Optimal tax

Optimal tax theory or the theory of optimal taxation is the study of designing and implementing a tax that reduces inefficiency and distortion in the market under given economic constraints.[1] Generally, this criterion consists of individuals' utility and the optimization problem involves minimizing the distortions caused by taxation.[2][3] A neutral tax is a theoretical tax which avoids distortion and inefficiency completely.[4][5] Other things being equal, if a tax-payer must choose between two mutually exclusive economic projects (say investments) that have the same pre-tax risk and returns, the one with the lower tax or with a tax exemption would be chosen by a rational actor.[3] Thus economists argue that taxes generally distort behavior.

In the Wealth of Nations, Adam Smith observed that

“…the economic incomes of private people are of three main types: rent, profit and wages. Ordinary taxpayers will ultimately pay their taxes from at least one of these revenue sources. The government may intend that a particular tax should fall exclusively on rent, profit, or wages – and that another tax should fall on all three private income sources jointly. However, many taxes will inevitably fall on resources and persons very different from those intended … Good taxes meet four major criteria. They are (1) proportionate to incomes or abilities to pay (2) certain rather than arbitrary (3) payable at times and in ways convenient to the taxpayers and (4) cheap to administer and collect.” [6]

Tax revenue

Generating a sufficient amount of revenue to finance government is arguably the most important purpose of the tax system. Optimal taxation, which is the theory of designing and implementing taxes that reduce inefficiency and distortion in the market through Pareto optimal moves under given constraints, is constantly debated.[7] Though inequality will always exist within even the most efficient markets, the goal of taxation is to eliminate as much inefficiency as possible and to raise revenue to fund government expenditures. With any tax, there will be an excess burden, or additional cost, to the consumer and the producer. Whenever the consumer purchases the taxed good or service, and the higher elasticity, or responsiveness, of the demanded product, the greater the excess burden is on either the consumer or producer. Those individuals or corporations who have the most inelastic demand curve pay the brunt of the excess burden curve. However, the tradeoff of placing larger taxes on inelastic goods is that the higher tax will lead to lower quantity exchanged and thus a smaller deadweight loss of reduced revenue.[7]

Horizontal and vertical equity

When discussing what a fair and optimal tax level would be, the principle of equity, both horizontal and vertical, is important. Equity is determined by first assessing an individual’s ability-to-pay. The idea of the ability-to-pay principle considers whether or not it is fair to tax someone higher just because that person has the ability and resources to pay. If it is decided that they should be required to pay more, the question of how much more arises. These questions can be analyzed through horizontal and vertical equity which are subsets of the ability-to-pay principle. Horizontal equity suggests it is fair if people who have equal ability-to-pay actually do pay the same amount in taxes. Vertical equity is the idea that people who have a higher ability-to-pay should actually pay more than those who have a lower ability-to-pay, as long as the increase in tax level is considered to be reasonable.[8]

Problems with horizontal equity consist of the idea that taxing individuals with the same ability to pay implies that two individuals earning the same income should be taxed equally. However, Randall Holcombe depicts a scenario where one of these people is single while the other married with children, and that charging these people the same amount does not correctly reflect their ability to pay. Conversely, this situation can also support the opposite argument. In this same example, if one individual chooses to spend his income to support his family, and another to travel, each individual now has less money to pay taxes with. However, this raises the question on how the government should treat these choices differently if at all for taxation purposes. As Holcombe showed through his examples, it is possible to apply different tax principles to the same situation and reach a different logical solution, but as these are normative issues, it can be difficult to reach a solution. So it is up to individual societies to determine what tax structure to implement.[8]

Vertical equity states that the government should implement higher taxes on those who have higher abilities to pay than those who have a lower ability to pay. However, problems immediately arise with vertical equity because not only do policy makers have to define what having a higher ability means, but they also have to determine what an appropriate increase in taxation is for those with a greater ability to pay. Practically, vertical equity provides no solution to these problems. Furthermore, because of the complexity of current tax policies, those who have greater incomes and greater ability to pay are able to avoid paying taxes in ways that those in the lower brackets cannot. However, the concept of vertical equity is necessary in considering how best to create and implement a fair tax code. Because it is widely agreed upon that those of higher incomes should pay more in taxes, this helps alleviate the tax burden on those whose ability to pay is lower. It is then up to policy makers to determine what this looks like and how much more higher-income earners should be required to pay.[8]

However, as with any tax, implementing higher taxes will negatively affect incentives and alter an individual’s behavior. In his article "Effects of Taxes on Economic Behavior," Martin Feldstein discusses how economic behavior determined by taxes is important for estimating revenue, calculating efficiency and understanding the negative externalities in the short run. In his article, like much of his research on this topic, he chooses to focus primarily on how households are affected. Feldstein recognizes that high taxes deter people from actively engaging in the market, causing a lower production rate as well as a deadweight loss. Yet, because it is difficult to see tangible results of deadweight loss, policy makers largely ignore it. Feldstein expresses his frustration that policy makers have yet to grasp these concepts and therefore do not make policy that correct this wrong.[9]

The thrust of thinking among some economists is that taxes on consumption are always more efficient than taxes on income, arguing that the latter have a greater disincentive effect. One problem with this analysis is defining what constitutes consumption and what constitutes investment.[3] Another problem is that the impact will vary from country to country, depending on the design of the tax system and the relative levels of different tax rates. A more nuanced empirical analysis is required to evaluate this issue. For lower-income working people, who spend most of their income, taxes on consumption also have a significant disincentive effect; while higher-income people may be motivated more by prestige and professional achievement than by after-tax income. Any gain in economic efficiency from shifting taxes to consumption may be quite small, while the adverse effects on income distribution may be large.[10]

Lump-sum taxes

One type of tax that does not create a large excess burden is the lump-sum tax. A lump-sum tax is a fixed tax that must be paid by everyone and the amount a person is taxed remains constant regardless of income or owned assets. It does not create excess burden because these taxes do not alter economic decisions. Because the tax remains constant, an individual’s incentives and a firm’s incentives will not fluctuate, as opposed to a graduated income tax that taxes people more for earning more.

Lump-sum taxes can be either progressive or regressive, depending on what the lump sum is being applied to. A tax placed on car tags would be regressive because it would be the same for everyone regardless of the type of car the owner purchased and, at least in the United States, even the poor own cars. People earning lower incomes would then pay more as a percentage of their income than higher-income earners. A tax on the unimproved aspects of land tends to be a progressive tax, since the wealthier one is the more land one tends to own and the poor typically do not own any land at all.

Lump-sum taxes are not politically expedient because they sometimes require a complete overhaul of the tax system. Lump-sum taxes are also unpopular when they are assessed per capita because they are regressive and make no allowance for a citizen's ability to pay.

A one-off, unexpected lump-sum levy which is proportional to wealth or income is also non-distorting. In this case, although wealth or income is penalised, the unexpected nature of the tax means that there is no disincentive to asset accumulation- as by definition those accumulating such assets are unaware that a portion of those assets will be taxed in the future.

Land value taxation

Henry George most notably championed the idea of a land value tax in Progress and Poverty, as a levy on the value of unimproved or natural aspects of the land, primarily location; it disregards the improvements such as buildings and irrigation.[11] Land value taxation has no deadweight loss because the input of production being taxed (land) is fixed in supply; it cannot hide, shrink in value, or flee to other jurisdictions when taxed.

Economic theory suggests that a pure land value tax which succeeds in avoiding taxation of improvements could actually have a negative deadweight loss (positive externality), due to productivity gains arising from efficient land use.[12][13] The taxation of locational values encourages socially optimal development on land in highly valued areas, like cities, since it reduces the incentive to speculate in land prices by leaving potentially productive locations vacant or underused.[14]

Despite its theoretical benefits, implementing land value taxes is difficult politically. However, land value tax is considered progressive, because the ownership of land values is more concentrated than other sources of revenue, such as personal income or spending.[15] George argued that because land is the fruit of nature (not labor) and the value of location is created by the community, the revenue from land should belong to the community.[16]

Commodity taxes

Frank P. Ramsey (1927) developed a theory for optimal commodity sales taxes in his article "A Contribution to the Theory of Taxation". The problem is closely linked to the problem of socially optimal monopolistic pricing when profits are constrained to be positive, known as the Ramsey problem. He was the first to make a significant contribution to the theory of optimal taxation from an economic standpoint, and much of the literature that has followed reflects Ramsey's initial observations.

He wanted to confront the problem of how to adjust consumption tax rates, under specified constraints, so that the reduction of utility is at a minimum. In an attempt to reduce excess burden of consumption taxes, Ramsey proposed a theoretical solution that consumption tax on each good should be "proportional to the sum of the reciprocals of its supply and demand elasticities".[17] However, practically, it is problematic to constrain social planners to one form of taxation. It is better to enable them to consider all possible tax structures.[18]

Using Ramsey’s rule as a basis for their papers, Peter Diamond and James Mirrlees propose an alternative to Ramsey’s proposition by allowing the planner to consider numerous tax systems, and their model has prevailed in taxation theories. In their first paper, "Optimal Taxation and Public Production I: Production Efficiency" Diamond and Mirrlees consider the problem of imperfect information exchanged between taxpayers and the social planner.[19] According to their argument, an individual’s ability to earn income differs. Though the planner can observe income, they cannot directly observe the individual’s ability or effort to earn income, so that if the planner attempts to increase taxes on those with high ability to earn an income, the individual’s incentives to earn a high-income decrease. They confront the government tradeoff between equality and efficiency that when higher taxes are imposed on those with the potential to earn higher wages, they are not incentivized to expend the extra effort to earn a greater income. They rely on what has been labeled the revelation principle where planners must implement a tax system that provides proper incentives for people to reveal their true wage-earning abilities.[19]

They continued this idea in the second installment of their paper "Optimal Taxation and Public Production II: Tax Rules", where they discuss marginal tax rate schedules for labor income.[20] If the policy maker implemented a tax increase in the marginal tax rate at a lower income, it discourages the individuals at that income from working hard. However, this same increase for high-income individuals does not distort their incentives because though it raises their average tax rate, their marginal tax rate remains the same. For example, giving $100 is worth more to a low-income earner than to a high-income earner. Diamond and Mirrlees came to the conclusion that the marginal tax rate for the top earner should be equal to zero and the optimal rate must be between zero and one. This provides the correct incentives for individuals to work at their optimal level.[20]

Developments in tax theory

William J. Baumol and David F. Bradford in their article "Optimal Departures from Marginal Cost Pricing" also discuss the price distortion taxes cause.[21] They examine the proposition that in order to reach the optimal point of allocating resources, prices that deviate from marginal cost are required. They recognize that with every tax, there is some sort of price distortion, so they state that any solution can only be the second-best option and any solution proposed is under that added constraint. However, their theory differs from other literature in this topic. First, it deals with quasi-optimal pricing, looking at four options for Pareto optimality with adjusted commodity prices. Second, they express their theory in more simplified terms which incurs a loss of realistic application. Third, it combines the three discussions: the welfare theory, the contributions of the regulations and public finance. They conclude that under constraints, the best possible theory to get close to optimality, which is not “best” at all, is the systematic division between prices and marginal costs.[21]

In his article entitled "Optimal Taxation in Theory", Gregory Mankiw reviews that current literature in theories on optimal taxation and analyzes the change in the tax theory over the past few decades. Like Diamond and Mirrlees, Mankiw recognizes the flaw in Ramsey’s model that planners can raise revenue through taxes only on commodities, but also points out the weakness of Mirrlees’s proposition. Mankiw argues that Diamond’s and Mirrlees’s theory is extremely complex because of how difficult it is to keep track of individuals producing at their maximum levels.[18]

Mankiw provides a summary of eight lessons that represent the current thought in optimal taxation literature. They include, first the idea considering horizontal and vertical equity, that social planners should base optimal tax schedules on income rates for labor, which marks the equality and efficiency trade-off. Second, the more income an individual makes, their marginal tax schedule could actually decrease because they are discouraged from working at their optimal production level. The solution is to, after individuals reach a certain income level, ensure that the marginal tax remains steady. Third, reaching an optimal tax level could mean flat taxes. Fourth, the increase in wage inequality is directly proportionate to the extent of income redistribution as revenue is distributed to low-income earners. Fifth, taxes should not only depend on income amounts, but also on personal characteristics such as a person’s wage earning capabilities. Sixth, goods produced should only be taxed as a final good and should be taxed uniformly, which leads to their seventh point that capital should also not be taxed because it is considered an input of production. Finally, policy makers should consider individuals’ income histories, which require reliance on different types of taxation to derive optimal taxation. Mankiw identifies that the tax policy has largely followed the theories laid out in tax literature because social planners believe that the flatter the tax, the better, there are declining top marginal rates in OECD countries, and taxes on commodities are now uniform and usually only final goods are taxed.[18]

Joel Slemrod in his paper "Optimal Taxation and Optimal Tax System", argues that optimal tax theory, as it stood when Slemrod wrote this paper, was an insufficient guide to determine tax policies because policy makers had yet to find a way to implement a tax system that enticed individuals to work at their optimal level.[22] As a solution, Slemrod proposes the theory of optimal tax systems a phrase he uses to refer to the normative theory of taxation. Slemrod advocates this theory because not only does it take into account the preferences of individuals, but also the technology involved in tax collecting. A practical application of this, for example, is implementing value-added taxes, a tax on the purchase price of a good or service, to correct tax evasion. He argues that any future tax literature in normative theory needs to focus less on consumer preferences and more on tax-collecting technology and the areas of the economy that affect tax collection.[22]

Income taxes

Another aspect of optimal taxation is determining income taxes, which can be regressive, flat, or progressive.

Individual income taxes

Emmanuel Saez in his article titled "Using Elasticities to Derive Optimal Income Tax Rates" derives a formula for optimal level of income tax using the both compensated and uncompensated elasticities.[23] Saez writes the tradeoff between equity and efficiency is a central consideration of optimal taxation, and implementing a progressive tax allows the government to reallocate their resources where they are needed most. However, this deters those of higher income levels to work at their optimal level. Saez cites Mirrlees’s non-linear income tax theory, but declares it to be limited. Instead, Saez argues that elasticities are the key in calculating optimal income tax rates. Obtaining an optimal tax formula for high-income earners is straightforward because by determining elasticities, Saez determined that marginal tax rate for labor income needs to be between 50 and 80 percent in order to be at an optimal level. Saez continued that using elasticities is advantageous because it shows the different possible results and finally that numerical simulations of optimal tax formulas can be used.[23]

James M. Poterba in an article called "Lifetime Incidence and the Distributional Burden of Excise Taxes" determines to show that household income measured over the long run varies less than when analysts measure it annually. Poterba shows that excise taxes, which are taxes on consumption, may be less regressive that previous calculations indicate because they only use annual income. Furthermore, he shows that this same theory can be applied to excise taxes placed on things like gasoline, alcohol and tobacco. When the expenditure on these items is considered in correlation to the total consumption over a lifetime, it is more equally dispersed than when measured annually. Poterba argues that people need to distinguish between annual and lifetime measurements, and a failure to do this leads to overstating the degree of inequality that burdens from taxes place on the groups earning different income levels.[24]

In the late 1970s, Arthur Laffer developed the Laffer curve, which demonstrates that there are two effects of changing tax rates: an arithmetic effect—if tax rates are lowered, revenue will be decrease by the same amount—and an economic effect—which provides incentives for individuals to increase their work output through low tax rates.[25] The higher the taxes placed on income are, the more people lose their incentives to earn more taxable income, which causes the taxable base to shrink. This in turn leads reduced revenue at a certain point because although taxes are higher, there are fewer people paying those taxes. Laffer constructed a graph to illustrate when this point occurs, though it does not actually determine whether a particular tax cut will raise or lower revenues. Laffer’s curve is widely used because it can be applied to all taxes, not just income taxes.[25]

For example, since only economic actors who engage in market activity of "entering the labor market" have an income tax liability on their wages, people who are able to consume leisure or engage in household production outside the market by say providing housewife services in lieu of hiring a maid are taxed more lightly. With the "married filing jointly" tax unit in U.S. income tax law, the second earner's income is added to the first wage earner's taxable income and thus gets the highest marginal rate. This type of tax creates a large distortion disfavoring women from the labor force during years when the couple have great child care needs.

The requirement that married people file jointly in the United States thus is considered to run counter to optimal tax theory and supply-side economics.

Corporate income taxes

Arnold Harberger has conducted research on optimal taxation for corporations. Corporation income tax is a tax imposed by the federal and state governments on the income a corporation receives. In the Journal of Political Economy, Harberger wrote an article called "The Incidence of the Corporation Income Tax" where he attempted to provide a theoretical framework to understand the effects that income tax on corporations has and to determine inferences of this tax in the United States.[26] He proposed the general-equilibrium nature, in which he assumes a two-sector economy (one corporate and the other not). In this model, Harberger theorizes that by redistributing the economy's resources, the market will move toward a constant equilibrium in the long-run where the elasticities of substitution are the same for both capital and labor and are then equal to the elasticity of substitution between the two goods being consumed. Furthermore, this can potentially apply to a broader range of conditions.[9][26]

In contrast to this, Michael Feldstein contradicts Harberger’s assumptions. Feldstein argues that one of Harberger’s theories great shortcomings is that up until the point he was writing the article, policy makers, when determining tax changes for corporate income tax, focused solely on the effects in personal income tax. Feldstein argues that policy makers should analyze these two aspects separately and he presented a method on how to input the net effect of the changes of the efficient corporate tax rates into the individual tax returns by focusing on the vital difference between real and nominal capital income. Feldstein recognizes the shortcomings of his own model though because of the lack of insufficient data to properly compare the rates of corporate and individual taxes.[9]

William Fox and LeAnn Luna propose another theory in a joint article called "State Corporate Tax Revenue Trends: Causes and Possible Solutions", in which they take on just one aspect of the debate—the role of this taxation and they purport to determine the extent of the damage done through a decrease in revenue and propose some ways they believe will reverse the trend. They determine that because the effective corporate income tax rate has fallen by one-third in two decades, the effective tax rate decline is the result of a tax base that is eroding in relation to a corporation’s income and profits. This is because legislation like discretionary taxes has narrowed the taxable base.[27]

One option to reduce the negative effect of corporate taxes on the level of private investment (and hence increase investment toward the level that would be obtained in a no-tax environment) is the provision of an investment tax credit or accelerated depreciation. In these cases, the rate of corporate tax payable becomes a negative function of the rate of profit reinvestment, and hence firms which increase their rate of reinvestment diminish their taxation liabilities.

In recent years, the concept of a corporate tax system incorporating deductions for "normal" profits (where normal is defined in relation to the long-term interest rate and the risk premium) has gained some attention as a tax system which could minimise the distortionary effect of corporate taxation on the level of investment, without reducing total taxation revenue. Such a taxation system would in effect levy a higher rate of tax on projects earning "superprofits" which will likely go ahead even when taxed at a very high rate, as the post-tax rate of return on capital is designed to still be significantly higher than the threshold or "normal" level. Conversely, the effective tax rate on marginal projects (with a return on equity closer to the "normal" level) will be minimised. One example of such a tax system is Australia's Minerals Resource Rent Tax.

When an investment tax credit or equity-based deduction of profits is applied, the optimal pre-deduction and average effective rate of taxation is generally increased as the distortionary effect of a given level of taxation is diminished. If the tax rate prior to the adoption of these provisions was optimal, there is an assumption that the net marginal benefit of increased taxation is zero in the locality of the optimum rate (the marginal costs and benefits sum to zero). If the distortionary costs of capital taxation are then lowered by equity deductions or investment tax credits, then it is clear that in the region of the previous optimal rate the net marginal benefit of increases in the rate will become positive, implying the tax rate should be raised upward from this level.

Sales tax

A third consideration for optimal taxation is sales tax, which is the additional price added to the base price of a paid by the consumer at the point when they purchase a good or service. Poterba in a second article called "Retail Price Reactions To Changes in State and Local Sales Taxes" tests the premise that sales taxes on the state and local level are fully shifted to the consumers.[28] He examines clothing prices before and after World War II. He recognizes that monetary policy is important to determine the response of nominal prices under a national sales tax and points to possible differences in taxes applied at the local level as to taxes applied at a national level. Poterba finds evidence reinforcing the idea that sales taxes are fully forward shifted, which raises the consumer prices to match the tax increase. His study coincides with the original hypothesis that retail sales taxes are fully shifted to retail prices.[28]

Donald Bruce, William Fox, and M. H. Tuttle also discuss tax revenues through sales tax in their article "Tax Base Elasticities: A Multi-State Analysis of Long-Run and Short-Run Dynamics".[29] In this article, they look at how personal state revenues and sales tax bases elasticities change for the short and long term in an attempt to determine the difference between them. With this information, the authors believe that states can both enhance and customize their tax structures, which can be used for careful resource planning. They found that for state personal income tax bases as compared to sales taxes, the average long-term income elasticity is more than doubled and the short-term display disproportionate results higher than the long-term elasticities. The authors contend with the conventional literature by declaring that neither the personal income tax nor the sales tax is, at least, universally, the more volatile tax. Though, the authors concede that in certain situations, the sales tax is more volatile, and in the long term, personal income taxes are more elastic.[29]

Furthermore, in understanding this argument, it must also be considered, as Alan Auerbach, Jagadeesh Gokhale, and Laurence Kotlikoff do in "Generational Accounting: A Meaningful Way to Evaluate Fiscal Policy", what the implications to optimal taxation are for future generations.[30] They propose that generational accounting represents a new method for fiscal planning in the long-run, and that unlike the budget deficit, this generational accounting is not arbitrary. Instead, it is a remedy for how to approach the generation burden and effects of fiscal policy on a macroeconomic level. Ethically, it is a problem to have low taxes now, and therefore low revenue now, because it inevitably puts the burden of responsibility to pay for those expenditures on future generations. So through generational accounting, it is possible to analyze this and provide the necessary information for policy makers to change the policies needed to alter this trend. However, according to Auerbach, politicians are currently only relying on accounting and are not seeing the potential consequences that will ensue in future generations.[30]

The incidence of sales taxes on commodities also results in distortion if say food prepared in restaurants is taxed but supermarket-bought food prepared at home is not taxed at purchase. If a taxpayer needs to buy food at fast food restaurants because he/she is not wealthy enough to purchase extra leisure time (by working less) he/she pays the tax although a more prosperous person who enjoys playing at being a home chef is taxed more lightly. This differential taxation of commodities may cause inefficiency (by discouraging work in the market in favor of work in the household).

See also


  1. Slemrod, J (1990). "Optimal taxation and optimal tax systems". Journal of Economic Perspectives. 4 (1): 158. doi:10.3386/w3038.
  2. Lars Ljungqvist and Thomas J. Sargent (2000), Recursive Macroeconomic Theory, 2nd ed, MIT Press, ISBN 0-262-19451-1, p. 444.
  3. 1 2 3 Simkovic, Michael. "Distortionary Taxation of Human Capital Acquisition Costs". Social Science Research Network.
  4. Rothbard, Murray. (1970) Power and Market: Government and the Economy, p. 65
  5. Business Dictionary.com
  6. Smith, Adam (2015). The Wealth of Nations: A Translation into Modern English. ISR/Google Books. p. 429. ISBN 9780906321706.
  7. 1 2 Bruce, Donlad; John Deskins; William Fox (2005). Auerbach, Alan, ed. "On the Extent, Growth, and Consequences of State Business Tax Planning". Corporate Income Taxation in the 21st Century. Cambridge University Press.
  8. 1 2 3 Holcombe, Randall (2006). Public Sector Economics; The Role of Government in the American Economy. New Jersey: Pearson.
  9. 1 2 3 Feldstein, Martin (2008). "Effects of Taxes on Economic Behavior". NBER (13745).
  10. Rhys Kesselman, Jonathan; Spiro, Peter S. (2014). "Challenges in Shifting Canadian Taxation Toward Consumption". Canadian Tax Journal. 62 (1): 1–39.
  11. George, Henry (1879). Progress and Poverty. New York: Page & Co.
  12. Tideman, Nicolaus (1995). Taxing Land is Better Than Neutral: Land Taxes, Land Speculation and the Timing of Development. Lincoln Institute of Land Policy. Retrieved 17 June 2014.
  13. Mattauch, Linus; Siegmeier, Jan; Edenhofer, Ottmar; Creutzig, Felix (2013), "Financing Public Capital through Land Rent Taxation: A Macroeconomic Henry George Theorem", CESifo Working Paper, No. 4280.
  14. Plassmann, Florenz. "The Impact of Two-Rate Taxes on Construction in Pennsylvania" (PDF). Retrieved 3 October 2013.
  15. Gaffney, Mason (1971). "The property tax is a progressive tax" (PDF). http://www.masongaffney.org/. Resources for the Future, Inc; Reprinted from the Proceedings of the Sixty-Fourth Annual Conference on Taxation sponsored by the National Tax Association. Retrieved 7 October 2013. External link in |work= (help)
  16. "Levying the land". The Economist. June 29, 2013. Retrieved 3 October 2013.
  17. Ramsey, Frank (1927). "A Contribution to the Theory of Taxation". Economic Journal. 37: 47–61. doi:10.2307/2222721.
  18. 1 2 3 Mankiw, Gregory; Matthew Weinzierl; Danny Yagan (2009). "Optimal Taxation in Theory". NBER (15071).
  19. 1 2 Mirrlees, James; Peter Diamond (1971). "Optimal Taxation and Public Production I: Production Efficiency". American Economic Review. 61: 8–27.
  20. 1 2 Mirrlees, James; Peter Diamond (1971). "Optimal Taxation and Public Production II: Tax Rules". American Economic Review. 61: 261–278.
  21. 1 2 Baumol, William; David Bradford (1970). "Optimal Departures from Marginal Cost Pricing". The American Economic Review. 60: 265–283.
  22. 1 2 Slemrod, Joel (1990). "Optimal Taxation and Optimal Tax Systems".
  23. 1 2 Saez, Emmanuel (2001). "Using Elasticities to Derive Optimal Income Tax Rates". Review of Economic Studies. 68: 105–229. doi:10.1111/1467-937x.00166.
  24. Poterba, James (1989). "Reexamination of Tax Incidence". American Economic Review. 79: 325–330.
  25. 1 2 Laffer, Arthur (2004). "The Laffer Curve: Past, Present and Future". The Heritage Foundation (1765): 1–18.
  26. 1 2 Harberger, Arthur (1962). "The Incidence of the Corporation Income Tax". Journal of Political Economy. 70: 215–240. doi:10.1086/258636.
  27. Fox, WIlliam; LeAnn Luna (2002). "State Corporate Tax Revenue Trends: Causes and Possible Solutions". National Tax Journal. 55: 491–508.
  28. 1 2 Poterba, James (1996). "Retail Price Reactions to Changes in State and Local Sales Taxes". National Tax Journal. 79 (49): 165–176.
  29. 1 2 Bruce, Donald; William Fox; M. H. Tuttle (2006). "Tax Base Elasticities: A Multi-State Analysis of Long-Run and Short-Run Dynamics". Southern Economic Journal. 73 (2): 315–341. doi:10.2307/20111894.
  30. 1 2 Auerbach, Alan; Jagadeesh Gokhale; Laurence Kotlkoff (1999). "Generational Accounting: A Meaningful Way to Evaluate Fiscal Policy". Journal of Economic Perspectives. 8: 73–94. doi:10.1257/jep.8.1.73.


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