individual to an increase in an income tax. The higher tax makes it morecostly to supply labor relative to taking leisure time, so the individual will want to substitute outof work and into leisure. But the higher tax will also mean that the individual has less income

and will want to work harder to make up for the income that has been taxed away. In this case,while the substitution effect makes it relatively more attractive not to work, the income effectcauses the individual to want to work more. The two effects work in opposite directions.

It is possible that the individual might work the same amount with or without the incometax, so the individuals labor supply curve will be perfectly inelastic. However, because there isstill a substitution effect, the individual will still be better off with a lump sum tax than with a taxon income. This can be illustrated in figure 10.9, which is similar to figure 10.8. Here theindividual worker has twenty-four hours a day to allocate to either work, which earns income, or


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leisure. The amount of leisure time is recorded on the horizontal axis, and the slope of thebudget constraint shows the rate at which leisure time can be transformed into income throughworking. With no income tax, the individual locates at point A, just as in the previous figure.

An income tax raises the relative price of earning income because the individual mustnow work more hours to take home the same amount of income, so the budget constraint rotates

inward, and the individual chooses to locate at point B. Note that at both points A and B, theindividual chooses sixteen hours of leisure a day and works eight hours a day. Because theindividual works the same amount regardless of the income received for working, theindividuals labor supply curve is completely inelastic.

However, in this case the inelastic labor supply curve is due to offsetting income andsubstitution effects. If the individual pays a lump sum tax designed to raise the same amount ofrevenue as the income tax, the budget constraint for the lump sum tax will pass through point Bbut will be parallel to the original budget constraint, and the individual will choose to be at pointC. At point C, the individual works more (takes less leisure) and the individuals after-taxincome rises from I1 to I2. As in figure 10.8, the excess burden of the income tax is thedifference in the welfare of the individual at point B as compared with point C. Because the

individual is on a higher indifference curve at point C, the individual is better off with the Jumpsum tax than with the income tax. It is apparent from looking at figure 10.9 that although theindividual does have a perfectly inelastic labor supply curve, the tax does cause the individual tosubstitute out of income, which is taxed, and into untaxed leisure. The individual works less atpoint B than at point C.


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Utility Functions and Excess Burden

A perfectly inelastic supply or demand curve implies that there will be no excess burden from atax in that market because the tax does not cause people to substitute out of the taxed good, sothe tax does not alter peoples behavior by changing their consumption patterns. Consumptionchanges only because people have less income and not because they substitute out of the goodbeing taxed. However, the example in the preceding section shows that a perfectly inelasticschedule can result from offsetting income and substitution effects, giving rise to an excessburden resulting from the substitution effect. A tax on the good causes people to substitute out ofthe taxed good. People actually do consume less because of the tax, although they consume morebecause of the reduced income. Thus, as long as there is some substitution effect in response to achange in the relative price of a good, there will be an excess burden from a tax in that market.

For a tax to have no excess burden, there must be no substitution effect that causesindividuals to substitute away from the taxed good because of its higher relative price. That caseis diagrammed in figure 10.10. The original budget constraint is X1Y1, and because of a tax ongood Y, the budget line shifts to X1Y1', and the individual consumes at point A. If the individualis taxed the same amount but relative prices are unchanged, the budget line would be X2 Y2. Forthere to be no substitution effect, the individual would still have to consume at point A, so theindividual's indifference curves must be 90 degree angles, like the indifference curve labeled Uo.In this case there is no substitution effect, so there is no excess burden. In figure 10.10, noindifference curve was drawn on original budget constraint X1Yl. Can you draw in theindifference curve on the original budget line under the assumption that the individual alwaysconsumes the same amount of Y no matter what the individual's income or relative prices? Canyou draw in an indifference curve on the original budget line under the alternative assumptionthat the individual does not substitute because of relative price changes, but that the good is anormal good and that consumption will rise when income rises?


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Although it is an interesting exercise to try to draw in the indifference curve on budgetconstraint X1Yl, that indifference curve is not relevant to the excess burden of taxation. Theexcess burden arises because of the substitution effect alone, and the income effect is irrelevant.As figure 10.10 illustrates, people must have very unusual preferences for a tax to have no excessburden, but the figure also allows us to imagine what makes the excess burden larger or smaller.

The closer indifference curves are to right angles, the less people will substitute because of pricechanges, which will reduce the excess burden. Individuals will substitute more whenindifference curves have little curvature, which will make the excess burden larger.

MINIMIZING THE EXCESS BURDEN OF TAXATION

This chapter deals mainly with the theory of taxation rather than specific applications of taxprinciples. Nevertheless, the reader should have a sense of the general magnitude of the welfarecost of taxation. Clearly, the tax system does influence the behavior of individuals, whether bydiscouraging the consumption of some goods relative to others, influencing an individualschoice of occupation, or altering a corporations production decisions.

One study has estimated that the welfare cost of the tax system in the United States is

between 13 and 24 cents per dollar of revenue raised.2 This is hardly an insignificant figure.Because government spending accounts for more than one-third of GDP, the results of this studysuggest that the welfare cost of the tax system is at least 5 percent of GDP. Given the magnitudeof the excess burden of taxation, there is good reason to want to try to minimize it.

The Ramsey Rule

The Ramsey rule, named after its originator, is a theoretical proposition explaining how theexcess burden of taxation can be minimized for a given amount of tax revenue to be raised.

3 The

Ramsey rule states that to minimize the excess burden of taxation, taxes should be placed ongoods in inverse proportion to the elasticity of demand for the goods. In other words, if the tax

on a good is represented by T and its elasticity of demand by E, then the condition defining theoptimal tax on goods 1 and 2 to minimize their combined excess burden can be stated as

TI/T2 = E2/El

Proving this proposition in a formal manner is a complex undertaking, but the logic behind it isrelatively straightforward.4

We have already seen that the more elastic the demand for a good is, the greater will bethe excess burden from a tax on that good. This implies that taxes should be placed on goodswith inelastic demands, assuming that supply elasticities are the same. Indeed, the Ramsey rulesummarized in the equation just given does specify that the larger tax is placed on the good with

the more inelastic demand and the smaller tax on the good with the more elastic demand. Thereason why the tax is shared between the goods rather than placed all on the most inelastic goodto minimize the excess burden is that as a tax becomes larger, its excess burden increases morerapidly than the size of the tax. This can be illustrated in figure 10.11

Figure 10.11 shows the marginal increase in the excess burden of taxation as a result of atax increase. For the sake of simplicity, we will consider a market in which the supply curve isassumed to be perfectly elastic. (This would be the case in the long run in a competitive constant-cost industry.) With equilibrium price P* and quantity Q* without the tax, a tax equal to T is


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placed on the good. The price rises to P* + T and the quantity falls to Q'. The amount of the taxcollected is the rectangle with the vertical side from P* to P* + T, shown by the short arrow, andhorizontal side from the origin to Q'. The excess burden is represented by the small shadedtriangle between Q' and Q*.

Now assume that the tax rate is doubled from T per unit to 2T per unit, as shown by thelonger arrow. However, because the higher tax will lead to a lower quantity being exchanged,the tax revenue will less than double as a result of a doubling of the tax rate. Note that the darklyshaded square, which was part of the tax revenue collected with the smaller tax, is no longercollected because the quantity exchanged in the market has fallen from Q' to Q". But while thetax revenue has not doubled, the excess burden of the tax has more than doubled, and nowencompasses the entire shaded area.

As figure 10.11 suggests, when a tax becomes larger, the excess burden from increasingthat tax grows faster than the corresponding tax revenue. Therefore, even though it makes senseto place larger taxes on goods with more inelastic demands, there is a trade-off between placingever-larger taxes on inelastic goods and placing some smaller taxes on goods with more elastic

demands. How should these taxes be placed to minimize the excess burden? This is where theRamsey rule comes in. The excess burden of the tax is minimized when taxes are levied ininverse proportion to the elasticities of demands for the goods.

This does represent a bit of an oversimplification for several reasons. First, we haveneglected to consider the elasticities of supply for the goods, but it should be evident that thesame type of relationship will hold. Also, we have assumed that goods are unrelated inconsumption (neither complements or substitutes), so that a tax on one good will not affect thedemand for another good. But these simplifying assumptions should not detract from an


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understanding of the underlying principle of the Ramsey rule, which is that to minimize theexcess burden of taxation, goods with relatively inelastic demands should be taxed more heavilythan goods with relatively elastic demands.

The Marginal Cost of Public Spending

The Ramsey rule gives the optimal mix of taxes for a given level of taxes. The principle behindthe Ramsey rule is that when a tax is placed on any given market, the excess burden of the taxincreases more than proportionally with the tax. With a linear demand curve, for example, adoubling of a tax rate produces four times the excess burden but less than twice the tax revenue.From this it follows that the cost of public projects exceeds the dollar amount spent on them, butit also follows that the larger government spending is already, the greater will be the cost ofincreasing government spending by a given amount.

Refer again to figure 10.11 for an illustration of this point. Assume that a public projectis proposed that will cost Q' T to complete, which will be raised by a tax in the market in figure10.11. If there are no taxes currently in that market, the cost of the project will be Q' T plus theexcess burden represented y the small shaded triangle between Q' and Q*. The excess burdenmust be included as one of the costs of undertaking the project. Now assume that the marketalready has tax T, and the project proposal suggests raising the tax to 2T. We have already seenthat increasing the tax from T to 2T will not double the revenue, but the marginal excess burdenis the shaded rectangle plus the shaded triangle between Q" and Q'. Compare the tax revenueand marginal excess burden from initially placing tax T on the market with increasing tax T to2T. The increase from T to 2T raises less additional revenue than the initial tax T, but themarginal excess burden is three times as large. The higher tax rates are already, the greater willbe the marginal excess burden of any additional taxes.5

One implication of this is that a project that might be justified based on a comparison ofthe dollar outlays of the project and the projected benefits of the project might not be cost-effective if the excess burden of taxation is included, and the higher taxes already are, the morelikely it is that the excess burden will be sufficiently high to cause a project not to be cost-effective. Some projects that would be justified on the basis that the benefits exceed the costs ifthe government were spending 15 percent of GDP will not be justified if the government isspending 35 percent of GDP, simply because the higher excess burden increases the social costof the project.6

ADDITIONAL COSTS OF THE TAX SYSTEM

It should be apparent by now that there are costs to taxation over and above the dollar amount oftaxes paid. The excess burden is one example, but there are other costs imposed by taxation aswell, including compliance costs, administrative costs, and political costs.

Compliance Costs

Anyone who has filled out an income tax form will be familiar with compliance costs, which arethe costs imposed on taxpayers to comply with the tax laws. Collecting and keeping records is abig part of compliance costs, as are the costs involved in filling out tax forms and filing taxes. Ifa taxpayer is audited, additional compliance costs are incurred in demonstrating to thegovernment that the taxpayer indeed is in compliance.

7


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Many individuals, and almost all businesses, find the tax laws so complex that they hireaccountants and tax lawyers to help them comply with the tax laws and to help find ways ofminimizing their tax burdens. The largest compliance costs are home in conjunction with theincome tax because it is the most complicated tax to compute, but even relatively simple taxes,such as the sales tax, have compliance costs.

Although compliance costs are difficult to measure, one study has estimated thatcompliance costs for the individual income tax in the United States are between 5 percent and 7percent of the revenue raised from the tax.8 Between 5 percent and 10 percent of compliancecosts are the result of taxpayers hiring professionals for tax assistance, but most of the costs aredue to the taxpayers time involved in complying with tax laws. The U.S. personal income taxuses about two billion hours yearly of taxpayers' time to comply. Because this includes only thepersonal income tax, it is clear that compliance costs are a significant part of the cost of taxationas a whole.

Administrative Costs

Whereas compliance costs are home by taxpayers, administrative costs are home by thegovernment to collect taxes. For example, the Internal Revenue Service (IRS) must print andmail forms to taxpayers, process the completed returns, and mail refund checks to those who aredue refunds. All these cost the government money. The IRS also has auditors to check ontaxpayer compliance, and the auditing procedure itself is expensive. Records must be kept forany type of tax, so administrative costs include tax collection and record keeping. Althoughadministrative costs are significant, most economists believe that in the United States,compliance costs exceed administrative costs by a considerable margin. That is, it coststaxpayers more money to pay their taxes than it costs the government to collect them.

Political Costs

Another cost associated with the tax system is the political cost home by taxpayers and thegovernment as a result of taxpayers trying to influence tax laws. The tax laws are always subjectto modification, and taxpayers continually attempt to change the tax laws in their favor. Forexample, Realtors have incurred considerable costs hiring lobbyists to try to retain-and, indeed,improve-the home mortgage interest deduction, one of the largest deductions on federal incometax returns. The lobbying effort of Realtors represents a real cost of using the tax system, andtheir efforts have paid off. In the major tax reform act passed in 1986, all personal interestexpenditures were eliminated as deductions from federal taxable income except the homemortgage interest deduction. This is a good example of the welfare cost of rent seeking, whichwas discussed in chapter 9. In this case, rent seeking has taken place to try to secure benefitsthrough the tax system.

Realtors are not alone, of course, in lobbying for favorable tax treatment. Businesseslobby to improve write-offs for depreciation, research and development, and so forth.Individuals who work at home try to modify the tax laws to make it more favorable to deductexpenses for home offices. It is difficult to estimate the political costs to both taxpayers and thegovernment that political activities aimed at influencing tax legislation generate, but, as noted inchapter 9, taxpayers have an incentive to expend up to the amount of the expected value of thechange in the tax law to get legislation passed. Political costs associated with the tax system mustbe substantial.


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EARMARKED TAXES

Earmarked taxes are taxes whose revenues are designated to a particular spending activity. Forexample, tolls collected at a toll bridge may be earmarked toward paying for the bridge, thefederal gasoline tax is earmarked toward the building of highways, and a federal tax on airline

tickets is earmarked toward airport and airway improvements. The largest earmarked tax is theSocial Security payroll tax, which is earmarked toward paying Social Security benefits torecipients. All these taxes are earmarked because the tax revenues from the particular source gotoward a particular spending area.

General Fund Financing versus Earmarking

General fund financing is the alternative to earmarking. With general fund financing, the taxrevenues are placed in a general fund, from which government programs are financed. Forexample, at the federal level, personal and corporate income taxes, and federal taxes from anumber of other sources, are collected and placed in the Treasury, and Congress then allocates

this money out of a general fund to finance expenditures on national defense, education, naturalresources, and other programs. Money is spent on these programs independently of where themoney is raised. As an alternative, the corporate income tax could be earmarked for nationaldefense in the same way that the Social Security payroll tax is earmarked for Social Security, butit is not. With general fund financing, the legislature has much more discretion over howrevenues are spent, whereas with earmarking, the revenues from the earmarked tax must be spenton a particular activity.

As with the taxes on gasoline and airline tickets, earmarked taxes are often used in casesin which the taxed activity is closely related to the ultimate use of the funds. In these cases,earmarked taxes are similar to user charges. However, as the hypothetical Defense Departmentexample suggests, the earmarked tax source need not be closely related to the ultimate

expenditure. Earmarked taxes only must be collected for a specific purpose.Earmarked taxes are most often used at the local level of government. For example,

schools are often funded by a specific portion of the local property tax, though school fundingmethods do vary considerably from state to state. Some states earmark property taxes forschools, while others finance their elementary and secondary education out of the general fund ofa larger budget, such as a city or county. In some areas, a portion of the sales tax could beearmarked for a specific purpose. For example, 1 percent of the sales tax might be earmarkedtoward financing a new courthouse or county jail.

The Advantages and Disadvantages of Earmarking

Funding government programs entirely by earmarked taxes lacks the flexibility of general fundfinancing because a particular tax base may be too small or too unstable to provide the revenuegeneration for a given program that citizens desire. The other side of that problem is that ifrevenues from an earmarked source grow larger than the level of expenditures that would bewarranted, too much might be spent on a particular area, or funds might build up unspent whileother government programs suffer from too little revenue. If citizens are allowed to vote on thelevel of expenditures of various government to decide programs for which taxes are earmarked,they have a much better opportunity to receive the amount of public sector output they find most


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satisfactory. For example, if citizens can vote on the amount of property tax revenue that will gotoward financing public schools, they are more likely to get the level of education they want thanif public schools are financed out of a general fund.

With general fund financing, policymakers will have significant discretion regarding theexpenditures that are made from tax revenues. This might help to increase the efficiency of

expenditures, but, in a political environment, sometimes policymakers can manipulate thebudgetary mix to increase spending on particular programs under general fund financing. Forexample, a city council might desire additional expenditures to improve the offices at city hall,while taxpayers are more interested in police and fire protection. Under general fund financing,it would be possible for the city council to allocate a larger-than-optimal share of the budget tocity hall improvements and a smaller-than-optimal share to police and fire protection. Voterswould then vote for a larger level of government expenditures to get the increased police and fireservices they want, and the city council could then get the money for the office improvementsthat it wants. By skewing the expenditure mix away from those expenditures voters most favor,policymakers can alter expenditures to increase the overall level of expenditures demanded byvoters.9

Earmarked revenue sources provide the benefit of making it clear to taxpayers how muchthey pay for particular activities of government. For example, most taxpayers have a better ideaabout how much the Social Security system costs them than how much they pay for nationaldefense. However, earmarked taxes are also less flexible than general fund financing. Still,earmarking has much to recommend it because the government is required to allocate revenuesto particular expenditures before the fact, making the cost of government clearer to taxpayers.

CONCLUSION

The principles of taxation can be divided into two general groups: positive and normative.Positive principles of taxation examine the effects of taxes on individuals and the economy. Twoimportant positive principles of taxation are tax shifting and the welfare cost of taxation. Taxshifting refers to who ultimately bears the burden of a tax. Taxes initially placed on one groupcan be shifted through the market so that they end up being home by another group. When a taxis placed on a particular market, the ratio of the tax ultimately home by the demanders orsuppliers is equal to the ratio of the slope of the demand curve to the slope of the supply curve.

The welfare loss of taxation, also called the excess burden or deadweight loss of taxation,is the cost a tax places on the economy over and above the tax revenues collected. In addition tocollecting revenue, a tax gives people an incentive to alter their behavior to reduce the amount oftax they pay. When people substitute out of taxed activities, this generates a welfare loss. Theless people are willing to substitute out of a taxed activity, the smaller will be the excess burdenof taxation. Therefore, the excess burden of taxation can be minimized by placing higher taxeson goods with relatively inelastic supplies or demands.

Other positive principles of taxation, such as earmarking of taxes and compliance,administration, and political costs, are also relevant to the evaluation of specific taxes. Thus,these positive principles of taxation will be applied to the analysis of specific taxes when they arediscussed in upcoming chapters. The general principles of taxation discussed in this chapterserve as a foundation for understanding the details of particular taxes that are used in theeconomy. The costs of raising tax revenues are significant as a percentage of the revenuesraised, and one of the goals of the tax system is to be as efficient as possible by minimizing thewelfare costs of taxation.


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Positive principles give us a good foundation for analyzing the tax system, but they onlytell us about the effects of taxes. Tax systems are designed not only to raise revenue efficientlybut also to raise it fairly. Thus, equity in taxation is an important issue. The fairness of a taxsystem can only be evaluated once the actual effects of a tax are understood. For example, wemight arrive at very different conclusions about the fairness of a tax if we did not take account of

the fact that the group that bears the burden of a tax might not be the group upon whom the tax isinitially placed. The next chapter extends the theme of this chapter by examining normativeissues related to tax system is a product of human design, through our political institutions.

QUESTIONS FOR REVIEW AND, DISCUSSION

1. What are the three methods by which the government can finance its expenditures?

2. Explain the difference between a unit tax and an ad valorem tax.

3. What is meant by tax shifting? Who bears the burden of an excise tax placed on the suppliersof a good? Who bears the burden of an excise tax placed on the demanders of a good?

Using a graph, compare the effects of a tax placed on the suppliers of a good with a tax ofthe same magnitude placed on the demanders.

4. Explain what the terms impact and incidence mean with regard to taxes. What determines theimpact of a tax? What determines the incidence?

5. In a market in which an excise tax is levied, how can one compute the ratio of the tax paid bythe suppliers to the tax paid by the demanders?

6. What is meant by the excess burden of taxation? How is the excess burden measured, andwhy does it arise? What can be done to minimize the excess burden of revenue raised by

taxation?

7. What makes a tax efficient? Discuss some of the issues involved in trading off equity andefficiency in the design of tax systems.

8. Can a tax have an excess burden if the supply curve in the market is completely in elastic?Explain, using labor supply as an example. Use your explanation to illustrate exactly whatgives rise to the excess burden of taxation.

9. What is the Ramsey rule? Explain the logic behind the Ramsey rule.

10. Assume that a public project is expected to cost $10 million in direct outlays and is expectedto produce $11 million in benefits. How will the excess burden of taxation affect thedetermination on whether this project wi11 be cost-effective? Is it possible that the projectcould be cost-effective if the government is small but not cost-effective if the government islarger? Explain your answer.

11. What is an earmarked tax? Discuss the advantages and disadvantages of earmarking. Wouldit be feasible to earmark all taxes?


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NOTES FOR CHAPTER 10

1. In Richard A. Musgraves classic treatise, The Theory of Public Finance (New York:McGraw-Hill, 1959), he states that the ratios of the elasticities are equal to the ratios of the

burdens of the tax shares of demanders to suppliers. This is not quite true for the arcelasticity, which would be appropriate for a discrete change of this type.

2. Charles L. Ballard, John B. Shoven, and John Walley, The Total Welfare Cost of the UnitedStates Tax System: A General Equilibrium Approach,National Tax Journal38, no. 2 (June1985): 125-40.

3. Frank P. Ramsey, A Contribution to the Theory of Taxation,Economic Journal37 (1927):47B61.

4. For a more detailed discussion of the Ramsey rule, see Chin W. Yang and Kenneth R. Stitt,

The Ramsey Rule Revisited, Southern Economic Journal 61, no. 3 (January 1995):767B74.

5. This point is made by Edgar K. Browning, The Marginal Cost of Public Funds,Journal ofPolitical Economy84, no. 2 (April 1976): 283B98.

6. Some estimates done in the 1980s suggest, first, that it is difficult to get a precise estimate ofthe excess burden of taxation at the margin but, second, that it would not be unreasonable tobelieve that the marginal excess burden of taxation is 25 percent or more of the amount ofrevenue raised by taxation. See, for examples, Charles L. Ballard, John B. Shoven, and JohnWhalley, General Equilibrium Computations of the Marginal Welfare Costs of Taxes in the

American Economic Review75, no. 1 (March 1985): 128B38; Charles Stuart,Welfare Costs per Dollar of Additional Tax Revenue in the United States, AmericanEconomic Review74, no. 3 (June 1984): 352B62; and Edgar K. Browning, On the MarginalWelfare Cost of Taxation,American Economic Review77, no. 1 (March 1987): 11B23.

7. Joel Slemrod, ed., Why People Pay Taxes: Tax Compliance and Enforcement (Ann Arbor:University of Michigan Press, 1993) discusses these compliance costs and the way in whichthey influence peoples decisions to obey tax laws.

8. Joel Slemrod and Nikki Sorum, The Compliance Cost of the U.S. Individual Income TaxSystem,National Tax Journal37, no. 4 (December 1984): 461B74.

9. This idea is explained in James M. Buchanan, The Economics of Earmarked Taxes,Journal of Political Economy71 no. 5 (October 1963): 457B69.

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02A Holcombe Capitulo 10