Melitz–Ottaviano Variable-Markup Trade Model

Melitz–Ottaviano variable-markup trade model is a cornerstone general-equilibrium framework in international economics and business and economics theory that integrates heterogeneous firm productivity with endogenous, variable price-cost markups driven by market size and import competition. Developed by economists Marc J. Melitz and Gianmarco I. P. Ottaviano in their January 2008 Review of Economic Studies article "Market Size, Trade, and Productivity", the model overcomes the most restrictive feature of the canonical 2003 Melitz model and the Krugman new trade theory: their reliance on Constant Elasticity of Substitution (CES) preferences, under which every firm charges an identical, constant percentage markup over marginal cost regardless of how many competitors enter the market or how large the economy becomes. By replacing CES preferences with a quasi-linear quadratic utility system (generalizing Ottaviano, Tabuchi, and Thisse, 2002) that generates linear downward-sloping demand curves, Melitz and Ottaviano obtain a finite choke price (cost cutoff c_D) at which demand hits zero without requiring fixed overhead production costs. In equilibrium, more productive firms (lower marginal cost c) charge higher absolute and percentage markups μ(c) = (c_D − c)/2 while passing only 50 percent of their cost advantage to consumers (incomplete pass-through), and larger markets (L) or bilateral trade liberalization exert a pro-competitive selection effect that lowers the cutoff cost c_D, forces the least productive domestic firms to exit, compresses markups for surviving high-cost firms, and boosts aggregate industry productivity.

In the benchmark Melitz model (2003) built on Dixit–Stiglitz (1977) CES monopolistic competition with elasticity of substitution σ > 1, a firm with marginal cost c sets its price equal to a constant proportional markup p(c) = [σ / (σ − 1)]c. While analytically tractable, CES demand imposes three strong counterfactual restrictions that contradict micro-econometric trade data:

1. Invariance of Markups to Firm Productivity: Under CES, a giant low-cost exporter and a marginal domestic producer charge the same ratio of price to marginal cost, σ/(σ − 1).
2. Absence of Pro-Competitive Markup Compression: Under CES, doubling the population L of a city or opening an economy to tough foreign import competition has zero direct effect on any surviving firm's price or markup; selection operates through the domestic factor market (bidding up real wages via fixed overhead demand).
3. Complete (100%) Exchange-Rate and Tariff Pass-Through: Because the price-cost ratio is fixed, a 10 percent tariff or cost shock raises a firm's consumer price by a full 10 percent, contradicting empirical evidence of incomplete pass-through (around 50 percent).

Melitz and Ottaviano (2008) resolve all three anomalies simultaneously by introducing a linear demand system in which the price elasticity of demand increases with the price charged by the firm and with the toughness of local competition.

Consumer Utility and the Choke Price

Consider an economy populated by L identical consumers, each endowed with 1 unit of labor (and initial holdings of a homogeneous numeraire good q₀^c > 0 produced under constant returns at unit wage w = 1). Each consumer c maximizes a quasi-linear quadratic utility function over the homogeneous numeraire q₀^c and a continuum of horizontally differentiated varieties i ∈ Ω:

The three preference parameters α > 0, γ > 0, and η > 0 have intuitive economic meanings:

• α > 0 and η > 0 govern the substitution pattern between the differentiated industry as a whole and the outside numeraire good q₀.
• γ > 0 measures the degree of product differentiation (love of variety) across varieties i ∈ Ω. As γ → 0, varieties become perfect substitutes and consumers care only about total industry consumption Q^c = ∫_i∈Ω q_i^c di.

Assuming positive consumption of the numeraire good (q₀^c > 0), the consumer's first-order condition with respect to variety i at price p_i is α − γq_i^c − ηQ^c = p_i. Let Ω* ⊂ Ω denote the subset of consumed varieties with positive demand (q_i^c > 0), let N denote the mass (measure) of competing varieties in Ω*, and let p̄ = (1/N) ∫_i∈Ω* p_i di denote the average price of competing varieties in the market. Summing across all L consumers yields the market-level linear demand curve for variety i:

Equivalently, demand q_i > 0 is positive if and only if the firm's price p_i lies below the endogenous choke price (maximum price threshold) p_max:

Notice that the choke price p_max is a summary statistic for the "toughness of competition" in the local market: as more competing varieties enter (N rises) or as rivals lower their average price (p̄ falls), the choke price p_max shifts downward, shifting every firm's demand curve inward and making demand more price-elastic at any given price.

Cost Cutoff c_D and Optimal Firm Pricing Rules

As in the Melitz model, a prospective entrant pays a sunk entry cost f_E > 0 to draw its marginal labor cost c (inverse productivity 1/φ) from a common distribution G(c) on [0, c_M]. Crucially, unlike Melitz (2003), there is zero fixed overhead production cost (f = 0): a firm produces positive output if and only if its marginal cost c lies below the market choke price p_max. Consequently, the marginal surviving firm in the market has marginal cost c_D exactly equal to the choke price:

Any entrant drawing c > c_D cannot cover its marginal cost even at zero output and exits upon entry; any firm drawing c ≤ c_D maximizes operating profit π(c) = (p(c) − c)q(c) subject to the linear demand curve q(c) = (L/γ)(c_D − p(c)). The first-order condition q(c) = (L/γ)(p(c) − c) pins down all five firm-level performance metrics purely as functions of the firm's own marginal cost c and the market cutoff c_D:

1. Optimal Price: p(c) = (1/2)( c_D + c )
2. Absolute Markup: μ(c) ≡ p(c) − c = (1/2)( c_D − c )
3. Output Quantity: q(c) = ( L / 2γ )( c_D − c ) = ( L / γ ) μ(c)
4. Sales Revenue: r(c) = p(c)q(c) = ( L / 4γ )[ (c_D)² − c² ]
5. Operating Profit: π(c) = ( L / 4γ )( c_D − c )²

To derive closed-form general-equilibrium aggregates, Melitz and Ottaviano adopt a Pareto distribution of firm productivity 1/c on [1/c_M, ∞) with shape parameter k ≥ 1, which corresponds to the cumulative cost distribution:

Here, k = 1 represents a uniform cost distribution, while k → ∞ represents degenerate homogeneous costs concentrated at c_M. Imposing the free-entry zero-expected-profit condition ∫₀^c_D π(c) dG(c) = f_E yields the closed-form equilibrium domestic cost cutoff c_D in an economy of population size L:

Examining how the cost cutoff c_D and equilibrium industry aggregates respond to a larger market size L reveals the signature Market Size Pro-Competitive Effect:

• Lower Cost Cutoff (↓ c_D) and Higher Aggregate Productivity: Because ∂c_D/∂L < 0, a larger market L attracts a larger mass of competing product varieties N = 2(k + 1)γ(α − c_D)/(ηc_D), which pushes down the choke price p_max = c_D. The least productive firms (with costs near the old c_D) are driven out of the market, raising average industry productivity.
• Lower Average Prices and Lower Average Markups: With a lower c_D, the average price p̄ = [(2k + 1)/(2k + 2)]c_D and the average markup μ̄ = c_D/(2k + 2) are lower in larger markets, while surviving low-cost stars expand output q(c) and earn higher total profits π(c) due to the scale factor L.
• Higher Firm Cost Dispersion vs. Lower Price Dispersion: Larger markets exhibit wider output and revenue skewness toward top firms, raising aggregate consumer welfare through three channels: more product varieties (N ↑), lower average prices (p̄ ↓), and lower price variance.

Domestic vs. Export Cutoffs (c_D and c_X) and Reciprocal Dumping

In an open economy with two countries l, h separated by an iceberg trade cost τ_lh > 1 (so a firm in country l with production cost c faces delivered marginal cost τ_lhc when selling in foreign market h), markets are segmented and each firm sets separate profit-maximizing prices at home and abroad:

• Domestic Survival Cutoff (c_D^l): A firm in country l sells domestically if c ≤ c_D^l, charging domestic price p_D^l(c) = (1/2)(c_D^l + c).
• Export Cutoff (c_X^l): The same firm exports to foreign market h if and only if its delivered marginal cost τ_lhc lies below the foreign market's choke price c_D^h:

Charging export price p_X^l(c) = (1/2)(c_D^h + τ_lhc) = (τ_lh/2)(c_X^l + c). Notice that because c_X^l < c_D^l, every exporting firm absorbs part of the iceberg trade cost τ_lh into a lower factory-gate markup on exports than on domestic sales (p_X^l(c)/τ_lh < p_D^l(c))—generating endogenous reciprocal dumping (Brander and Krugman, 1983) across the entire continuum of heterogeneous exporters.

Bilateral vs. Unilateral Trade Liberalization

When bilateral trade barriers τ fall, import competition intensifies in both countries, lowering the domestic cost cutoffs c_D^l and c_D^h just like an expansion in market size L: high-cost domestic firms exit, surviving domestic markups are compressed, and market share shifts toward low-cost exporters, generating welfare gains from both inter-firm reallocation (the Melitz model channel) and pro-competitive markup reductions (the Melitz–Ottaviano channel). Moreover, when countries differ in size (L_h > L_l), the larger country serves as a stronger focal export hub in the presence of trade costs (a generalized home-market effect akin to New Economic Geography).

How does the Melitz–Ottaviano (2008) model differ from the original Melitz (2003) model?

The original Melitz model (2003) assumes Dixit–Stiglitz Constant Elasticity of Substitution (CES) preferences, where every firm charges an identical constant percentage markup σ/(σ − 1) over marginal cost and selection occurs through fixed overhead costs f > 0 bidding up real wages. The Melitz–Ottaviano (2008) model uses quasi-linear quadratic preferences yielding linear demand curves with a finite choke price c_D: markups vary across firms (μ(c) = (c_D − c)/2), no fixed production costs are needed for selection, and larger markets or trade openness directly compress firm markups via tougher product-market competition.

Why do more productive firms charge higher markups in the Melitz–Ottaviano model?

Because a firm with lower marginal cost c faces a linear demand curve with choke price c_D, it sets its optimal price halfway between its marginal cost c and the market choke price c_D: p(c) = (c_D + c)/2. Thus, when a firm's cost c is lower by 1.00 unit of numeraire, it passes 0.50 units to consumers as a lower price and retains the remaining 0.50 units as a higher absolute markup μ(c) = (c_D − c)/2 (and a higher percentage markup over c).

Why do exporting firms engage in "dumping" (charging a lower factory-gate markup on exports than at home)?

When a firm exports to a foreign market across an iceberg trade barrier τ > 1, its delivered marginal cost τc is closer to the foreign market's choke price c_D* than its domestic cost c is to the domestic choke price c_D. Because the firm passes only 50 percent of the trade cost τ onto foreign consumers, its net-of-transport export price p_X(c)/τ is lower than its domestic price p_D(c).

1. Melitz, M. J., & Ottaviano, G. I. P. (2008). "Market Size, Trade, and Productivity." Review of Economic Studies, 75(1), 295–316. https://doi.org/10.1111/j.1467-937X.2007.00463.x
2. Melitz, M. J. (2003). "The Impact of Trade on Intra-Industry Reallocations and Aggregate Industry Productivity." Econometrica, 71(6), 1695–1725. https://doi.org/10.1111/1468-0262.00467
3. Ottaviano, G. I. P., Tabuchi, T., & Thisse, J.-F. (2002). "Agglomeration and Trade Revisited." International Economic Review, 43(2), 409–435. https://doi.org/10.1111/1468-2354.t01-1-00021
4. Syverson, C. (2004). "Market Structure and Productivity: A Concrete Example." Journal of Political Economy, 112(6), 1181–1222. https://doi.org/10.1086/424743
5. De Loecker, J., Goldberg, P. K., Khandelwal, A. K., & Pavcnik, N. (2016). "Prices, Markups, and Trade Reform." Econometrica, 84(2), 445–510. https://doi.org/10.3982/ECTA11042