Optimal Taxation and Market Power

Overview

This paper asks whether and how optimal income taxation should change when firms have market power. The question is motivated by the documented rise in economy-wide markups since 1980, which has compressed the labor share, widened the gap between worker and entrepreneurial income, and generated allocative inefficiency through excessive pricing.

The authors develop a Mirrleesian optimal taxation framework augmented with three features absent from the canonical literature: (i) oligopolistic intermediate goods markets with endogenous, variable markups, (ii) heterogeneous firm productivities, and (iii) two occupational groups—wage-earning workers and profit-earning entrepreneurs—whose abilities are private information. Entrepreneurs strategically set prices under Cournot competition, which means that the tax system affects profits both through a firm’s own behavior and through the responses of its competitors. This strategic interaction is the critical novelty relative to prior work that assumes monopolistic competition.

The main theoretical contribution is the derivation of optimal tax formulas for both labor income and profit income that decompose into four named components: (i) the Mirrleesian incentive component, which reflects the standard trade-off between redistribution and labor supply distortions; (ii) the Pigouvian component, which corrects for the externality from market power by subsidizing labor and entrepreneurial effort to offset the output shortfall from high markups; (iii) the Reallocation Effect (RE), which shifts the profit tax to redirect labor inputs from low-markup firms to high-markup firms where labor is inefficiently scarce, and which emerges only under heterogeneous markups; and (iv) the Indirect Redistribution Effect (IRE), which uses changes in competitors’ product prices—a channel present only under oligopolistic (not monopolistic) competition—to redistribute income between entrepreneurs.

For the labor income tax, the dominant force is the Pigouvian component. As average markups rise, the Pigouvian subsidy to labor supply grows, mechanically reducing optimal labor income tax rates. The profit tax is shaped by all four components in opposing directions; the net quantitative effect is resolved empirically.

The model is calibrated to match distributions of labor income (from the Current Population Survey), profits (from Compustat-based data in De Loecker, Eeckhout, and Unger 2020), and firm-level markups (also from De Loecker, Eeckhout, and Unger 2020, using the cost-minimization approach) for the US in 1980 and 2019. The cost-weighted average markup rose from 1.25 in 1980 to 1.33 in 2019, with the increase concentrated at the top of the markup distribution.

The central quantitative prescription is that the optimal labor income tax rate should decline by 7.7 percentage points between 1980 and 2019 (average optimal rate falls from 22.0 percent to 14.3 percent), while the optimal profit tax rate should rise by 2.2 percentage points on average (from 58.4 percent to 60.5 percent) and by 29.1 percentage points at the top. The decline in the labor income tax is driven primarily by the rise in average markups reducing the Pigouvian component. The increase in the profit tax, especially at the top, is driven primarily by the Mirrleesian component operating through the skill gap, which rises because higher markups reduce profit elasticity. The Pigouvian and reallocation components push in the opposite direction on the profit tax, but the Mirrleesian effect dominates.

The optimal profit tax structure is regressive for large, high-markup firms—reflecting the RE, which requires lower tax rates for high-markup firms to incentivize labor reallocation toward them—but less regressive in 2019 than in 1980, reflecting the distributional tightening from rising markup inequality.

Robustness checks across parameter values for the social welfare curvature k, the span of control ξ, and the elasticity of substitution σ confirm that the directional results hold: labor income tax rates decrease and profit tax rates increase from 1980 to 2019 across all parameter configurations. Extensions to nonlinear sales taxes and conditioning on markups confirm that even when the planner can observe markups directly, the first-best is not achievable because markups are endogenous to entrepreneurs’ unobservable decisions.

Q&A

Q1: What is the fundamental difference between this paper’s model and prior work on optimal taxation with market power?

Prior work using monopolistic competition (e.g., Gürer 2021; Boar and Midrigan 2019) assumes each entrepreneur holds monopoly power in its own market, so no strategic interaction exists between firms. Under monopolistic competition, entrepreneurs price to maximize utility given competitors’ choices, and the envelope theorem implies that tax changes have no first-order effect on prices or utility through the pricing channel—the Indirect Redistribution Effect (IRE) disappears. In this paper, entrepreneurs compete in Cournot oligopolistic markets with a finite number of firms I, so each firm’s pricing depends on competitors’ output. A change in one firm’s output (induced by taxation) shifts competitors’ prices, opening a redistribution channel through product markets that is entirely absent in monopolistic competition. Additionally, the Reallocation Effect (RE) emerges only when firm-level markups are heterogeneous, which requires oligopolistic (not perfectly competitive) markets.

Q2: What are the four components of the optimal tax formula and how does each relate to market power?

The optimal tax wedge for both labor and profit income decomposes into four components. First, the Mirrleesian component reflects the standard trade-off between redistribution and the efficiency cost of taxation; in the presence of market power, it is modified because the skill gap for entrepreneurs depends on markups through the profit elasticity. Second, the Pigouvian component corrects the externality from market power, which causes prices to exceed marginal cost and output to be inefficiently low; it implies a subsidy to both worker and entrepreneurial effort, scaled by the reciprocal of the average markup (for the labor tax) or firm-level markup (for the profit tax). Third, the Reallocation Effect (RE) applies only to the profit tax and reflects that labor should be shifted toward high-markup firms where it is inefficiently underemployed; it reduces the tax rate for firms whose markup exceeds the average. Fourth, the Indirect Redistribution Effect (IRE) captures redistribution through competitor price changes under oligopolistic interaction; it can either raise or lower the profit tax rate depending on the distribution of social welfare weights and the cross-inverse demand elasticity.

Q3: What happens to the labor income tax formula as average markups rise?

The labor income tax formula contains a Pigouvian component equal to the reciprocal of the employment-weighted average markup. As average markups rise, this reciprocal falls, reducing the optimal labor income tax rate. Quantitatively, the optimal average labor income tax rate declines from 22.0 percent in 1980 to 14.3 percent in 2019, a decrease of 7.7 percentage points. In a purely competitive benchmark economy, the top labor income tax rate would be around 60 percent (consistent with Saez 2001); in the calibrated model with market power, it is 34.2 percent in 1980 and 28.7 percent in 2019. The Pigouvian component accounts for essentially the entire difference because the Mirrleesian component, when calibrated to the same labor income distribution, is unchanged.

Q4: How does the Mirrleesian component cause the top profit tax rate to rise with market power?

The Mirrleesian component of the profit tax is driven by the skill gap, defined as the proportional rate of change in the composite entrepreneur ability measure. The skill gap depends on markups through the profit elasticity: as markups rise, profit elasticity falls (since profit elasticity is approximately the reciprocal of markup minus the span-of-control parameter minus the inverse of the labor supply elasticity term), which increases the skill gap. A higher skill gap amplifies the income divergence across entrepreneur types, increasing the Mirrleesian incentive to redistribute at the top. Quantitatively, Figure 5 shows that the rise in the skill gap from 1980 to 2019 tracks almost exactly the change in the inverse of profit elasticity, confirming that markup changes—not changes in the ability distribution—are the primary driver of increased Mirrleesian pressure on top profit taxes.

Q5: How does the Reallocation Effect influence the structure (progressivity) of the profit tax?

The RE term equals the ratio of the average markup to the firm-level markup minus one: RE(θe) = μ/μ(θe) − 1. For firms with markups above the average, RE is negative, reducing their optimal tax rate; for firms below the average, RE is positive, increasing it. This implies that the optimal profit tax should be regressive relative to markup (i.e., high-markup firms face lower marginal tax rates), even though the overall profit tax rises on average. This provides a novel rationale for why the profit tax schedule in practice is less progressive—or even regressive—for large firms. As markups rise across the distribution, the reallocation effect pushes down the top profit tax but does not offset the larger increase from the Mirrleesian component in the quantitative exercise.

Q6: What is the Indirect Redistribution Effect and why does it disappear under monopolistic competition?

The IRE captures the change in entrepreneurial utility that arises because a tax reduction for one entrepreneur increases their output, which reduces the prices of substitute goods produced by competitors, thereby lowering competitors’ incomes. Under oligopolistic competition with I > 1 firms per market, the cross-inverse demand elasticity is nonzero, so competitor prices are sensitive to any one firm’s output decision, and this redistribution channel is open. Under monopolistic competition (I = 1), each entrepreneur is the sole producer in its market; competitors’ prices do not depend on the firm’s output, the cross-inverse demand elasticity is zero, and the IRE vanishes by the envelope theorem. The IRE is also absent in perfectly competitive economies. Empirical evidence for the US suggests the hazard ratio of profits is sufficiently high that the IRE generally pushes toward a lower top profit tax rate, but the Mirrleesian effect dominates in the quantitative results.

Q7: What is the quantitative effect of rising markups on the optimal tax rates, and what drives the net change in the profit tax?

The model calibrated to 1980 and 2019 US data prescribes a decline in the optimal average labor income tax rate of 7.7 percentage points (from 22.0 to 14.3 percent) and an increase in the optimal average profit tax rate of 2.2 percentage points (from 58.4 to 60.5 percent). At the top of the profit distribution, the increase is 29.1 percentage points. The net profit tax increase results from four opposing forces: the Pigouvian component falls (pushing toward lower taxes) and the RE decreases for high-markup firms (also pushing down the top rate), while the IRE and especially the Mirrleesian component rise (pushing up top rates). The Mirrleesian effect is the dominant force, driven by rising markup inequality reducing profit elasticity and widening the skill gap for top entrepreneurs.

Q8: How does the counterfactual analysis isolate the role of markups from productivity changes?

The counterfactual fixes the markup distribution at its 1980 level while holding the 2019 productivity distribution constant, then solves for optimal taxes. The result is that high-profit entrepreneurs would face lower optimal tax rates under 1980 markups than under 2019 markups, while low-profit entrepreneurs would face higher rates. Decomposing the difference, the Pigouvian component and the RE are larger for high incomes under 1980 (lower) markups, making the profit tax more regressive, while the IRE and the Mirrleesian component are smaller under 1980 markups, producing a lower top rate. The increase in the Mirrleesian component due to the markup increase from 1980 to 2019 is identified as the primary reason top profit taxes rise. This isolates the markup channel from the productivity channel in accounting for changes in optimal taxes.

Q9: What does the robustness analysis reveal about parameter sensitivity?

The main qualitative result—labor income taxes decline and profit taxes rise from 1980 to 2019—holds across a broad parameter space. The optimal profit tax rate is largely insensitive to the social welfare curvature parameter k: across k ∈ {0.77, 1, 3}, the average optimal profit tax rate is approximately 58 percent in 1980 and 61 percent in 2019. The optimal average labor income tax rate is more sensitive to k: for k = 0.7, 1, and 3, the 1980 rates are 20.3, 26.7, and 44.6 percent, and the 2019 rates are 12.5, 19.4, and 39.1 percent, respectively. Changes in the span-of-control parameter ξ and the substitution elasticity σ do not affect the labor income tax wedge schedule directly but do influence it indirectly through the markup distribution. The directional results are confirmed for all tested parameter configurations.

Q10: What is the role of the “additivity property” from prior externality literature, and why does it fail here?

The additivity property from the Pigouvian externality literature (see Kopczuk 2003; Sandmo 1975) states that the Pigouvian correction is separable from other components of the optimal tax formula, implying that rising markups would simply decrease the optimal tax rate (since 1/μ falls). This property holds under simplifying assumptions that abstract from the general equilibrium and incentive effects of market power. In the present model, the additivity property does not hold because markups enter all four components of the optimal tax formula—not just the Pigouvian term—through the skill gap (Mirrleesian component), the RE, and the IRE. As a result, rising markups can increase the optimal profit tax rate even though the Pigouvian component falls, because the skill gap and Mirrleesian force dominate.

Q11: Can the government attain the first-best by conditioning taxes on markups?

No. The paper demonstrates that even if the planner can observe and condition taxes on firm-level markups, the first-best is not achievable. The reason is that markups are endogenous to the entrepreneurs’ unobservable decisions: an entrepreneur’s markup depends on their privately known type and chosen output. When the planner designs a mechanism that conditions on markup, the incentive constraint facing entrepreneurs remains the same as in the benchmark model, because the promise-keeping constraints are independent of the entrepreneur’s true type when markups are observable. The optimal allocation with markup-conditioned taxes is shown to be equivalent to the second-best with nonlinear sales taxes, which still falls short of the first-best.

Q12: What are the policy implications for the design of the profit tax schedule?

The model yields three concrete prescriptions for the joint design of labor and profit income taxes in the context of rising market power. First, labor income taxes should be reduced and top profit taxes should be increased as market power rises. Second, for large, high-productivity firms the profit tax should be designed to be appropriately regressive to enhance allocative efficiency through the Reallocation Effect—this provides a new normative justification for why profit tax schedules observed in practice are often less progressive than labor income taxes. Third, while profit taxes should be regressive for large firms, the degree of regressivity should decrease as market power rises, reflecting the trade-off between efficiency and equality: higher markups increase the Mirrleesian pressure for redistribution at the top, reducing the optimal regressivity.

Key Concepts

Mirrleesian component (of the optimal tax formula): The standard incentive component of the optimal tax, capturing the trade-off between direct redistribution and the efficiency cost of taxation. In the presence of market power, this component is modified because the skill gap for entrepreneurs depends on markups through the profit elasticity: higher markups reduce profit elasticity, widen the skill gap, and amplify the Mirrleesian force toward higher top profit taxes.

Pigouvian component: The correction in the optimal tax formula for the externality from market power. Because oligopolistic pricing causes output to be inefficiently low, the optimal tax subsidizes both worker and entrepreneurial labor supply. In the labor income tax formula, the Pigouvian component is the reciprocal of the employment-weighted average markup; in the profit tax formula, it is the reciprocal of the firm-level markup. As average markups rise, the Pigouvian component reduces the optimal labor income tax rate.

Reallocation Effect (RE): A component of the optimal profit tax formula that captures the efficiency gain from reallocating labor inputs from low-markup firms (where labor’s marginal product is high relative to value) to high-markup firms (where labor demand is inefficiently low). It equals the ratio of the average markup to the firm-level markup minus one. It implies a lower optimal marginal tax rate for firms with markups above the average, producing a regressive structure in the profit tax for large firms. This effect is absent under monopolistic competition (uniform markups) and in competitive markets.

Indirect Redistribution Effect (IRE): A component of the optimal profit tax formula specific to oligopolistic competition, capturing redistribution through competitor prices. Lowering the marginal tax rate of a high-productivity entrepreneur raises their output, which reduces the prices of substitutable goods produced by their competitors, thereby lowering competitors’ incomes and redistributing toward workers who benefit from lower prices. This effect is present only when the cross-inverse demand elasticity is nonzero—i.e., only under oligopolistic (Cournot) competition with multiple firms per market—and vanishes under monopolistic competition and in the limit as the number of firms grows to infinity.

Skill gap (for entrepreneurs): The proportional rate of change in the composite entrepreneur ability measure with respect to entrepreneur type, analogous to the Mirrleesian skill gap for workers. Under market power, the entrepreneur skill gap depends on the markup through the profit elasticity: as firm-level markups rise, profit elasticity falls, the skill gap increases, and the income dispersion across entrepreneurs widens, which amplifies the Mirrleesian incentive to redistribute at the top and raises the optimal top profit tax rate.

Symmetric Cournot Competitive Tax Equilibrium (SCCTE): The equilibrium concept used in the paper. It is a combination of a tax system, symmetric allocation, and symmetric price system such that all agents (final goods producer, entrepreneurs of each type, workers) are optimizing, strategic interaction in the intermediate goods market is a Cournot Nash equilibrium within each granular market, and all commodity and labor markets clear. Strategic interaction is restricted to within each granular market (firms in the same market compete), so decisions across markets are taken as given.

Composite ability: A combined measure of entrepreneur productivity that determines equilibrium allocations and optimal taxation in the nested-CES economy. It aggregates the entrepreneur’s raw ability (affecting output capacity) and the demand parameter (affecting the market-level markup). The markup-relevant component and the quantity-relevant component are not perfect substitutes in the composite, since equilibrium prices depend on their specific composition while equilibrium quantities depend only on their combined value.