Optimal Indirect Taxation Under Imperfect Competition



1. Introduction

It is commonly suggested in economic textbooks that indirect taxation or market power generates “deadweight loss” or “excess burden” to society, because they distorts the relative prices of commodities. The magnitudes of the welfare losses depend on the slopes of demand and supply (or marginal cost) curves. In order to minimize the aggregate deadweight loss, an optimal indirect tax structure should prescribe higher tax rates for commodities that have low price elasticities of demand or supply, especially when the demand functions for different commodities are independent (Ramsey, 1927; Hotelling, 1938; Baumol and Bradford, 1970; Myles, 1989; and others). Another popular view is that direct taxation is more efficient than indirect taxation.

Atkinson and Stiglitz (1972) suggest that the conventional theories on indirect taxation be unsatisfactory because they are based on restrictive assumptions including the absence of income effects and the independence of demand functions. They consider a model where all commodities are taxable but “leisure” is not.[1] A government chooses a set of indirect tax rates to maximize consumer surplus conditional on raising certain revenue. They characterize the conditions that an optimal tax structure should satisfy. It is suggested that when the marginal disutility of labor is constant, the optimal taxes should be inversely proportional to the price elasticity of demand. But when labor supply is completely inelastic, a uniform tax rate on all goods is optimal. The paper also suggests that with additive utility functions, the government should tax more heavily the goods that have low income elasticities of demand.  Consistent with the view that indirect taxation results in distortion in consumer choices, in another paper Atkinson and Stiglitz (1976) suggest that when production technologies are linear and consumer preferences are weakly separable in labor supply and produced goods, the second best outcome can be achieved by nonlinear income taxation alone.

This paper reconsiders the welfare effects of indirect taxation. The model resembles that of Atkinson and Stiglitz (1972) but is more general. Assume that all commodities are taxable but “leisure” is not. In some of the markets firms have market power. Tax revenue is viewed as the rent of governmental coercion power and gross profit is viewed as the rent of market power. A government can decide how the total rent is divided between itself and firms, through corporate income taxes for instance. The government chooses an indirect tax structure to maximize consumer surplus conditional on raising a certain amount of rent to finance public services and private entrepreneurship. This model has perfect competition as a special case, where producer prices equal to the marginal costs. Consumers maximize their utilities by choosing consumption bundles and labor supplies. This paper does not model the specific games played in individual industries.

Instead it just assumes that all the markets have stable equilibria under a given tax structure.[2]

This paper first characterizes the social optimal resource allocation conditional on a certain amount of rent being collected, and then observes whether an indirect tax structure can materialize such an allocation through market mechanism. The analyses suggest that when all commodities are taxable, the optimal indirect tax structure can indeed induce the social optimal outcome. Such a tax structure should equalize the after-tax Lerner indexes of vice versa. The optimal taxation corrects the price distortion caused by market powers. The finding is in contrast to the views suggesting that an optimal indirect tax structure should depend on the substitutability or complementarity among commodities and labor. In particular, this paper disagrees with Atkinson and Stiglitz (1972). Although it has Atkinson and Stiglitz (1972)’s model as a special case, this paper does not find any role of price or income elasticities in shaping the optimal indirect taxation. This paper also shows that when labor supplies are sufficiently inelastic, the optimal indirect tax structure leads to social welfare gain rather than deadweight loss. In other words, a well-designed indirect tax structure tends to be Pareto-improving. Hence indirect taxation could be superior to direct taxation from efficiency perspective. This finding is also in contrast to the conventional views on taxation.

This paper relates to the school of studies exploring how indirect taxation helps correcting the distortion caused by market powers. Guesnerie and Laffont (1978), Dillén (1995) and others consider efficiency-restoring indirect taxation when firms engage in Bertrand-Nash games. The studies are based on general equilibrium frameworks. Konishi, Okuno-Fujiwara and Suzumura (1990) analyze self-financed tax and subsidy schemes with a general equilibrium model, paying special attention to market entry and exit. Auerbach and Hines (2001) use a partial equilibrium model to show that governments with perfect information and access to lump-sum taxes can provide corrective subsidies that render outcomes efficient in the presence of imperfect competition. But relaxing either of these two conditions removes the government’s ability to support efficient resource allocation. avoids modeling the strategic interactions among firms. The results are more general as long as stable equilibria always exist. The policy implications are also easier to perceive.

Recent studies of indirect taxation under imperfect competition often concern with comparing specific versus ad valorem taxes, which are welfare-equivalent under perfect competition. Delipalla and Keen (1992) compare specific and ad valorem taxations in two models of oligopoly, with and without free entry. They find that ad valorem taxation implies a relatively low consumer price, high tax revenue and (when entry is precluded) low profits. Ad valorem taxation dominates specific taxation from the welfare perspective. Anderson, Palma and Kreider (2001) find that ad valorem taxes are welfare-superior to specific taxes in the short run when production costs are identical across firms. They also find that cost asymmetry, strategic value, market entry, and other factors may affect the relative efficiency of specific and ad valorem taxes. Blackorby and Murty (2007) nevertheless show that if a monopoly sector is imbedded in a general equilibrium framework and profits are taxed at one hundred percent, the specific taxation and ad valorem taxation are welfare-equivalent. The current paper considers specific taxation only, but the results hold for ad valorem taxation too. It is consistent with Blackorby and Murty (2007)’s view that the two types of taxation may be equivalent in a general equilibrium model.

The rest of the paper proceeds as follows. Section 2 comments the conventional wisdom about market power and indirect taxation. Section 3 presents a model of indirect taxation in an economy with imperfect competition. It characterizes the optimal indirect tax structure and analyzes its social welfare effects. Section 4 concludes the paper.

2. Conventional wisdom

In an imperfect competitive market like monopoly, oligopoly and monopolistic competition, or a market with indirect taxation, the consumer prices of commodities are typically higher than the marginal costs. The resulted gross profits or tax revenue can be viewed as the rent of market power or governmental coercion power. “Deadweight loss” or “excess burden” occurs when the rent is less than the consumers’ loss from the powers. In economic textbooks the deadweight loss caused by market power is often illustrated by Figure 1.

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The equilibrium is Pareto-inefficient since a feasible reallocation of resource can generate a Pareto improvement. Starting from equilibrium output Q*, if the economy can manage to produce one more unit of the commodity at the marginal cost (which is slightly higher than MC* ) and sell it to the consumer who is willing to pay the highest price (which is slightly lower than p* ), the total social welfare would be improved (by an amount slightly less than p*−MC*).  In this sense, market power leads to inefficiently low output can increase to the perfectly competitive level, the social welfare gain is represented by the area of triangle DL. Hence the deadweight loss from market power can be represented by triangle DL.

However this argument is based on a partial equilibrium framework. It implicitly assumes that all other commodity markets are perfectly competitive. If a consumer spends more on the commodity in consideration, he would have to spend less on some other commodities. If those markets are imperfectly competitive and thus the commodities are priced above their marginal costs, spending less in those markets would reduce the producer surplus there.  This is a loss that must be accounted in the welfare analysis, and it may offset the suggested welfare gainp*−MC*.  Hence from the perspective of general equilibrium, the argument tends to overestimate the harm of market power in each individual market.

Market power leads to social welfare loss when the “degree” of competition differs across industries. In that case the relative prices do not fully reflect the relative scarcities of the commodities. Therefore consumer choices, which are based on relative prices, are distorted. Nevertheless, to some extent the market powers in different markets cancel out with each other. Indeed, if all commodities had the same percentage markups, the price distortion would completely disappear. In that case market power generates welfare loss only by distorting labor supply.

The conventional view of the deadweight loss caused by indirect taxation is similar to that caused by market power. The welfare loss is also represented by a triangle in a demand-supply diagram, often referred as Harberger triangle in memory of Harberger’s when all commodities are taxable, the Harberger triangles tend to overestimate the welfare loss caused by indirect taxation.  Ramsey (1927) characterizes the optimal indirect taxation that minimizes the “decrement of utility”.

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A government has to raise certain tax revenue to finance public services. It also has to allow certain gross profits for firms in order to promote investment. In this paper, tax revenue is viewed as the “rent” of governmental coercion power and gross profit is viewed as the “rent” of market power. Suppose that the government can figure out the optimal amount of total rent and decide how to allocate the rent between firms and itself, through corporate income taxes for instance. The government chooses an indirect tax structure to maximize consumer utility conditional on raising a certain amount of rent. Denote the gross profit of the firms from each consumer as

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3.2 The optimal indirect tax structure

I will first define and characterize a social optimal resource allocation of the economy, and then observe whether such an allocation can be achieved through indirect taxation. A social optimal resource allocation is one that can be attained when a “social planner” can make decisions for not only the government but also the consumers. The after-tax

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The social optimal outcome can be achieved although labor is non-taxable, because an income tax is equivalent to a uniform indirect tax structure. In order to correct the price distortion caused by market powers, indirect taxation should be discriminating across industries. The industries that are more competitive should be taxed more heavily. Lower tax rates or even subsidies should be imposed on less competitive industries, especially those with very low marginal costs like information goods. If such a tax structure results in fairness problems in practice, a well-designed corporate income tax system may be desirable. But theoretically such problems are unlikely to incur because the tax burdens are mostly on the shoulder of consumers when the markets are highly competitive.

Proposition 2 is in contrast to Ramsey (1927)’s tax rule. According to our model where all commodities are taxable, an optimal indirect tax structure may not prescribe a higher tax rate for a commodity that has a smaller price elasticity of demand or supply. Actually the optimal tax rates have nothing to do with the price elasticities. However, a tax on a commodity with very low price elasticities, like land, is close to an income tax. Hence is could be nearly efficient except distorting labor supply. From this perspective, the view of taxing more heavily land might be sensible. But one shall realize that such a “quasi” income tax cannot correct the price distortion caused by market power. As previously suggested, Ramsey tax rule is more sensible when many commodities of the economy are non-taxable.

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The commodities considered in this model are final goods rather than intermediate goods. Final goods enter the utility functions of consumers but intermediate goods do not. In the real world there are numerous intermediate goods and services. Many of them are also taxed, through value-added taxes for instance. The optimal indirect taxation only requires that the after-tax Lerner indexes of all final goods are the same. If the government has the flexibility of structuring the tax rates among intermediate goods and final goods, it should be easier to reach the social optimal outcome.

3.3 Does indirect taxation result in deadweight loss?

An important question about indirect taxation is whether the after-tax resource allocation is efficient compared to that without the taxation. In this subsection I will compare three possible resource allocations of the economy: the perfectly competitive outcome without taxation, the imperfectly competitive outcome without taxation, and the imperfectly competitive outcome with an optimal indirect taxation. The first one is a hypothetical outcome of course. It is often viewed as the “first-best” outcome.

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With imperfect competition, the social welfare consists of consumer surplus, producer surplus, and tax revenue. Producer surplus and tax revenue are expressed in monetary units,

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With a transfer equaling to the compensating variation, the consumer’s wellbeing can be restored to the before-tax level at the after-tax prices. Hence to conduct the welfare evaluation of the taxation, we can hypothetically transfer the tax revenue back to the consumer, and then compare the consumer’s wellbeing with the before-tax level.[7 ]The indirect taxation is said to result in deadweight loss if the compensated wellbeing is less than the before-tax level. We can also evaluate the welfare effect of market power with this approach.

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It implies that with an indirect tax structure and a transfer payment system, it is possible for a government to make all parties better off. If indirect taxation does result in deadweight loss or excess burden in practice, it should be due to the suboptimality of the tax structure, or highly elastic labor supply.

A change of real wage rate leads to an income effect and a substitute effect on labor supply. The two effects are often in opposite directions. Hence the elasticity of labor supply is an empirical issue. Many studies indeed find small elasticity of labor supply. For instance, Kosters (1967) finds very weak tax effects for male hours-of-work for those who are working, and somewhat stronger but still small effects on participation.The findings are confirmed by MaCurdy, Green and Paarsch (1990). Mroz (1987) finds similar weak tax effects on female hours-of-work for working women. See Heckman (1993) for a review of the literature.

This paper assumes fixed market structures for all industries. If there were free entry, the number of firms would be endogenous, so be the total fixed cost. In that case, the first-best outcome also requires thenumber of firms being optimally chosen. As found by Salop (1979), Mankiw and Whinston (1986), Suzumura and Kiyono (1987) and others, market mechanism often leads to excess entry of firms when there isincreasing return to scale. Therefore in order to reach the literally first-best outcome, the government must choose not only the optimal tax structure, but also the optimal number of firms for each industry. It cannotcompletely rely on the market to determine the entry of firms. Indeed, an optimal indirect tax structure only warrants post-entry efficiency. It cannot warrant efficient entry.

4.  Concluding Remarks

This paper intends to clarify some widespread misunderstandings about indirect taxation. It finds that in an economy where all commodities are taxable, an optimal indirect tax structure should manage to equalize the after-tax Lerner indexes of all commodities. Such a tax structure, which prescribes higher tax rates for markets with more intensive competition, corrects the price distortion caused by market powers and thusinduces socially efficient choices from consumers. This paper also finds that when consumers’ labor supplies are sufficiently inelastic, the optimal indirect taxation leads to potential Pareto improvement rather thandeadweight loss for the society. Therefore indirect taxation could be more efficient than direct taxation. The findings are in contrast to the conventional views of indirect taxation, particularly that of Atkinson andStiglitz (1972). Nevertheless this paper only offers a benchmark model for optimal taxation. In practice a tax structure should also reflect the various transaction costs involved in taxation.

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351-367.

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II: Tax Rules,” Vol. 61, No. 3, pp. 261-278.

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[1 ] When all commodities are taxable, whether income is taxable is not crucial, because an income tax is equivalent to a proportional indirect tax on all commodities. But a tax on “leisure” differs from a tax on income.

[2 ] This paper does not explicitly define the objective of the firms either. Kreps (1990, pp. 727), Dierker and Dierker (2006), and others suggest that it might be inappropriate to assume that imperfectly competitivefirms simply maximize their profits in a general equilibrium model.

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[5] Equivalently, one can treat the commodity prices as control variables of the planner. In that case the tax rates have to ben viewed as endogenously determined.

[6] In the case of imperfect competition, there is no assurance that equalities (26) can be achieved through indirect taxation. In the case that (26) cannot be exactly achieved, the government may not be able to induce the social optimal outcome unless it has more control variables.

[7 ]Note that the monetary transfer is calculated with the consumer’s after-compensation consumption, not his before-compensation consumption. Details please refer to Mas-Colell, Whinston and Green (1995, Chapter 3.I).

Previously published by the Peking University- China Center for Economic Research,

Hao Wang

I am grateful to C. C. Yang for his enlightening comments and suggestions. I also thank Been-Lon Chen, Tomoya Ida, Lixing Li, Shin-Kun Peng, Ivan Png, and workshop participants at the Institute of Economics, AcademiaSinica (Taipei), and the 9thInternational Conference of Japan Economic Policy Association (Tokyo) for helpful comments. All errors are mine.

Optimal Indirect Taxation under Imperfect Competition

Abstract: This paper considers indirect taxation in an economy where all commodities are taxable. Tax revenue is viewed as the “rent” of governmental coercion power, and gross profit is viewed as the “rent” of market power. A government maximizes consumer surplus conditional on raising certain tax revenue and gross profit. I first characterize the social optimal resource allocation where a planner can make decisions for the government and consumers. Then I show that the government can realize the social optimal outcome through an indirect tax structure. The optimal taxation should equalize the after-tax Lerner indexes of all commodities. Another finding is that the optimal indirect taxation generally results in welfare gain rather than deadweight loss when labor supply is sufficiently inelastic.

Keywords: Indirect tax, Deadweight loss, Excess burden, Imperfect competition

JELCodes:D59, H21, L16

 

Assistant Professor of Finance, Tsinghua University, Beijing, China