Price as Indicator for Quality?

Transcription

1 Price as Indicator for Quality? by Jøren Drud Hansen and Jøren Ulff-Møller Nielsen Department of Economics Aarhus School of Business University of Aarhus Denmark Abstract This paper examines the relation between price differences and quality differences in an oliopoly model with intra-industry trade, where oods are horizontally as well as vertically differentiated. The analysis demonstrates that the ratio of prices is not linked to the ratio of qualities in any simple way. The paper therefore questions the procedure of usin unit value differences between exported and imported oods as criteria for disentanlin intra-industry trade in a vertical and a horizontal part. Keywords: Horizontal product differentiation; Vertical product differentiation; Intraindustry trade; Price ratio; Quality ratio; Unit values. JEL: F, F3. Correspondin author: Associate professor Jøren Ulff-Møller Nielsen, Department of Economics, Aarhus School of Business, University of Aarhus, Prismet, Silkeborvej, 7 th floor, DK-8000 Aarhus C, Denmark. JUM@ASB.DK Acknowledments: We are rateful for valuable comments from Nicolas Schmitt, Simon Fraser University, and other participants at Canadian Economics Association, Annual Meetin, Vancouver 007.

2 . Introduction A substantial part of international trade is intra-industry trade (IIT) that is trade in similar products or within industries. The reason for such two-way trade is internal scale economies and hence, imperfect competition on the markets. In some cases the internationally traded oods are completely homoenous and IIT is due to reciprocal dumpin behavior between the producers. In other cases the oods are differentiated and the two-way flows reflect the differences of preferences or differences of income or wealth between consumers. The products may as suested by Lancaster (966, 979) be horizontally or vertically differentiated. Two products are horizontally differentiated, when both products have a positive demand, whenever they are offered at the same price. This is the case if the two products have the same set of characteristics, but in different proportions. In such cases all variants will be demanded, at least for limited price differences. Two products are vertically differentiated, i.e. differentiated with respect to quality, if the absolute amount of all characteristics between the two products differs. The variant which has more characteristics in some or all dimensions has a hiher quality for all consumers and hence, the rank of prices reveals the rank of qualities. In a seminal paper Abd-el-Rahman (99) suests usin the ratio of export and import prices to disentanle intra-industry trade into IIT in horizontally and vertically differentiated oods. By usin unit values of exports and imports as proxies for export and import prices he classifies IIT as horizontal, if the unit value of export to unit value of import differs less than a specific thresholds value of typically 5 percent, while it is classified as vertical IIT, if this ratio of unit values exceeds 5 percent. This procedure for classification of IIT has been followed in a lare number of empirical studies, see e.. Greenaway et al. (994, 995); Greenaway et al. (999); Aturupane et al. (999); Hu and Ma (999); Blanes and Martin (000); and Gullstrand (00). Based on Shaked and Sutton (987) we claim that in practise two-way trade flows very often consist of products which are differentiated both horizontally and vertically. To illustrate this point let us look at footwear. Footwear is certainly a ood with many different functions dependin on weather conditions etc. (e.. sandals, boots, urban footwear and city shoes). And also qualities may differ quite much dependin on the materials (e.. leather or composition leather) and desin. And besides, within a iven quality sement for a iven function (e.. city shoes of leather for men) many different brands may be available with some consumers preferrin one to another and other consumers the opposite (for identical prices). A classification of IIT into two cateories is therefore strictly speakin a misrepresentation. In a less riorous approach, applyin a benchmark of +/- 5 percent difference of unit values may illustrate a simple roupin of trade data into a cateory, where quality difference seems to be less important and a cateory, where it seems to be more important. However, such a procedure is problematic unless a stron positive correlation exists between prices and qualities.

3 The aim of this paper is to analyse the relation between price and quality in a duopoly model with both horizontal and vertical product differentiation. The analysis is purely theoretical and to avoid unnecessary formal complications several simplifyin assumptions are introduced. Basically, we assume that one producer is located in each of two countries. Moreover, we assume the producers have access to the same technoloy and face the same factor prices, i.e. cost symmetry exists. What differentiates the quality of each of the two producers product is difference in market size and trade costs. The solution for prices and qualities in Nash equilibrium offers a framework for an analysis of prices as proxy for qualities in international trade characterized by intra-industry trade. The results show that even thouh price and quality ratios are positively correlated in some, but not all cases, the expressions for qualities and prices differ and the ratio of prices is thus in eneral an imprecise indicator of the ratio of qualities. Especially the role of marinal production costs (relative to the costs of developin quality) are shown to be crucial for the weak price-quality ratio association. The paper is oranized as follows. Section develops and solves the model which builds on Hansen and Nielsen (006). Section 3 applies the solutions of the model to an analysis of the (possible) link between the ratio of qualities and the ratio of prices and based on this formal analysis the empirical disentanlin of intra-industry trade in a vertical and horizontal part is discussed. Section 4 discusses the issue in a more eneral framework referrin also to empirical investiations. Section 5 concludes.. The basic model The model presented below describes in a two country/two producer context market equilibrium and trade pattern in a market where the products are differentiated both horizontally and vertically. The basic specification of these two dimensions of tastes of the consumers has been suested by Garella (003, 006) in a closed economy and later used for analysin forein trade in Hansen and Nielsen (006). The world consists of two countries, and, with one producer of a differentiated product in each. Vertically, the quality of the product is characterised by a quality indicator θ (θ 0). In the horizontal dimension, each consumer has an address or ideal variant characterised by x, where x = [0,]. Each consumer is assumed to consume one unit only of the differentiated ood. The consumer chooses the variant which offers the larest utility ain, iven by the ross utility of consumin the ood minus the costs of acquirin it. These costs consist of the price at the ate of the producer plus trade costs, in case the consumer prefers the forein ood. The consumers in each country are uniformly distributed with respect to x in the interval 0 to. However, the two countries miht be asymmetrical in size. The number of consumers is normalised to in country and to σ in country, and throuhout the followin analysis, it is assumed that σ. The producer s horizontal position is exoenously iven contrary to the vertical position, where the quality level is a strateic variable. Horizontally, the producers are assumed to 3

4 have opposite locations, so the country based firm is located within the territorial boundary of the respective country. Hence, for a consumer at the address x, the horizontal distance to the producer in country is x and (-x) in country, respectively. However, if the consumer demands the forein ood, he incurs trade costs at per unit. Each of the producers aims to maximise his profit. Althouh the markets are partially semented by trade costs, it is assumed impossible for the producer to distinuish between domestic and forein buyers. Each producer therefore chares a uniform price i.e. price discrimination is nelected. For the consumer in country, the utility of consumin one unit of the ood produced by the domestic or the forein producer is iven by an additive separable specification of the vertical and horizontal dimensions 3 : u = v+ θ tx p (a) and u = v+ θ t x p (b) ( ) For a consumer in country, the utility of consumin one unit of the forein ood or alternatively the domestic ood is iven by: u, = v+ θ tx p (c) and u, = v+ θ t( x) p (d) where v is the consumer s reservation price for that ood, t a parameter for utility loss per unit increase in the horizontal distance between a consumer and a producer, p prices obtained by producers and trade cost 4. The first subscript indicates the market (country) and the second the supplier (producer). We assume that the consumer s attachment to the preferred variant measured by the size of the parameter t is stron. As appears from the followin formal analysis, this assumption secures that qualities are strateic substitutes for the two companies. Turnin to the costs, quality may influence costs throuh two channels. First, marinal production costs may depend on quality. For example, cars are typically produced with D Aspremont et al. (979) have shown that two producers choose maximal horizontal distance at the market if the transport cost or utility loss is a quadratic function of distance. However, in the followin we use linear distance costs. In subsection Price discrimination we discuss the implication for our result for the case where producers price discriminate in the forein market (reciprocal dumpin). 3 The additive specification of quality in the utility function has been suested by Mussa and Rosen (978) and has later been used in several analyses e.. Tirole (988). Another specification of quality in the utility function is to use a multiplicative specification, where basic utility depends on consumption of other (nondifferentiated) oods, which varies proportionately with the quality indicator of the differentiated ood. This alternative specification has been introduced by Gabszewicz and Thisse (979) and later used by Shaked and Sutton (98) and Boom (995), amon others. 4 The specification of the utility function disreards diversity of tastes with respect to quality. In most other papers in this tradition, the effect on utility of quality in the individual utility function is assumed to depend both on a ood specific indicator of quality and a consumer specific parameter related to the weiht the consumer puts on quality, see e.. Tirole (988). 4

5 and without extra equipment, and installin extra equipment in the car raises unit variable production costs. Secondly, hiher quality of a ood often appears as a result of an R&D activity and in such cases the firm also incurs sunk costs when it develops quality. Most price theory predicts a pass-throuh of marinal production costs on prices, and if quality only affects marinal costs, it seems quite obvious that prices would reflect quality. This link between prices and qualities is less obvious if sunk costs are needed to develop quality, and in the followin we therefore concentrate on this case. To keep the analysis simple we assume that the two firms costs functions are symmetric and iven by: Ci = cqi + ½ θi ; i =, () where c is (constant) marinal production costs and ½θ i is the flow equivalent fixed costs of the sunk costs for developin quality. The fixed costs increase more than proportionately with respect to quality due to diminishin returns of R&D activity. By convenient choice of units for costs, the parameter in the fixed term of the cost function is set to ½, and hence c captures also the weiht of variable costs to fixed costs. 5 Market equilibrium The producers use the quality level and price as strateic variables. It is assumed that each producer in a first-stae ame chooses his quality level and subsequently chooses prices in the second-stae ame. The Nash equilibrium is derived by backward induction i.e. by derivin the prices for iven qualities, and then determinin qualities 6. On a iven market, a competitive ede exists between the two producers defined as the location of a marinal consumer, who is indifferent whether to buy the variant from one or the other producer. In country, the competitive ede x% is determined by: v+ θ tx p = v+ θ t( x) p which ives %x = + ( + ) + ( θ θ) t p p t (3a) Similarly, the competitive ede in country is iven by %x = + ( ) + ( θ θ) t p p t (3b) Total demand for product and, Q and Q, respectively, is iven by: 5 The assumed cost function is a special case of the costs function : C i = ( c+ λθ i i ) Q i + ½ ϕθ i i ; i=,, where c is constant marinal costs independent of quality, λ ii θ is marinal production cost dependent on quality with the parameter λ i indicatin the dependence of production costs on quality, ϕ i the cost effectiveness of the firm in developin quality. For λ i = 0 and ϕ i =, for i=, we et (). 6 To simplify, the formal analysis is based on a set of constraints on the parameters, which rule out special cases and corner solutions. Especially two simplifyin assumptions should be noticed. First, it is assumed that the two markets are fully covered, i.e. each consumer in both countries buys one unit of the ood. Secondly, it is assumed that the horizontal preference is relatively stron with the implication that the quality of oods is substitutes in the competitive ame between the two producers. Formally the constraints are presented in the Appendix. 5

6 Q = x% + σ x% = t and: Q = ( x% ) + σ ( x% ) ( σ) t ( σ)( p p ) ( σ ) ( σ)( θ θ ) = t ( σ ) t ( σ)( p p ) ( σ ) ( σ)( θ θ ) (4a) (4b) Profits, π i, for the two producers are iven by: π = p c Q ½ θ ; i=, (5) ( ) i i i i Prices and levels of output for the two producers are determined by a Bertrand optimisation for a iven set of qualities for the products. The solution is reported in the Appendix and discussed more extensively in Hansen and Nielsen (006). Insertin the Bertrand solution into (5) translates the two profit functions to functions of qualities only. This allows us to deal with the first ame: determination of quality levels. Each of the two producers is assumed to optimise the quality of his product for a iven quality of the competitor s product. This ives the final solution for qualities (6a) and (6b) and insertin this result into the Bertrand solution ives the prices (7a) and (7b). The full solution is reported in the Appendix. ( + σ ) ( σ ) 3 ( 9t ( + ( + σ) ( σ ) 3 9t ( + σ ) θ = θ = + ( ) 3( σ ) t ( + σ) ( 9t ( + σ) ) 3( σ ) t ( + σ) ( 9t ( + σ) ) p = t+ c p = t+ c+ (6a) (6b) (7a) (7b) Let us take a closer look at the relations between prices and qualities based on (6a)-(7b). First of all, we observe that the quality levels as well as the prices are equal in the special cases where either trade costs are zero or market sizes are equal. In the more eneral cases with trade costs and differences in market sizes, the producer in the lare economy will choose a hiher quality and chare a hiher price compared to the producer in the small economy. More specifically it follows from the results (6a)-(7b) that quality and price for the producer in the lare economy increases with respect to trade costs and market size, respectively, while the opposite is the case for the producer in the small economy. This pattern follows from the assumption that quality demands fixed costs. It is easier to recover fixed costs for a firm, when it is located on the bi market, and quality 6

7 and price will therefore be hiher for the producer on the bi market compared with the producer on the small market. Moreover, for the same reason, the comparative advantae of developin quality for the producer on the bi market increases with trade costs and hence, the quality and price lead for this producer therefore increases with trade costs. Notice finally that contrary to the price levels, the Nash equilibrium for the quality levels do not depend on the marinal production costs. This result follows directly from the specific assumption that variable production costs are independent of the level of quality of the product. 3. The (lack of) correlation between relative prices and relative qualities The model presented in Section questions basically a classification of trade into the two cateories, intra-industry trade in vertically and horizontally differentiated products. The two products differ both by quality and by characteristics associated with individual preferences of the consumer. The model also demonstrates that prices and qualities are endoenously determined variables throuh the producers attempt to optimize profit, i.e. qualities and prices depend on a set of parameters (σ,t,c,). The ratio of qualities follows from (6a) and (6b): θ q = = θ ( + σ) ( σ ) + 3 ( 9t ( + ( + σ) ( σ ) 3 ( 9t ( + (8) The ratio for prices is determined by (7a) and (7b) which ives: ( ) c( ) ( ) ( ( ( ) c( ) ( ) ( ( ( ) + σ + σ σ c + σ + + θ + p 3 3t 9t + 3t r = = = p + σ + σ σ c( + σ ) + θ + 3 3t 9t + 3t (9) If relative prices are a ood proxy for relative qualities, these two ratios should have a (hih) positive correlation. To find out whether this is the case, we make a comparative static analysis of the Nash equilibrium, i.e. for alternative values of the parameters, σ, t and c respectively we investiate the solutions (8) and (9) and hence, conclude on the relation between relative prices and relative qualities. The formal part of the analysis is reported in the Appendix. For trade costs we have as explained in section that q/ and r/ are both positive, i.e. a marinal increase of trade costs increase both relative quality and relative price. 7

8 This ensures a positive correlation between relative quality and relative price. The relative price thus shadows relative quality, but the link between the twin ratios is not proportionate. Turnin to the impact of relative market size σ, we also have that q/ σ>0 and r/ σ>0, i.e. a marinal increase of relative market size increases both relative quality and relative price and variation in σ therefore also leads to a positive correlation between relative quality and relative price. The producer in the larer market has an advantae in quality development throuh the distribution of R&D over larer sales. Quality and price will therefore increase relative to the producer on the smaller market. The positive correlation between quality and price ratios also holds for the strenth of the horizontal preference t, but here q/ t <0 and r/ t<0. For increasin values of t consumers are more loyal to their preferred variant and therefore the benefits of quality development are diminished for both producers. They will therefore act more similar with respect to both qualities and prices. To sum up, the role of trade costs, market size σ, and horizontal preferences t all reveals a positive correlation between relative prices and qualities. But it should be noticed that for each of these determinants the link between relative quality and relative price is specific and not proportionate. Variation in marinal production costs breaches this pattern of a positive link between relative quality and relative price. The marinal production cost does not influence relative quality in contrast to relative price. To be more specific; q/ c = 0, while r/ c<0 and moreover, q=r for c=0. These relations are illustrated in Fiure, where q = q is constant, while r decreases monotonically towards for increasin c. For especially hih values of marinal costs, the relative price is thus a poor indicator of the relative quality, since hih marinal costs (and at the same time relatively low R&D expenditures) influence prices only. FIGURE HERE The comparative static analysis thus hihlihts some caveats in usin the price ratio as indicator for quality. There is no link between ratio of quality and ratio of price for variation in marinal costs. To put it differently, even if marinal production costs are kept constant, a iven price ratio does not correspond to a specific quality ratio as this is the outcome of the values of all determinants of the Nash equilibrium. As discussed in relation to the cost function () in a more eneral framework quality may be related partly to sunk costs and partly to marinal production costs. However, what matters for the conclusions is that the marinal production costs influence qualities and prices differently and this will also prevail for more eneral specifications of the relation between costs and quality. Extension of the model to such a more eneral framework may improve the correlation between price and quality ratios, but the problem of usin price as an indicator for quality exists, when sunk costs are important for quality. Price discrimination The conclusions above do not chane, if producers are able to price discriminate. A recalculation of the optimization, now based on price discrimination, does not chane the result for the quality ratio iven by (9). The result for the price ratio in international trade 8

9 p /p, i.e. producer s price on market (p ) relative to producer s price on market (p ), is iven by an expression which functionally differs from the expression of quality ratio 7. Also in case of price discrimination the price ratio miht therefore be a flawed indicator of quality ratio. The unit value approach As mentioned in the introduction, the ratio of unit values of exports to imports has been used as an indicator for quality differences across countries (for a iven product/industry). In empirical studies flows of IIT have been disentanled into a horizontal or vertical part dependin on whether the ratio of unit values were below or above a threshold value, which typically has been set to 5%. However, this procedure for identification of the two types of IIT may in some cases be problematic as illustrated in Fiure. Let us assume that in the special case, where the marinal production costs are zero and r=q, r (and q) exceeds the 5% threshold used in the unit value approach, that is has a value above.5. For modest marinal costs (c< ĉ ) international trade is thus empirically classified as vertical, while for lare marinal production costs (c> ĉ ) trade is classified as horizontal, and in both cases the quality ratio is the same! The unit value methodoloy may therefore have a lare element of arbitrariness in disentanlin oods dependent on the relative importance of variable and fixed costs for iven qualities. Fiure ives another illustration of the inbuilt problem of the unit value approach for a case where both trade costs and market size varies at the same time. As discussed above, all first order derivatives of the quality ratio and the price ratios with respect to trade costs and market size respectively are positive. For a iven price ratio r =r a trade-off therefore exists between trade costs and market size. The specific iso-price ratio curve correspondin to the benchmark price ratio at r =.5 is shown in Fiure. The price ratios exceed.5 for all points above the benchmark r -curve, while the opposite is the case for all points below the r -curve. FIGURE HERE For a iven quality ratio, q, a trade-off also exists between and σ. However, the two expressions for r and q differ in their functional form and this translates into different shapes of the trade-offs. This is illustrated in Fiure where the iso-quality curve q intersects the benchmark iso-price ratio curve r (whether the q -curve intersects the r - curve from below or above is irrelevant for the followin aruments). The two points A and B on the iso-quality curve thus represent the same quality ratio, but different price ratios. In A the price ratio is below.5 and the case will be perceived as trade with 7 ( ) ( ) ( 9t 4σ ) ( 9t ( + ( 9t 4) ( 9t ( + 3 t+ c p r = = p 3 t+ c 9

10 horizontally differentiated products. In B the price ratio is above.5 indicatin trade with vertically differentiated products. The price ratio may therefore be a flawed indicator of the quality ratio, since bilateral trade between two pairs of countries with differences in size and trade costs, but with the same quality ratios, may result in different trade classifications. 4. Discussion Price and quality are thus only loosely connected. As noticed in Nielsen and Lüthje (00) a strikin empirical observation is a lare instability of the ratio of unit values over time. However, this may not surprise iven the complex expressions for prices and qualities in the model presented above. The conclusions based on our simple model are consistent with other empirical observations of IIT. Greenaway et al. (994, 995) and Fontané and Freudenber (997) find that IIT between developed countries are dominated by vertical IIT. This is seeminly a paradox as trade between similar countries, in this case developed countries, is expected to be dominated by horizontal IIT. However, the measured lare share of vertical IIT may be an optical phenomenon due to the unstable link between quality and price. For developed countries consumption and trade are dominated by quality products, i.e. cateories of products, where sunk R&D costs are very important in contrast to marinal production costs. But as the ratio of prices (unit values) varies inversely with marinal production costs for a iven quality ratio (see Fiure ), trade flows are thus biased to be classified as vertical IIT for developed countries, when the ratio of unit values is used as criteria. The formal analysis above has been simplified by the assumptions of preference and cost symmetry. Countries may differ with respect to factor endowments, technoloy, wealth and household distribution of wealth. Each of these variables play a key role for trade as demonstrated in both old and new international trade theory. However, a eneralization of the model by takin into account the above determinants for trade leads to even more complex expressions for prices and qualities and the problem of usin unit values as proxy for qualities therefore persists. It is therefore not a surprise that testin trade theories based on disentanlin IIT into a horizontal and a vertical part has not been very successful to express it mildly. Especially reressions for vertical IIT have failed to confirm the expected sins for some of the explanatory variables (see Cabral et al. 007). Factor endowments (and technoloy) have especially attracted attention in trade studies. Main stream theory in international trade predicts that countries, rich in human and physical capital have a hih per capita income and a comparative advantae in R&D activities. Due to the relatively cheaper R&D costs, those countries are expected to export hih quality products. In such cases of stron asymmetry between the countries, the unit values may rouhly indicate quality as shown in a number of recent empirical studies. Schott (004) finds that export unit values increase systematically with exporters per capita income and similar results are found in an analysis of Hummels and Klenow 0

11 (005). Turnin to imports Hallak (006) finds that rich countries tend to import relatively more from countries that produce hiher quality oods. Finally, a study by Hallak and Schott (005) deviates from the standard procedure of equatin export price with quality by developin a methodoloy to decompose countries observed export prices into quality and quality-adjusted-price components, the latter measurin variations in product prices induced by factors other than quality, e.. currency misalinment. 5. Conclusions This paper questions the use of prices as indicator for quality. Based on a simple duopoly model with both horizontally and vertically differentiated oods it is shown that the relation between prices and qualities is complex and in some cases prices are therefore a flawed indicator of qualities. This conclusion also appears for alternative theoretical approaches. The new-new trade theory, developed amon others by Melitz (003), assumes horizontal product differentiation of the Dixit-Stilitz love of variety type. Firm heteroeneity is assumed as productivity or marinal costs differ between firms. Due to this intra-industry costs asymmetry firms chare different prices, althouh the products are not differentiated vertically at all. Based on the above conclusions it may therefore be considered to abandon disentanlin IIT data into the two cateories: horizontal and vertical IIT. An alternative would be to return to IIT reressions without such a separation accordin to the perceived product differentiation types. Usin quantile reression techniques could be a fruitful path for explainin non-disentanled IIT, since the explanatory variables may differ accordin to the quantile of IIT observations we operate in (see Koenker and Hallock, 00). References Abd-el-Rahman, K., (99). Firms competitive and national comparative advantaes as joint determinants of trade composition. Weltwirtschafliches Archiv, 7: Aturupane, C., S. Djankov, and B. Hoekman (999). Horizontal and vertical intraindustry trade between Eastern Europe and the European Union. Weltwirtschafliches Archiv/Review of World Economics 35(): 6-8. Blanes, J. V., and C. Martin (000). The nature and causes of intra-industry trade: Back to comparative advantae explanation? The case of Spain. Weltwirtschafliches Archiv/Review of World Economics 36(3): Boom, A. (995). Asymmetric international minimum quality standards and vertical differentiation. Journal of Industrial Economics 43: 0-9.

12 Cabral, M., R. Falvey, and C. Milner (007). Vertical intra-industry trade and differences in endowments: Revisitin the empirical evidence. Mimeo. D Aspremont, C., J. Gabszewicz, and J.-F. Thisse (979). On Hotellin s stability in competition, Econometrica 7: Fontané, L. and M. Freudenber (997). Intra-industry trade methodoloical issues reconsidered. CEPII Workin paper Gabszewicz, J. J. and J-F Thisse (979). Price competition, qualities and income disparities. Journal of Economic Theory 0: Garella, P. G. (003). The Effects of Minimum Standards: Better or Worse Products? WP 484, Department of Economics. Univerity of Bolona. Garella, P. G. (006). Innocuous Minimum Quality Standards. Economics Letter 9(3): Greenaway, D., R. C. Hine, and, C. R Milner (994). Country specific factors and the pattern of horizontal and vertical intra-industry trade. Weltwirtschaftliches Archiv 30: Greenaway, D., R. C. Hine, and C. R., Milner (995). Vertical and horizontal intraindustry trade: A cross industry analysis for the UK. Economic Journal 05: Greenaway, D., C. Milner, and R. J. R. Elliott (999). UK intra-industry trade with the EU North and South. Oxford Bulletin of Economics and Statistics 6(3): Gullstrand, J. (00). Does the measurement of intra-industry trade matter? Weltwirtschafliches Archiv/Review of World Economics 38(): Hallak, J.C. (006). Product quality and the directions of trade. Journal of International Economics 68: Hallak, J. H. and P. Schott (005). Estimatin cross-country differences in product quality. Mimeo. Hansen, J. D. and J. U.-M. Nielsen (006). Economic interation and quality standards in a duopoly model with horizontal and vertical product differentiation. Journal of Economic Interation (4): Hu, X., and Y. Ma (999). International intra-industry trade of China. Weltwirtschafliches Archiv/Review of World Economics 3():8-0

13 Hummels, D. and P. J Klenow (005). The variety and quality of a nation s exports. The American Economic Review 95(3): Koenker, R. and K. F. Hallock (00). Quantile Reression. Journal of Economic Perspectives, 5(4): Lancaster, K. (966). A new approach to consumer theory. Journal of Political Economy LXXIV: Lancaster, K. (979). Variety, equity and efficiency. New York: Columbia University Press. Melitz, M. J. (003). The impact of trade on intra-industry reallocations and areate industry productivity. Econometrica Vol. 7(6) Mussa, M. and S. Rosen (978). Monopoly and product quality. Journal of Economic Theory 8: Nielsen, J. U.-M. and T. Lüthje (00). Tests of the empirical classification of horizontal and vertical intra-industry trade. Weltwirtschaftliches Archiv 38(4): Schott, P. (004). Across-product versus within-product specialization in international trade. Quarterly Journal of Economics 9(): Shaked, A. and J. Sutton (98). Relaxin price competition throuh product differentiation. Review of Economic Studies, 49: 3-3. Shaked, A., and J. Sutton (987). Product differentiation and industrial structure. The Journal of Industrial Economics XXXVI( ): Tirole, J., (988). The Theory of Industrial Oranization. The MIT-Press, Cambride, Mass. Appendix Fully covered markets The uncovered market appears if the price of the best buy for some consumers in one or both markets exceeds the utility of consumin the ood i.e. if the price is too hih. The most aressive price settin appears, if the trade costs are so hih that the markets are completely semented into two monopoly markets. In this case of semented markets the markets are uncovered for p > ( v+ t) and p = ( v+ θ t) θ 3

14 The inverse demand function for each of the two monopolists in the uncovered market is iven by 8 : t p = v+ θ tq and p = v+ θ Q σ where Q = x and Q = σ ( x ) Solutions for maximum operatin profit in the above price interval are iven by: σ Q = ( v+ θ c) and Q = ( v+ θ c) t t The corner solution of the covered market in case of quality levels at zero thus appears by insertin Q = and Q =σ and = = 0 in these expressions. This ives v = c+t. A sufficient condition for fully covered markets is thus: v c + t. (A) Bertrand equilibrium the second stae ame Insertin (4a) and (4b) in (5) and maximizin each producer s profit with respect to his own price, ives the followin price reaction functions for the producer in country and, respectively: ( σ ) p = p + ( θ θ) + ( t+ c) (A) (+ σ ) ( σ ) p = p+ ( θ θ) + ( t+ c) (A3) (+ σ ) Solvin (A) and (A3) with respect to prices ives Bertrand equilibrium: ( σ ) p = + ( θ θ ) + 3( t+ c) 3 (+ σ ) and: ( σ ) p = ( θ θ) + 3( t+ c) 3 (+ σ ) (A4) (A5) Usin (A4) and (A5) in (4a) and (4b) ives the quantity demanded or output in equilibrium: Q = 3 ( + σ) t ( σ ) + ( + σ)( θ θ) 6t (A6) and: Q = 3 ( + σ ) t+ ( σ ) ( + σ)( θ θ) 6t (A7) Quality equilibrium the first stae ame 8 For all lower prices the markets are covered and hence perfectly inelastic with respect to the price. 4

15 The results (A4) (A7) allow us to deal with the first-stae ame: determination of quality levels. Profits in the Bertrand equilibrium are iven by (5). Maximizin π with respect to θ and π with respect to θ by usin (A4) (A7) ives the quality reaction function for the producer in country and country, respectively: θ = ( σ) θ ( σ ) 3( σ) t (9t-( σ ) ) (A8) θ = ( σ) θ ( σ ) 3( σ) t (9 t ( σ ) ) (A9) It is assumed that: ( σ ) t ( + σ )+ (A0) 9 3 ( + σ ) The condition secures qualities as strateic variables. It follows from (A8) and (A9) that the condition is a sufficient condition for neatively sloped quality reaction functions. Furthermore (A0) is a necessary condition for solutions for positive levels of qualities in Nash equilibrium. Solvin (A8) and (A9) ives the quality levels in Nash equilibrium (6a) and (6b). The prices and output in Nash equilibrium are derived by insertin (A8) and (A9) into (A4)- (A7). This ives for prices (7a), (7b) and for quantities: 3( σ ) Q = ( + σ ) ( 9t ( + (A) 3 = θ and: 3( σ ) Q = ( + σ ) + ( 9t ( + (A) 3 = θ Usin these results, the profits in Nash equilibrium for the two companies are iven by: θ π = ( p c) Q 9 t ( + σ ) 3( σ ) = + ( + σ ) (A3) 8( + σ ) ( 9t ( + ( 9t ( + θ = + σ ( ) 5

16 π = c Q ( p ) ( σ ) ( 9t ( + ( + σ ) θ ( σ ) ( σ ) 9 t ( + σ ) 3 = = θ ( t ) ( σ ) (A4) Modest trade costs relative to production costs Meaninful solutions also require non-neative prices in Nash equilibrium. From (7a) and (7b) we have the followin rank of prices: p > p Hence, all prices are non-neative if p 0. Insertin this constraint into (7a) ives 3( σ ) c ( ) t ( + σ) ( 9t ( + σ) ) This is fulfilled for all non-neative values of c if: 3( σ ) + σ 9t + σ ( )( ( )) i.e. non-neative prices appear if t is relatively lare and relative small. Comparative static analysis of quality and price ratios Differentiatin (8) and (9) and usin (6a) and (6b) ives the results below. ) Marinal costs, c: q = 0 c r ( + σ ) ( θ θ) = < 0 c 3 c( + σ ) ( θ + ) 3t ) Trade costs, : q ( σ ) ( θ + θ ) = ( > 0 (9t ( + σ)) θ ( c + σ ) ( θ + θ + ) r ( σ ) = ( 3t > 0 (9t ( + c( + σ ) ( θ + ) 3t 6

17 3) Relative market size, σ : ( + z) q = ( z) 3 3 c + + z r = 3 3t c + z 3 3t where : ( σ ) ( + σ ) z = (9t ( + and hence we have : z ((9t ( + σ) + ( σ )( + σ)) = > 0 σ (9t ( + σ) ( + σ) z q = σ > 0 σ 3( z) 3 c z ( + ) r = t σ > 0 σ c 3( 3 + z) 3t 4) Horizontal preferences, t: θ θ 9( σ ) = = < 0 t t (9t ( + θ θ + θ ( ) q = t < 0 t θ θ 4( c + σ)( σ ) ( θ + θ) r t (9t ( + = < 0 t c( + σ ) ( θ + ) 3t 7

18 Fiures to the text Fiure : The dependence of quality and price ratio on marinal production costs r, q q = q.5.00 r V ĉ H c Note: H and V are horizontally and vertically differentiated products respectively accordin to the standard empirical method for disentanlin differentiated products. Fiure : The benchmark iso-price ratio curve and iso-quality ratio curve σ A B q r =.5 Note: The quality and price ratio curves are just sketched. 8