Gießen, Chapter 4: Increasing returns to scale 4.1 Empirical observations 4.2 Homogeneous products External economies of scale Contestable markets Oligopolies 4.3 Differentiated products Love of variety Ideal variety

4.1 Empirical observations  Volume of trade largest between „similar“ countries within OECD (more than 50% of world trade).  Substantial intra-industrial trade (more than 25%)  Trade grows faster than world income  Growing importance of transactions within multi- national corporations  Trade liberalization and free trade associations should have led to a restructuring of production and changes in factor income – not observed, all factor incomes grow at the same pace. Gießen,

4.2 Homogeneous products External economies of scale Production function of representative firm: x i = f(v i,  ) (1) where  denotes the positive external effects which are beyond the control of firm i (e.g. domestic output of the commodity, world output, total domestic income etc.) Gießen,

Justifications:  Cheaper inputs for larger industries (however, begs the question of where cheaper inputs come from)  Approximation of model with price equal to average cost in equilibrium (however, compare to contestable markets)  Technical progress cannot be appropriated (however, begs the question where it comes from).  Learning by doing – larger well trained labor force. Gießen,

Autarky equilibrium Unit cost function: b j = b j (w,  ), b j  < 0, b j w = a j. a j = (a 1j,…,a ij,…a Mj ) = vector of inputs per unit of output of good j. Equilibrium conditions: p a = b(w a,  a ) (2) v = Ax a (3) Trade equilibrium p  b(w,  ) (4) v = Ax (5) Gießen,

Welfare gains from trade: Graham (1923): Free trade may reduce welfare through reallocation of resources from industries with scale economies to those without. Kemp and Negishi (1970): Reallocation in opposite direction ensures gains from trade. Helpman and Krugman (1985): Sufficient condition for gains from trade:  p j f j (v j a,  )   p j f j (v j a,  a ),(6) i.e. at world market prices „on average“ factor productivity is greater than in autarky, given the factor allocation of autarky and  instead of  a. Gießen,

Proof: Idea: Show that (6) implies feasibility of c a = x a in the free trade equilibrium, then apply WARP: px a   p j f j (v j a,  )  G(p,v,  ) = GDP-function. Alternative sufficient condition for gains from trade:  b j (w,  a )x j a   b j (w,  )x j a (7) i.e. at world market prices costs of production of autarky outputs are smaller in the free trade equilibrium than in the autarky equilibrium. The proof is similar to the one above: Gießen,

Proof: (4) and (7) imply px a   b j (w,  )x j a   b j (w,  a )x j a, and by definition b j (w,  a ) = wa j (w,  a )  wa j (w a,  a ), hence px a   wa j (w a,  )x j a = w  a j (w a,  )x j a = vw = G(p,v,  ), Thus x a = c a is feasible in the free trade equilibrium which cannot be inferior to the autarky equilibrium. Gießen,

Trade structure In addition to different technologies (Ricardo) and/or different factor endowments (Heckscher-Ohlin) different utilization of economies of scale as cause of comparative advantage: Predictions about trade structure become even more difficult. Sufficient condition for traditional results to hold: external effects are the same for all countries in the free trade equilibrium. Gießen,

Examples: a) Ricardo: Production functions: f j (v j,  ) =  j (  )v j /a j, F j (V j,  ) =  j (  )V j /A j (8) The domestic country will export good one if a 1 /a 2 < A 1 /A 2. This does not rule out the possibility that in autarky we get [  2 (  a )a 1 ]/[  1 (  a )a 2 ] > [  2 (  A )A 1 ]/[  1 (  A )A 2 ], hence predictions about trade patterns may not be possible by using only information about autarky. Gießen,

b) Heckscher-Ohlin All countries have identical production functions: x j = f j (v j,  ) (9) i.e. external effects are the same and have the same effects in all countries in the free trade equilibrium – predictions about trade patterns using information after trade takes place are possible. c) Counterexample: sector- and country-specific externalities: x j = x j a v j /a j (10) Firm perceives infinite costs without domestic production. Gießen,

Factor price equalization: Approach: determination of FPE-set (allocations of factor endowments between countries which allow replication of integrated equilibrium through free trade equilibria). Focus on country- and sector specific external scale economies – assumed to exist for subset I E of all goods. Their production functions are x i = f i (v i,x i ), i  I E (11) Subset of goods produced with constant returns to scale: I C. Gießen,

Integrated equilibrium conditions: p i = b i (w,x i ) (12) v i =  a ji (w,x i )x i (13) where v i denotes the vector of factor inputs in industry i and a ji is the input of factor j per unit of output of industry i. The set of all factor allocations compatible with FPE (denoted as  ) is defined analogously to the standard case with the additional requirement that the integrated equilibrium output of goods with increasing returns to scale can be produced in one country: Gießen,

 = {v 1,...,v J |  ij  0,  j ij =1  i  I, ij  {0,1}  i  I E } v j =  i ij v i  i  J (14) where ij denotes the share of country j of the vector of factor inputs in industry i in the integrated equilibrium, and v j denotes the vector of factor endowments of country j. For two countries and three industries, one of which has external economies of scale, the set  is shown in figure 4.1. Gießen,

Figure 4.1 FPE-set for industry 1 being capital intensive and enjoying increasing returns to scale.

Remarks:  The diagonal need not belong to .  The equilibrium is not unique with respect to the structure of production.  Increasing returns to scale will generate division of labor and trade even between identical countries.  It need not be the relatively capital rich country that produces the capital intensive good, absolute size also matters.  Net factor import is uniquely determined. Gießen,

Figure 4.2: Indeterminacy with respect to the location of industry 1

Non-uniqueness Integrated economy, two goods, one factor, production function x 1 = x 1  v 1 /a 1. Let v = 1,v 1 < 1/2. The following figure (4.3) shows  for this case: 0  ___________Q__________Q‘___________  0* v h measured from left to right. Let 0Q = Q‘0* = v 1. v h between Q and Q‘: integrated equilibrium is reproduced, location of industry 1 indeterminate. v h < v 1 : integrated equilibrium reproduced if industry 1 is in foreign country. Second equ.: Industry 1 in home country, foreign country firms perceive infinite production costs. Gießen,

Non-uniqueness cont’d Let v 1 > 1/2.  is shown in figure (4.3): 0  ___________Q’_ _ _ _ _ _Q___________  0*  consists of the solid lines 0Q‘ and Q0*.  v h between Q‘Q: integrated equilibrium cannot be reproduced.  v h in 0Q‘: integrated equilibrium reproduced, industry 1 in foreign country.  Industry 1 in home country: no FPE.  Both countries produce good 1: FPE, but no reproduction of integrated world equilibrium. Gießen,

4.2.2 Contestable markets Extension of Bertrand model to industries with sub- additive cost-functions: c(  x i ) <  c(x i ) Reasons: Economies of scale, fixed costs. Crucial assumptions: no sunk costs, no entry or exit costs. Dasgupta-Stiglitz: Theory well funded, but not well founded. Main difference to previous model: scale economies are internal for firms and known to them. Gießen,

Integrated world equilibrium: additional condition: c i (w,x i (p i ))  p i  p i < p i * rules out „inefficient“ equilibria (see Figure 4.5 below)

Sufficient condition for gains from trade:  c i (w,x i )x i a   c i (w,x i a )x i a Non-existence of free trade equilibrium: Integrated economy, two goods, one factor, production function x 1 = x 1  v 1 /a 1. Let v = 1,v 1 < 1/2. The following figure (4.6) shows  for this case: 0  ___________Q__________Q‘___________  0* v h measured from left to right. Let 0Q = Q‘0* = v 1. v h between Q and Q‘: w greater in country that produces good 1  provokes entry from other country, but two firms cannot co-exist in a contestable market. Gießen,

4.2.3 Oligopolies One-shot Cournot-model  Market concentration and trade: Even if two countries are identical, free trade increases competitive pressure and lowers prices as compared to autarky  Oligopoly and transport costs: may lead to asymmetric oligopoly in each country, but above effect still possible. Gießen,

Concentration in partial equilibrium k identical consumers, n firms, market demand: X(p) = kx(p). Firm i maximizes  i (x i ) = x i p([  j  i x j + x i ]/k) – c(w,x i ), (15) FOCs: p + p‘x i /k = c x (w,x i ) (16) Identical firms  x i = kx(p)/n Elasticity of demand of representative consumer:  = - x‘(p)p/x Gießen,

Substituting this into (16) yields p[1 – 1/n  (p)] = c x (w,kx(p)/n) = pR -1 (17) Suppose there is free trade between two perfectly identical countries (same number of identical consumers and firms). Instead of (17) we get p[1 – 1/2n  (p)] = c x (w,kx(p)/n) (18) i.e. the price goes down even though no commodity flows will be observed. Sufficient condition for gains from trade: output in oligopolistic industries grows (pro-competitive effect of trade). Gießen,

The direction of trade Depends not only on costs and on pre-trade prices, but also on the number of firms and consumers:  Identical countries except for the number of firms: country with larger number of firms exports (but also had lower pre-trade price).  Identical costs, but different number of firms and consumers: net exporter is country with larger firms/consumers ratio.  Identical countries except for costs: country with smaller costs is net exporter. Gießen,

In general no clear prediction on the basis of only one variable possible: cost advantages may be over- compensated by market size, etc. Reason: Less efficient firms may still be active in a Cournot-equilibrium. Gießen,

General equilibrium trade patterns Equilibrium condition for a Cournot-oligopoly: p[1 – 1/n  (p)] = c x (w,kx(p)/n) = pR -1 (17) implying R = [1 – 1/n  (p)] -1 (19) “Wedge” between price and marginal cost: 1 − R -1 Let R i denote the „mark-up” perceived by firm i. Constant returns to scale imply that resources are allocated s.t.  R i -1 p i x i is maximized (Helpman 1984). Gießen,

Factor abundancy: If all firms in a country perceive the same R i then differences in output will depend solely on differences in supply functions, hence with identical production functions on differences in factor endowments. R i ‘s most likely to be identical across countries with factor price equality. Gießen,

Factor price equalization Integrated world economy: Two types of industries: I o oligopolies, I c competitive industries. Equilibrium conditions:  := c x x/c….elasticity of costs, measure for increasing returns to scale.  := 1/  =  c/c x,  c = average cost. Consequently, pR -1 = c x can be written as pR -1 =  c/ . Gießen,

Collecting terms, the equilibrium conditions are A(w)x c + A(w)x O = v Factor price equalization (and reproduction of integrated world equilibrium) requires that factor allocation is compatible with number of firms of the oligopoly in each country.

Gießen,

Figure 4.7: FPE-set, industry 1: oligopoly, industries 2 and 3: competitive.

Gießen, Net import of all factors‘s services: possible for a country with a large share in oligopolistic industries. Suppose s j (share of country j in world GDP) satisfies s j > v 1 j /v 1 =...= v N j /v N i.e. share in world GDP is greater than share in factor endowments: possible due to profits.

Gießen, Figure 4.8: capital rich country exports embodied capital services and imports embodied labor services. C’: share in factor income, C”: share in world GDP.

Gießen, Figure 4.9: capital rich country imports embodied capital services and embodied labor services. C’: share in factor income, C”: share in world GDP.

Market segmentation Introduction of transport costs t: Example: two identical countries, each with one firm. Home market: 2 firms, asymmetric Cournot model: domestic firm has marginal costs c, foreign firm has marginal costs c + t. Equilibrium conditions: p(x d + x f ) + x d p‘(x d + x f ) = c, p(x d + x f ) + x f p‘(x d + x f ) = c + t. Equilibrium with x d > x f > 0 exists for t < p m – c. p m = monopoly price. Gießen,

Welfare effects: w = u(x d + x f ) – c(x d + x f ) – tx f dw = u’(x d + x f )(dx d + dx f ) – c(dx d + dx f ) – tdx f – dtx f Normalize u(x) s.t. u‘(x) = p: dw = (p – c – t)(dx d + dx f ) + tdx d – dtx f Note that dt < 0  dx d < 0 < dx f 1.x f dt...cost reduction  w , but x f = 0 if t = p m – c. 2.(p – c – t)(dx d +dx f )  w  (export increase), but 0 if t = p m – c. 3.tdx d...  w  (replacement of domestic shipments through exports). dw/dt > 0 at t  p – c.

Gießen, Figure 4.10: Gains and losses due to changes of t.