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An Introduction to State and Local Public Finance
Thomas A. Garrett and John C. Leatherman

III. Principles of Tax Analysis

State and local governments use a variety of taxes to raise revenues. State governments favor sales taxes, excise taxes and personal income taxes, whereas local governments predominately rely on property taxes. On the surface it appears that raising revenues is a fairly benign process - state and local government officials simply adopt a tax or change an existing rate and the required revenues are obtained. What is missed in this simple process are the impacts tax adoption and changes have on individuals, markets and other government revenues. Effective tax policy requires understanding the basic economics of taxation. This chapter explores the basic principles of tax analysis.

The first section discusses the distributional effects of taxation, focusing primarily on evaluating the burden of taxation on selected groups of individuals. Efficiency concerns are presented next, with a look at the efficiency costs of taxation and the efficiency-equity trade-off. The final section introduces two models of taxation, the Ramsey Rule and the Laffer curve. While both models focus on revenue generation, each model makes different assumptions regarding the motives and goals of governments in raising revenues. Full understanding of this chapter requires some knowledge of microeconomics, calculus and econometrics. The calculus portions can be skipped, however, without a loss of understanding the basic theoretical ideas.

A. Distributional Effects of Taxation - Tax Incidence

Tax incidence is concerned with which groups of individuals are paying a larger percentage of tax revenue than other groups. An important point in tax incidence analysis is that taxes cause changes in individuals’ behavior. Those individuals bearing the ultimate burden of the tax may be different than the individuals on whom the tax was initially levied. The more a group of individuals is willing to change their behavior to avoid the tax, the smaller the burden of taxation will be for those individuals.

i. Single-Market Analysis of Tax Incidence

Evaluating tax incidence is most commonly done using a competitive, single-market framework. Although the impacts of taxation on other markets is ignored here for simplicity, the reader should be aware that changes in one market always have impacts on other markets. Single-market analysis is termed partial equilibrium analysis.

a. A Unit Tax on Buyers and Sellers

Suppose that before the imposition of a tax the gasoline market is in equilibrium and the equilibrium price per gallon is $1.00 and the equilibrium quantity is 1,000 gallons. As will be shown, the economic impact of a tax is the same regardless of whether the tax is levied on buyers or sellers. However, first consider the situation where a tax of $0.30 per gallon is levied on sellers of gasoline. This scenario is shown in Figure 1a.

Initial market equilibrium is shown by point A at the intersection of Demand 0 and Supply0. Imposing a tax on sellers of gasoline causes the supply curve for gasoline to decrease by the amount of the tax. The new supply curve is Supply1, with the distance between Supply0 and Supply1 equal to the amount of tax. With the tax in place, consumers are now paying $1.15 per gallon, an increase of $0.15 per gallon before the tax. Sellers now receive $1.15 per gallon, shown by the intersection of Demand0 and Supply1 at point B. However, sellers are responsible for paying the tax, so the $1.15 received by sellers is the tax inclusive price. As shown by point C, sellers receive only $0.85 per gallon of gasoline after paying the tax. Note that the imposition of the gasoline tax has reduced the quantity of gasoline bought and sold from 1,000 gallons to 900 gallons.

The revenue burden of consumers and sellers is determined by the rectangular areas shown in Figure 1a. Consumers’ share of tax revenue is $135, computed from the area of the top rectangle. Similarly, sellers’ share of tax revenue is also $135, computed from the area of the bottom rectangle. Total tax revenues collected equal $270, which is the sum of the consumers’ share and sellers’ share. In this example both consumers and sellers bear the same revenue burden.

Before proceeding, it is important to note that the above burden on sellers is really a burden on individuals rather than a physical business entity. A burden on sellers may result in lower profits, lower employee wages, etc. So although we say the burden of taxation falls on ‘sellers,’ the reader should realize that the burden really falls on all individuals associated with the taxed business.

The economic impact of the tax is the same regardless of which group is initially taxed. Consider Figure 1b which shows the economic impact of a $0.30 gasoline tax now levied on buyers rather than sellers. Again, the initial equilibrium price of $1.00 per gallon and equilibrium quantity of 1,000 gallons is shown by point A, the intersection of Demand0 and Supply0. Imposing a $0.30 tax on buyers of gasoline decreases the demand for gasoline by the amount of the tax, shown by the new demand curve Demand1. As a result of the tax, sellers now receive $0.85 per gallon, shown by the intersection of Demand1 and Supply0 at point C. Consumers also pay $0.85 per gallon, but this is the tax exclusive price. With the $0.30 tax, consumers ultimately pay $1.15 per gallon ($0.85 plus $0.30 tax). In this case, sellers receive $0.85 per gallon, the same as they received net-of-tax when the tax was levied on sellers. Consumers also pay $0.85 per gallon, but this is net-of-tax. With the tax levied on consumers, consumers must pay $1.15 per gallon, the same price paid when the tax was levied on sellers.

The revenue burden for consumers and suppliers is the same as before. Both consumers and sellers each face a burden of $135, with the total burden again equal to $270. The results from both examples highlight an important aspect of tax incidence - in a competitive market, a unit tax levied on sellers has the same market effects as a unit tax levied on buyers. Thus, the revenue burdens of buyers and sellers will be the same regardless of whom the tax is initially levied upon.

b. A General Rule of Tax Incidence

An important point regarding tax incidence is that those individuals less likely to change their behavior will ultimately bear a greater burden of the tax. The price elasticity characterizes willingness to change behavior.

Figures 2a and 2b illustrate the importance of price elasticity and tax incidence. In Figure 2a, the price elasticity of supply is less than the price elasticity of demand. This is determined by examining the slope of the supply and demand curves - a change in price has a smaller impact on the quantity supplied than it does on the quantity demanded. Using the previous example of a $0.30 gasoline tax levied on suppliers, the imposition of a $0.30 tax per gallon on suppliers results in a final price to consumers of $1.05 and a net-of-tax price received by sellers of $0.75. The quantity of gasoline supplied again falls to 900 gallons. The revenue burden to consumers is now $45 (area of top rectangle), whereas the revenue burden on suppliers is $225 (area of bottom rectangle). Notice that the overall revenue burden is still $270. Because suppliers change their behavior less than consumers, suppliers bear a larger portion of the final tax burden.



Figure 2b considers the case where demand is more inelastic than supply. That is, consumers are less responsive to changes in price than suppliers. The result of a $0.30 tax levied on suppliers reduces the initial supply, resulting in a price to consumers of $1.25. Sellers also receive $1.25, but this is the tax inclusive price. The net-of-tax price received by sellers is now $0.95. The revenue burden to consumers is now $225 and the burden on suppliers is only $45, with the overall revenue burden again remaining the same at $270. Because demand is less responsive to price changes than is supply, consumers will bear a greater portion of the overall tax burden.

The final revenue burden will primarily fall on those individuals less likely to change their behavior in the presence of a price increase. In other words, the group of individuals having a smaller price elasticity of demand or supply will bear the greater burden of taxation.

B. Efficiency

Recall from microeconomics that competitive markets result in an efficient allocation of resources. Efficiency is said to occur when 1) the marginal social benefits of consuming a good are equal to or are greater than the marginal social costs of producing that good, or similarly 2) any additional consumption or production of a good is not possible without making another party worse off. A graphical depiction of efficiency in the market for milk is shown in Figure 3.

The supply curve for a commodity can be equated to the marginal social costs (MSC) of production - it reveals the additional costs for producing additional gallons of milk. As we are considering a competitive market, the price a seller receives is equal to the marginal costs of production. As we are also assuming no spill-over costs to other parties, the marginal cost of production is equal to the marginal social costs of production. Similarly, the demand curve reveals the marginal social benefits of consumption (MSB), or the additional benefits received from consuming additional units of a commodity, with the price reflecting consumers’ willingness to pay for additional units of the commodity. Marginal benefits of consumption decrease due to decreasing marginal utility of consumption.

The equilibrium price for a gallon of milk is $2.00 and the equilibrium quantity is 100 gallons. This is an efficient outcome because MSB = MSC. Any further production over 100 gallons would create a situation where MSC > MSB, suggesting that society should decrease milk production Similarly, any production less than 100 would create a situation where MSB > MSC, suggesting that milk production should be increased. Notice that any other price besides $2.00 is not sustainable in a competitive market. At $3.00 a gallon, quantity supplied (150) exceeds quantity demanded (50), and MSB > MSC. This excess supply puts downward pressure on prices. Likewise, at only $1.00 a gallon, quantity demanded (150) exceeds quantity supplied (50) and again MSB > MSC. Excess demand puts upward pressure on prices. Only at $2.00 is the market in equilibrium, and at this equilibrium the market produces an efficient outcome.

Tax policy often creates market inefficiencies because the tax inclusive price is fixed above the equilibrium price. For example, suppose that in Figure 3 a $1.00 a gallon tax is levied on milk, raising the total price to $3.00 and decreasing the quantity of milk to 50 gallons. With the tax, MSB > MSC. Although society would be better off with increased milk production, the tax prevents this increase in production from occurring. Both consumers and suppliers are harmed by the tax. The loss to consumers is represented by triangle ABD, which shows the loss in consumer surplus - the benefits to society from consumption. Without the tax, the consumer surplus would be the area under the demand curve above the price of $2.00. With the tax, however, consumers lose ABD in consumption. Similarly, the loss to producers is represented by a loss in producer surplus, or the benefits to producers from increased production. Producer surplus in the absence of the tax would be the area below the price of $2.00 and above the supply curve. The loss in producer surplus resulting from the tax is area ACD. The total loss to society is the sum of consumer losses and producer losses and is termed the excess burden of taxation, or deadweight loss of taxation.

The reader should see the relationship between efficiency and tax incidence. If a tax does not force individuals to change their behavior, then no efficiency cost is created. The tax incidence simply falls on those individuals directly taxed. However, if the tax does force individuals to alter their behavior then an efficiency cost is created and determining tax incidence is more difficult as consumers and sellers change their behavior to avoid the tax.

Although the above analysis has demonstrated the inefficiencies caused by taxation, the imposition of a tax may actually restore market efficiency in some cases. This predominately occurs in the case of externalities, which are negative (or sometimes positive) unintended spill-over effects to third parties. In essence, the producers of a negative externality, such as a steel producer emitting pollution from its factory, do not consider the external costs of steel production (the pollution) when determining its production decisions. As a result, the market provides an amount of steel production that is greater than the efficient amount because the external costs of steel production are not considered. A tax levied on steel producers that is equivalent to the external costs of steel production (pollution) will decrease the supply curve for steel producers and restore efficiency conditions at MSB = MSC. In the case of a market failure, such as a negative externality, governments can use taxes to restore market efficiency.

i. Computing The Efficiency Loss From a Tax

This section derives the expressions for computing the efficiency loss in a single-market due to the imposition of a unit tax and an ad valorem tax. Efficiency loss was shown graphically in Figure 3. The analysis here makes two assumptions. The first assumption is that of a linear demand curve. Second, a horizontal supply curve is assumed, meaning any amount of the product can be supplied at the market price, but that none will be supplied if the price falls below the equilibrium price (perfectly elastic supply). The analysis becomes more complicated with an upward sloping supply curve.

a. Efficiency Loss From A Unit Tax

First consider the imposition of a unit tax, T, such as an excise tax on gasoline, shown in Figure 4. At point A, MSB = MSC. With the tax, however, the new price is P + T and now MSB > MSC. The deadweight loss of taxation is represented by area ABC. A general expression for the deadweight loss of taxation, or excess burden (EB), is outlined below.

The excess burden is triangle ABC. The area of any triangle is found by finding ½ · base · height. The base of the triangle is the change in quantity demanded, or dQ. Similarly, the height of the triangle is the change in price, or dP. Thus,

EB = ½ · base · height = ½ · dQ · dP

The change in price is simply the tax, T (from P + T - P). An expression for dQ can be obtained from the formula for the price elasticity of demand, :

Solving the price elasticity of demand expression for gives:

Plugging the expressions for and into the formula for EB and rearranging terms yields the following expression for excess burden:

The excess burden of taxation is dependent upon the price elasticity of demand and the tax rate. The reader should note, however, the expression above suggests that the excess burden of taxation is zero if the price elasticity of demand is zero. This is an artifact of the single-market analysis done here. In reality, even if the price elasticity of demand for the taxed commodity is zero, there will still be an impact on other markets as consumers change their consumption of other commodities.

b. Efficiency Loss From an Ad Valorem Tax

Deriving the expression for the efficiency loss from an ad valorem tax, t, is almost identical to that of a unit tax. The only difference is in the expression for dP. Under an ad valorem tax, dP equals P ·t rather than just T under a unit tax. With an ad valorem tax, the tax-inclusive price is P (1 + t), so dP = P (1 + t) - P = P t.

With a new expression for dP and the same expression for dQ as under a unit tax, the expression for the excess burden of an ad valorem tax is:

ii. The Efficiency/Equity Tradeoff

The above sections have shown that the imposition of tax generally creates market inefficiencies. It is important to realize, however, that there exists an efficiency/equity tradeoff when evaluating taxes. Although most taxes create inefficiencies, tax revenues are used in the production of social goods, such as education and public welfare. The main idea behind these programs is to create a more ‘equitable’ society in terms of providing all individuals a subsistence level of education and income. It should be clear as to why the efficiency/equity tradeoff exists. Without taxes, markets would function more efficiently. Production levels would be higher, consumers would have more goods available to them, prices would be lower and mean incomes would be higher, although there would be a greater variance in incomes across individuals. With greater efficiency there will exist greater societal inequality because there are no revenues to be allocated from one portion of society to another. If we are concerned with equity, however, the distribution of tax revenue will result in a more equitable distribution of income (a lower variance) across individuals, but the inefficiencies created will cause relatively higher prices, lower mean incomes, and a lower availability of goods. Whether we should have a more equitable or more efficient society is a matter of opinion and is frequently a topic of political debate.

C. Two Models of Optimal Taxation

This portion of section III presents two famous models of optimal taxation. The first model considered is the Ramsey Rule. This model assumes that governments attempt to minimize the excess burden (efficiency loss) of taxation subject to given revenue requirements. The ‘optimal’ tax rate under the Ramsey rule is the rate that minimizes the excess burden of taxation while still generating the required revenues.

The Laffer curve is the second model of taxation presented. This model assumes that governments will attempt to generate as much revenue as possible without any regard to the efficiency losses caused by taxation. Only constitutional constraints and other legislation can limit the government’s desire for increased revenue. This view of government has been coined the "Leviathan" model of government (see Brennan and Buchanan, 1977). The Laffer curve considers the inverse relationship between tax rates and tax bases and the impact of this relationship on tax revenues. The analysis reveals that a higher tax rate is not always the maximizing rate - a lower tax rate may actually raise more tax revenues than a higher tax rate.

i. The Ramsey Rule

The previous sections have shown that while taxes do generate revenue benefits, taxes also create an excess burden on society. Obviously policy makers are confronted with an assumed trade-off - they need to generate a given amount of revenue, but generating this revenue will impose an additional cost on society. Within this framework, the problem for policy makers is to find tax rates that satisfy their revenue constraints but also minimize the deadweight loss to society. The following model of optimal taxation derives an expression for the ‘optimal’ commodity tax, optimal in terms of generating the required revenue while at the same time minimizing the deadweight loss to society. The model, termed the Ramsey Rule, produces the conditions set forth by (Ramsey, 1927), who argued that the excess burden of taxation will be minimized by setting the ratio of tax rates inversely proportional to price elasticities of demand for both products.

Suppose there are two goods X and Y. Assume that policy makers wish to levy ad valorem taxes on both goods and the supply curves for both goods are perfectly elastic (horizontal). While these taxes will generate revenues, they will also create a loss to society. The problem for the policy maker then becomes selecting tax rates that minimize the excess burden given certain revenue constraints. This problem can be expressed as:

min{EBx + EBY} subject to R = tx · Px · X + ty · Py · Y

where EBX and EBY are the excess burdens from taxing good X and from taxing good Y, each equal to the expression of the excess burden under an ad valorem tax shown in the previous section. R is the revenue raised from goods X and Y, tx · Px · X is the revenue raised from good X (where X is the quantity of good X), and ty · Py · Y is the revenue raised from good Y (where Y is the quantity of good Y). The Lagrangian for the above problem is:

Taking first-order conditions yields:

          (1)

         (2)

From (1), . From (2),

Equating ’s provides

Rearranging terms yields the conditions for optimal commodity taxation:

Taxes on goods X and Y should be levied so that the ratio of tax rates is equal to the inverse ratio of the price elasticities of demand for both goods. If the above conditions are satisfied, the excess burden of taxation will be minimized and the revenue constraints will be met.

Although insightful, the Ramsey Rule has some limitations. The above model assumes there are only two commodities in the economy, a rather unrealistic assumption. The analysis also becomes more complicated if the assumption of a perfectly elastic supply curve is dropped. In this case, the expressions for the excess burden will include a term for the price elasticity of supply. Furthermore, satisfying the above rule assumes knowledge of the price elasticities of demand for both commodities. Finally, the above model assumes that policy makers actually care about minimizing the deadweight loss to society when levying taxes. Much of the literature in the field of public choice casts doubt on this assumption, arguing that government officials attempt to generate as much revenue as possible to further their political agendas without any regard for the efficiency costs created by taxation.

Despite several drawbacks, the model presented above illustrates the problem of optimal commodity taxation. It nicely incorporates the concepts of efficiency and highlights the efficiency/equity tradeoff discussed in the previous section. As an exercise, the reader may wish to perform the above analysis for a per unit tax rather than an ad valorem tax. This requires the assumption that both a unit tax and an ad valorem tax will generate the same amount of revenues, or T = t · P, where T is the per unit tax rate and t is the ad valorem tax rate. Working through the above problem using per unit taxes should provide the reader the same final expression for the optimal tax rates.

ii. Tax Rates, Tax Bases and Tax Revenues - The Laffer Curve

Basic microeconomic theory suggests that an increase in price reduces the quantity of the product consumed because consumers substitute from the higher priced good to a lower priced good. Imposing a tax or increasing a tax rate leads to a reduction in consumption as consumers substitute away from the now higher price good. A detailed analysis of this behavior change was presented earlier in this section. The important issue addressed here, however, is the impact this substitution away from the taxed product has on tax revenues.

Recall that the tax base is the activity being taxed - retail sales is the tax base for the sales tax, income is the tax base for the personal income tax, etc. There is a negative relationship between tax rates and tax bases. For example, consider yourself and the personal income tax. If the personal income tax rate was zero, you would work a given number of hours a week, say 45 hours. As the tax rate increases (approaching 100 percent) you will slowly work fewer hours, substituting leisure for work. This substitution will continue as tax rates are continually increased until some point where you would choose not to work at all. At this point you will have completely substituted leisure for work. In this extreme case there is no longer a wage income tax base.

This substitution away from the taxed activity directly impacts tax revenues. Tax revenues are equal to the tax rate multiplied by the tax base, or R = t · B, where R = revenues, t = the tax rate, and B = the tax base. So, if the personal income tax rate is 10 percent and personal income is $100,000, personal income tax revenues are $10,000. Recalling the inverse relationship between tax rates and tax bases and using the above revenue formula, the reader should see that the revenue impact of a tax change depends upon the magnitude of the change in t or B. Suppose tax rates are increased. Holding the tax base constant, the rate increase should increase revenues. But the tax base is not constant, and will in fact become smaller under the tax rate increase. Thus, t rises but B falls. The final impact on revenues is not clear. If t rises more than B falls revenues will increase, whereas if t rises less than B falls revenues will fall. An equal change in t and B will keep revenues constant.

What the above example shows is that tax revenues are impacted by changes in the tax rate and the tax base. The economist Arthur Laffer suggested that beyond some tax rate, higher tax rates will shrink the tax base so much that revenues will actually decline. The Laffer curve shows the relationship between tax rates and tax bases and their impact on revenues. The derivation of a hypothetical Laffer curve is shown in Figure 5.

The left-hand side figure shows the inverse relationship between tax rates and tax bases. A Laffer curve is constructed using the relationship between tax rates and tax bases and the above revenue formula. At a tax rate of zero revenues will be zero. As the tax rate initially increases, revenues increase because the initial increase in the tax rate does not cause a greater substitution away from the taxed activity. However, as the tax rate continues to increase, more individuals will substitute away from the taxed activity until at some point, represented by point B in Figure 5, tax revenues actually begin to fall. The process also works in reverse. At very high tax rates, revenues will be relatively low. As the tax rate falls, more people substitute into the taxed activity, increasing the tax base. Beyond a certain point, however, the decrease in the tax rate will be greater than the increasing tax base and revenues will fall.

The Laffer curve relationship gained much popularity in the 1980s under Ronald Reagan. His reduction in marginal federal income tax rates from 70 percent to 33 percent was criticized as being a gift to the rich at the expense of the poor. However, according to data from the IRS, tax revenues from the top 1 percent of income earners actually increased by over 50 percent between 1980 and 1990. Although tax rates were reduced, the rich as a group actually paid more in taxes under the 33 percent rate than under the 70 percent rate because the tax reduction caused a massive increase in work and investment.

What Figure 5 and the above discussion suggest is that there is a revenue maximizing tax rate, and because of the inverse relationship between tax rates and tax bases, generating additional revenues may not always be obtained by simply increasing tax rates. A continual increase in tax rates by state and local officials may not guarantee an increase in tax revenues - beyond some point tax rate revenues will actually begin to fall. Thus, within the context of the Leviathan view of government, although governments will attempt to generate as much revenue as possible, additional revenue is not always had by a simple increase in the tax rate.

a. Empirical Estimation of the Optimal Tax Rate Using the Laffer Curve

State and local officials should understand the relationship between tax rates, tax bases and tax revenues when conducting tax policy. However, just an understanding of the Laffer curve may not be adequate for tax policy. Ghaus (1995) finds that a well-defined sales tax Laffer curve does exist at the local level, and that the optimal sales tax rate is dependent upon the property tax rate, housing preferences, the wage rate, and income. Actually estimating a Laffer curve and finding the optimal tax rate (optimal in terms of revenue maximization) will provide state and local officials evidence about whether an increase or decrease in rates will cause revenue to rise or fall.

As a foundation for empirically estimating a Laffer curve, consider the following mathematical derivation for a Laffer curve:

Tax revenues, R, are equal to the tax rate, t, times the base, B, or

R = t · B                                     (1)

The inverse relationship (assumed linear) between tax rates and tax bases can be expressed as:

                             (2)

Substituting (2) into (1) provides:

  (3)

As the assumed goal of governments is to maximize revenues, differentiating (3) with respect to t gives the following first-order condition:

                 (4)

Note that the second derivative of (4), , is < 0, confirming that the optimal is indeed a maximum. Solving (4) for the optimal tax rate, , results in the following expression:

                           (5)

Empirical estimation of a Laffer curve is based on the revenue equation (3). Specified as a linear regression model, equation (3) for a single tax becomes:

The subscript i denotes the units of observation, such as individual counties or states. A regression of tax revenues on the tax rate and the tax rate squared will provide estimates for the coefficientsand(an overall constant term,, should also be included in the model). Using these estimates, the optimal tax rate can be computed by using (5).

There are some assumptions inherent in the above methodology, however. First, equation (3) assumes only tax rates impact tax revenues - no other explanatory variables are included in the model (see Ghaus, 1995). Omitting relevant variables can result in biased and inconsistent estimates for and . Second, the regression results from (3) assume that the optimal tax rate is the same over all units of observation. So for an analysis of say, 50 counties, only one optimal tax rate for all counties can be computed. To allow optimal tax rates to differ across units of observation, additional independent variables such as socioeconomic or government characteristics need to be interacted with the tax rate and included in equation (3). This will provide a more complicated expression for t*, but t* will now vary across units of observation. Third, the above regression model assumes a cross-sectional analysis, that is, data across units of observation for a single time period. It is also possible to have time series data on tax revenues and tax rates for a single city, county or state. Empirical estimation is the same, except now the appropriate subscript would be a t, denoting each time period. The optimal tax computed from a time series model would provide a single optimal rate for all time periods included in the analysis.

The Laffer curve framework for finding the optimal tax assumes that the goal of governments is to maximize revenues with no concern about the societal costs of taxation. Under the Ramsey Rule, the optimal tax was found under the assumption that governments try to minimize the deadweight loss of taxation subject to a revenue constraint. Clearly, the optimal tax for both models may not be the same given the underlying assumptions of each model.

D. Conclusion

This section provided an introduction to the principles of tax analysis. Tax incidence was first addressed, with an emphasis on determining the revenue burden of taxation. The key point regarding tax incidence is that individuals who are less likely to alter their behavior to avoid the tax will bear a higher burden of the tax. So although a tax may be initially levied on one group, if members of this group change their behavior to avoid the tax, the final incidence of the tax will fall on other groups. After discussing tax incidence, the inefficiencies created by taxation were discussed. This portion of the section began by first providing an overview of efficiency and then provided graphical and mathematical derivations for the excess burden, or deadweight loss, of taxation. The next issue addressed was the efficiency/equity tradeoff of taxation. Here, time was spent addressing the tradeoff between efficient markets and a more equitable society. The final sections presented the Ramsey Rule and the Laffer curve, two models of optimal taxation. Given the revenue needs of governments and the inefficiencies of taxation, each model was used to derive an expression for the optimal tax rate, optimal in terms of 1) minimizing the efficiency costs of taxation while subject to a revenue constraint in the case of the Ramsey Rule, or 2) revenue maximization in terms of the Laffer curve.

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