Melitz, M. J. & G. I. P. Ottaviano University of Munich July 22, 2011 & 1 / 20
& & 2 / 20
My Bachelor Thesis: Ottaviano et al. (2009) apply the model to study gains from the euro & 3 / 20
Melitz and Ottaviano (2008) set up a model similar to Melitz (2003) featuring monopolistic competition firm heterogeneity & 4 / 20
Melitz and Ottaviano (2008) set up a model similar to Melitz (2003) featuring monopolistic competition firm heterogeneity In addition, they model a linear demand system (with a homogenous good) endogenous markups, which respond to the toughness of competition in the market (feedback channel) & 4 / 20
Melitz and Ottaviano (2008) set up a model similar to Melitz (2003) featuring monopolistic competition firm heterogeneity In addition, they model a linear demand system (with a homogenous good) endogenous markups, which respond to the toughness of competition in the market (feedback channel) This new, highly tractable framework allows market size differences to play a role incorporates all (conventional) channels for welfare gains allows for analysis of various trade liberalization scenarios between several asymmetric countries & 4 / 20
I Preferences L consumers in each country share preferences U = q0 c + α qi c i Ω di 1 2 γ i Ω (q c i ) 2 di 1 2 η ( qi c i Ω over a continuum of differentiated varieties q i, i Ω and a homogenous good q 0 (numeraire with q c 0 > 0 by assumption). ) 2 di γ > 0 is the degree of product differentiation between varieties, so if γ 0 consumers only care about total consumption of all varieties Q c = i Ω qc i di α, η > 0 govern substitutability between q i & q 0, α or η = relative increase in demand for Q c & 5 / 20
II Demand Each consumer maximizes U s. t. the budget constraint = inverse demand: p i = α γq c i ηq c for all q c i > 0 Hence, we arrive at the linear market demand system: q i Lqi c = αl ηn + γ L γ p i + ηn L ηn + γ γ p, i Ω, where N is the measure of consumed varieties (Ω Ω) and p = 1 N i Ω p i di is the average price. & 6 / 20
II Demand Each consumer maximizes U s. t. the budget constraint = inverse demand: p i = α γq c i ηq c for all q c i > 0 Hence, we arrive at the linear market demand system: q i Lqi c = αl ηn + γ L γ p i + ηn L ηn + γ γ p, i Ω, where N is the measure of consumed varieties (Ω Ω) and p = 1 N i Ω p i di is the average price. In contrast to CES preferences, the price elasticity of demand ɛ = ( q i / pi)(p i /q i ) = [(p max /p i ) 1] 1 is not exclusively determined by product differentiation γ. & p max is the upper price bound, where demand for q i equals 0. 6 / 20
III Welfare Plugging qi c into U yields the following expression for welfare (indirect utility): U = I c + 1 2 ( η + γ ) 1 (α p) 2 + 1 N N 2 γ σ2 p, I c denotes the income of the consumer σ 2 p is the variance of prices & 7 / 20
III Welfare Plugging qi c into U yields the following expression for welfare (indirect utility): U = I c + 1 2 ( η + γ ) 1 (α p) 2 + 1 N N 2 γ σ2 p, I c denotes the income of the consumer σ 2 p is the variance of prices Welfare U rises with decreases in the average price p & increases in the variance of prices σ 2 p increases in N = love of variety 7 / 20
IV Production Markets for labor & the homogenous good: Each consumer inelastically supplies 1 unit of labor L, which is the only input factor of production. q 0 produced with constant returns to scale at unit cost assuming perfect competition for L & q 0 = w = 1 & 8 / 20
IV Production Markets for labor & the homogenous good: Each consumer inelastically supplies 1 unit of labor L, which is the only input factor of production. q 0 produced with constant returns to scale at unit cost assuming perfect competition for L & q 0 = w = 1 Monopolistic competition in the differentiated sector: After having incurred sunk entry cost f E (R & D), firms draw their marginal cost c (unit labor requirement) from the distribution G(c) with support on [0, c M ]. Then, they find out whether they can produce or not. Production technology is also CRS (no fixed prod. cost) & 8 / 20
V Firm Performance Firms which can cover their marginal cost c produce the profit-maximizing quantity q(c) = L γ [p(c) c], otherwise they exit. The firm with cost c D is just indifferent whether to produce: p(c D ) = p max = c D (< c M by ass.) & 9 / 20
V Firm Performance Firms which can cover their marginal cost c produce the profit-maximizing quantity q(c) = L γ [p(c) c], otherwise they exit. The firm with cost c D is just indifferent whether to produce: p(c D ) = p max = c D (< c M by ass.) Then, each firm s performance depends only on its cost draw c and the cutoff c D : p(c) = 1 2 (c D + c) µ(c) = 1 2 (c D c) q(c) = L 2γ (c D c) r(c) = p(c)q(c) = L 4γ (c2 D c2 ) π(c) = r(c) q(c)c = L 4γ (c D c) 2 & 9 / 20
VI & Zero expected profits in equilibrium = Free entry (FE): cd 0 π(c) dg(c) = L 4γ cd 0 (c D c) 2 dg(c) = f E. & 10 / 20
VI & Zero expected profits in equilibrium = Free entry (FE): cd 0 π(c) dg(c) = L 4γ cd 0 (c D c) 2 dg(c) = f E. Using these results, we can determine the cutoff: c D = 1 (γα + ηn p) ηn + γ and the zero cutoff profit (ZCP) condition: N = 2γ η α c D c D c, where c = [ c D 0 c dg(c)]/g(c D) is the average cost of surviving firms. This yields the equilibrium number of firms N and entrants N E = N/G(c D ). & 10 / 20
VII Parametrization of Technology Assuming productivity 1/c is Pareto distributed implies the power cost distribution of surviving firms: ( ) c k G(c) =, c [0, c D ] c D & 11 / 20
VII Parametrization of Technology Assuming productivity 1/c is Pareto distributed implies the power cost distribution of surviving firms: ( ) c k G(c) =, c [0, c D ] c D Given this assumption, the cost cutoff is: [ 2(k + 1)(k + 2)γ(cM ) k f E c D = L ] 1 k+2 The zero cutoff profit (ZCP) condition then implies: & N = 2(k + 1)γ η α c D c D 11 / 20
VIII Outcome The cutoff c D uniquely determines the averages of all firm-level performance measures: c = k k+1 c D p = 2k+1 µ = 1 2 2k+2 c D 1 k+1 c D q = r = L 2γ L 2γ π = f E (c M ) k (c D ) k 1 k+1 c D = (k+2)(c M) k f (c D ) k+1 E 1 k+2 (c D) 2 = (k+1)(c M) k f (c D ) k E & 12 / 20
VIII Outcome The cutoff c D uniquely determines the averages of all firm-level performance measures: c = k k+1 c D p = 2k+1 µ = 1 2 2k+2 c D 1 k+1 c D q = r = L 2γ L 2γ π = f E (c M ) k (c D ) k 1 k+1 c D = (k+2)(c M) k f (c D ) k+1 E 1 k+2 (c D) 2 = (k+1)(c M) k f (c D ) k E...as well as welfare, which increases with a lower cutoff c D : U = 1 + 1 ( 2η (α c D) α k + 1 ) k + 2 c D & 12 / 20
I 2 countries indexed l, h = H, F (for simplicity, can be extended) that only differ in size L l and trade barriers (same preferences and technology) per-unit trade costs τ l > 1 (no fixed export costs) & 13 / 20
I 2 countries indexed l, h = H, F (for simplicity, can be extended) that only differ in size L l and trade barriers (same preferences and technology) per-unit trade costs τ l > 1 (no fixed export costs) Due to CRS and segmented markets, firms maximize domestic and export profits independently s. t. the same demand condition as in the closed economy. This leads to the following cutoff rules: cd l = pl max c l X = pmax/τ h h = cd h /τ h for firms exporting from l to h As before, cutoffs summarize all performance measures, in particular: p l D (c) = 1 2 (cl D + c) pl X (c) = 1 2 (cl X + c) & 13 / 20
II Assuming Pareto productivity distribution, free entry implies: L l (c l D )k+2 + L h ρ h (c h D )k+2 = γφ, where φ 2(k + 1)(k + 2)(c M ) k f E (technology index) and ρ l (τ l ) k (0, 1) measures freeness of trade. & 14 / 20
II Assuming Pareto productivity distribution, free entry implies: L l (c l D )k+2 + L h ρ h (c h D )k+2 = γφ, where φ 2(k + 1)(k + 2)(c M ) k f E (technology index) and ρ l (τ l ) k (0, 1) measures freeness of trade. This system of equations can be solved for the cutoffs: ] 1 k+2, l = H, F. c l D = [ γφ L l 1 ρ h 1 ρ l ρ h The mass of firms N l in the open economy is then given by & N l = 2(k + 1)γ η α c l D c l D 14 / 20
III The expressions for all average firm performance measures are analogous to the closed economy and so is the term for welfare: U l = 1 + 1 2η (α cl D ) ( α k + 1 ) k + 2 cl D & 15 / 20
III The expressions for all average firm performance measures are analogous to the closed economy and so is the term for welfare: U l = 1 + 1 2η (α cl D ) ( α k + 1 ) k + 2 cl D Melitz and Ottaviano (2008) show that c l X < cl D, so only relatively more productive firms export. Furthermore, it can be shown that in the trade equilibrium reciprocal dumping occurs: px l (c)/τ h < pd l (c), c cl X. This arises due to the homogenous good and equals a no-arbitrage condition. & 15 / 20
IV The cost cutoff is lower in the open economy: c l D < c D Similar outcome as in Melitz (2003), but through a different channel: [...] import competition increases competition in the domestic product market, shifting up residual demand price elasticities for all firms at any given demand level. This forces the least productive firms to exit. [...] the increased competition induces a downward shift in the distribution of markups across firms. Although only relatively more productive firms survive (with higher markups than the less productive firms who exit), the average markup is reduced. The distribution of prices shifts down due to the combined effect of selection and lower markups. [...] average firm size and profits increase - as does product variety. & 16 / 20
IV [...] In this model, welfare gains from trade thus come from a combination of productivity gains (via selection), lower markups (pro-competitive effect), and increased product variety. Hence, the model captures altogether: pro-competitive effect selection (& reallocation) effect variety effect = combined modelling of all these welfare channels in one framework! & 17 / 20
IV [...] In this model, welfare gains from trade thus come from a combination of productivity gains (via selection), lower markups (pro-competitive effect), and increased product variety. Hence, the model captures altogether: pro-competitive effect selection (& reallocation) effect variety effect = combined modelling of all these welfare channels in one framework! Market size still matters, as trade barriers preclude full integration of markets: If L H > L F, then ceteris paribus c H D < cf D. & 17 / 20
Bilateral (symmetric) liberalization decrease in symmetric trade costs τ H = τ F = τ increases competition in both markets: cd H, cf D =... = U & 18 / 20
Bilateral (symmetric) liberalization decrease in symmetric trade costs τ H = τ F = τ increases competition in both markets: cd H, cf D =... = U Unilateral liberalization (of country H) τ H or ρ H while ρ F = const. = c H D & cf D The liberalizing country suffers a welfare loss while its trading partner gains! In the short run, the pro-competitive effect drives down cd H, but in the long run the relocation of firms from H to F causes cd H & cf D & 18 / 20
Melitz, M. J. (2003). The impact of trade on intra-industry reallocations and aggregate industry productivity. Econometrica, 71(6):1695 1725. Melitz, M. J. and Ottaviano, G. I. P. (2008). Market size, trade, and productivity. Review of Economic Studies, 75(1):295 316. Ottaviano, G. I. P., Taglioni, D., and Mauro, F. D. (2009). The euro and the competitiveness of european firms. Economic Policy, 24(57):553. & 19 / 20
Thank you for your attention! & 20 / 20