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Scale Economies, Product Differentiation, and Monopolistic Competition

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Scale Economies, Product Differentiation, and Monopolistic Competition Scale Economies, Product Differentiation, and Monopolistic Competition By Kiminori Matsuyama (Permanently) Work in Progress Last Updated: March 17, 2009; 11:34:51 PM Page 1 of 129 Overview • Introduction • Endogenous Technologies in Competitive Models with External Economies of Scale • Competitive Models with Internal Economies of Scale • Monopolistic Competitive Models with Internal Economies of Scale 9 Tradeable Differentiated Goods: Gains from Product Variety and Intra-Industry Trade 9 Nontradeable Differentiated Goods: Agglomeration Effects, 9 Costly Trade in Differentiated Goods: Home Market Effect and Economic Geography. • Extensions; Firm Heterogeneity, Multi-Product, Variable Mark-Up etc. (Unfinished) • Bibliography Page 2 of 129 Introduction • Competitive, CRS models of trade stress gains from trade between dissimilar countries. Yet, a bulk of trade is done between similar countries. Aside from those with non- homothetic preferences, models with CRS do not sit well with this observation. • IRS implies that even (inherently) identical countries can gain from trade, by each specializing in different activities. • Agglomeration is one of the most salient features of the economic landscape. Yet, it is difficult to explain in a world with CRS, where every country has access to the same technologies. • Of course, the Ricardian theory allows for technological differences across regions and countries. • Aside from the geography and climate, however, it is difficult to think of technology differences to be exogenous factors. And if we are to endogenize technology in order to understand how the technological differences across countries emerge and persist, we must confront the problem of how to incorporate IRS in general equilibrium framework. Page 3 of 129 Part IV look at various ways of introducing IRS in general equilibrium framework. • External Economies of Scale, where each producer faces CRS but externalities generate IRS at sectoral or economy levels. This is also a useful way of endogenizing technologies within the competitive framework. • Internal Economies of Scale within the competitive framework. • Internal Economies of Scale within the Monopolistically Competitive framework, where different firms produce Differentiated Products. Within this framework, we consider models with differentiated products that are 9 Costlessly Tradeable to see the Gains from Trade due to Increased Product Variety,and Intra-Industry Trade 9 Nontradeable to see Agglomeration Effects 9 Subject to the Iceberg Trade Costs to see the Home Market Effect and Economic Geography. • We also review some recent works that relax some restrictive features of the basic monopolistic competition models (firm heterogeneity, multi-product, and variable mark-up, etc.) Page 4 of 129 Endogenous Technologies: External Economies & Increasing Returns External economies are a simple way of introducing sector-wide or economy-wide increasing returns without departing from the competitive framework. Here, I follow mostly Helpman and Krugman (1985; Ch.3). Let us modify the neoclassical production functions as follows: j Production Function of a sector-j firm: x j = F (v j ;ξ j ), j which maps the firm’s input, vj to its output, xj. Holding ξj constant, F (•;ξ j ) satisfies all the standard properties of neoclassical productions, including the linear homogeneity. j Since F (•;ξ j ) is linear homogeneous, we may define: Unit Cost Function of a sector-j firm: C j (w;ξ ) ≡ Min wa F j (a ;ξ ) ≥ 1 j a j { j j j } Unit Input Function of a sector-j firm: a (w;ξ ) ≡ Arg min wa F j (a ;ξ ) ≥ 1 j j a j { j j j } Page 5 of 129 An element, ξj, captures the external effects; they are: • representing all sorts of factors that affect productivity of sector-j, such as knowledge and experiences, the shared inputs, etc. • endogenous, determined in equilibrium, depending on the actions taken by the others. • beyond the control of each (infinitesimal) firm, hence exogenous from the point of view of each firm. j λ j j Example: Let ξj = Xj = ∑xj be the total output andF (v j ;ξ j ) = (ξ j ) F (v j ), 0 < λj < 1. Then, j λ j j X j = Σx j = F (Σv j ;ξ j ) = (X j ) F (V j ), where Vj = ∑vj. 1 j 1−λ Or X j = []F (V j ) j , which has the homogeneity of degree, 1/(1–λj) > 1. Thus, external economies generate sector-level increasing returns. Yet, the assumption that each firm takes ξj as exogenous enables us to stay within the competitive framework. Page 6 of 129 What factors enter ξj is an important assumption. One may consider a variety of alternatives. That is, ξj may contain factors that are • Country-specific and sector-specific, such as the total output or employment in the country’s sector-j, such as Xj. (The most common assumption) • Sector-specific but not country-specific; German and Japanese automakers migh learn a lot from each other, while German furniture makers might not learn much from German automakers. • Country-specific but not sector-specific; Japanese consumer electronics industries and automakers might learn from each other. • Region (bigger than a country)-specific; Europeans might learn more from each other. • Region (smaller than a country)-specific; Urban externalities might be restricted to a particular metropolitan area. etc. Note that these geographical and sectoral scopes are assumed. This could be a major drawback of this approach, as the scope external effects might depend on the environment. For example, government restrictions on trade or factor flows might change the extent to which these external effects are country-specific. Page 7 of 129 Autarky Equilibrium: In vector notation, (P=C): p A = C(w A;ξ A ) = w A A(w A;ξ A ) (RC): A(w A,ξ A )X A = V A A A A A A A A A A (DC): X = [e p ( p )/ e( p )]( p X ) = [ep ( p )/ e( p )](w V ) Integrated Equilibrium (IE): (P=C): p I = C(wI ;ξ I ) = wI A(wI ;ξ I ) (RC): A(wI ,ξ I )X I = V I I I I I I I I I I (DC): X = [e p ( p )/ e( p )]( p X ) = [ep ( p )/ e( p )](w V ) Can we replicate the IE when factors become immobile? The answer depends critically on the scope of external effects. Page 8 of 129 Global External Economies of Scale: When the external effects are entirely global in geographical scope (e.g., Japanese and German engineers can still learn from each other, even though they cannot relocate across borders), the answer is YES, under the same condition in Part 3. O* I I a1(w ;ξ )x*1 I I I a2(w ;ξ )x 2 V* I I a2(w ;ξ )x*2 I V 2 = V2 + V*2 I I a2(w ;ξ )x2 E V I I a2(w ;ξ ) a (wI;ξI)xI I I 1 1 a1(w ;ξ )x1 I I a1(w ;ξ ) O I V 1 = V1 + V*1 Page 9 of 129 National External Economies of Scale: What if the external effects are national in geographical scope? To keep things simple, suppose that they are sector-specific. To achieve the same level of productivity as in IE, it is necessary to concentrate each line of productions that are subject to externalities in one country. Let Nc = # of CRS sectors; NI = N − Nc = # of IRS sectors due to external effects. Example: M = Nc = 2; N = 3. Only j = 3 is subject to country-specific external economies of scale. O* • To replicate IE, assign Sector-3 to I I I Home (Foreign) inside the Green a3(w ;ξ )x 3 (Blue) Parallelogram. •E • Outside of these parallelograms, IE I •E V 2 cannot be replicated. I I • Factor proportion similarity does not a2(w )x 2 I a3(w;ξ ) I •E ensure FPE, let alone IE. a2(w ) (See the Red Dot, E) I I a1(w )x 1 I a1(w ) O I V 1 Page 10 of 129 Example: M = Nc = 2; N = 3. Only j = 2 is subject to country-specific external economies of scale. O* • To replicate IE, assign Sector-2 to a (wI)xI Home (Foreign) inside the Green 3 3 (Blue) Parallelogram. •E • In the overlapping area, sector-2 may I V 2 be assigned to either country. (See I I I a (w) •E a (w ;ξ )x the Red Dot E.) 3 2 2 I I • Outside of these parallelograms, IE a2(w ;ξ ) •E I I cannot be replicated. a1(w )x 1 I a1(w ) O I Notes: V 1 • We may hope for replicating IE when Nc =N − NI ≥ M, the condition ensuring the IE set has the full dimensionality in the factor space. • Patterns of trade may be indeterminate even when the IE can be replicated (as depicted by the Red dot, E). But, the factor content of trade is uniquely determined. • There may be multiple equilibriums, only a few of which replicates IE. Other equilibriums that fail to replicate IE, even though some of them might achieve FPE. • If national external economies are not sector-specific, there will be additional constraints, as a set of sectors may have to be located in the same country. Page 11 of 129 Example: M = Nc = 1; N = 2. Let j = 1 be the IRS sector and j =2 be the CRS sector. Integrated Equilibrium (IE): I 1 I I I 2 I (P=C): p1 = C (w ; X1 ), p2 = C (w ) I 1 I I 2 I (RC): L = C (1, X1 )X1 + C (1)X 2 2 I I I I (DC): C (1)X 2 = α2( p )(w L ). 1 I I 2 I Let L(1) ≡ C (1, X1 )X1 , L(2) ≡ C (1)X 2 .
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