Multi-Product Firms at Home and Away: Cost- Versus Quality-Based Competence

We develop a new model of multi-product firms which invest to improve both the quality of their individual products and of their brand. Because of flexible manufacturing, products closer to firms' core competence have lower costs, so they produce more of them, and also have higher incentives to invest in their quality. These two effects have opposite implications for the profile of prices. Mexican data provide robust confirmation of the model's key prediction: firms in differentiated-good sectors exhibit quality-based competence (prices fall with distance from core competence), but export sales of firms in non-differentiated-good sectors exhibit the opposite.


Introduction
What makes a successful exporting …rm? This question has attracted much interest from policy makers, keen to design e¤ective export promotion programs, and from academics, keen to understand the implications of globalization for economic growth. Two answers have been proposed. The …rst focuses on …rm productivity. Studies by Clerides, Lach and Tybout (1998) and Bernard and Jensen (1999), among others, have found that …rms self select into export markets on the basis of their successful performance at home. This evidence inspired the theoretical work by Melitz (2003) where only the most productive …rms …nd it worthwhile to cover the extra costs of exporting. The second answer focuses on product quality. A growing body of work has provided evidence that successful exporters charge higher prices on average, suggesting that quality matters. 1 This study integrates these two views and shows both theoretically and empirically that …rms may choose to compete on the basis of either cost or quality depending on the characteristics of the products they sell and the markets in which they operate. 2 Unlike other studies which have compared the behaviour of di¤erent …rms, and emphasized the between-…rm extensive margin, we focus on the portfolio of products sold by multi-product …rms, and highlight what Eckel and Neary (2010) call the "intra-…rm extensive margin."Our theoretical innovation is to construct a model of multi-product …rms in which the quality of goods is determined endogenously by …rms' pro…t-maximizing decisions. Because of ‡exible manufacturing, products closer to a …rm's core competence have lower costs. As a result, they produce more of those products, but they also have higher margins on them, and therefore higher incentives to invest in their quality. These two e¤ects have opposite implications for the pro…le of prices and, depending on which e¤ect dominates, the model implies one of two possible con…gurations which we call "cost-based"and "quality-based" competence, respectively. The former corresponds to the case where a …rm's core products are sold at lower prices, in order to induce consumers to buy more of them. In the words of Jack Cohen, founder of the UK supermarket chain Tesco, …rms "pile 'em high and 1 Kneller and Yu (2008), Kugler and Verhoogen (2008), Mandel (2009), Manova and Zhang (2009), and Verhoogen (2008). 2 Hallak and Sivadasan (2009) also integrate the productivity and quality approaches in a model of international trade by assuming two sources of exogenous …rm heterogeneity: productivity and "caliber", the latter being the ability to produce quality using fewer …xed inputs. Provided exporting requires attaining minimum quality levels, their model explains the empirical fact that …rm size is not monotonically related to export status, and predicts that, conditional on size, exporters sell products of higher quality and at higher prices. However, they con…ne attention to single-product …rms. sell 'em cheap". As a result, the pro…le of prices across a …rm's products is inversely correlated with its pro…le of sales. By contrast, quality-based competence corresponds to the case where the dominant e¤ect comes from …rms' investing more in enhancing the quality of their core products. As a result, these products command quality premia, and so the pro…le of prices across a …rm's products is positively correlated with its pro…le of sales.
Our model not only allows for di¤erent pro…les of prices but also makes predictions about which kinds of goods should exhibit which pro…le. In particular, it predicts that a higher level of product di¤erentiation encourages …rms to invest relatively more in the quality of individual varieties than in the quality of their overall brand. As a result, quality-based competence should be more in evidence in sectors where products are more di¤erentiated. We test this prediction using a rich Mexican data set already used by Javorcik (2007, 2010).
Most previous empirical studies of multi-product …rms at plant level have been constrained to use data on export sales only, or to combine export and production data at di¤erent levels of disaggregation. 3 By contrast, a unique characteristic of our data is that it provides consistently disaggregated information on both the home and export sales of all goods produced by a large representative sample of manufacturing establishments. 4 As we show, the Mexican data provide robust con…rmation of the model's key prediction: comparing price pro…les with sales pro…les, we …nd that …rms in di¤erentiated-good sectors exhibit quality-based competence to a much greater extent than …rms in non-di¤erentiated-good sectors, both at home and abroad. The contrast is particularly striking in export markets, where Mexican producers in non-di¤erentiated-good sectors engage in cost-rather than quality-based competence. Our results are robust to focusing attention on a variety of subsamples, including only those products sold both at home and abroad, only those plants which sell on the home market and also select into exporting, and only single-plant …rms.
Our paper builds on and extends the existing literature on multi-product …rms in international trade. While there already existed a large literature on multi-product …rms in the theory of industrial organization, our model is one of a number of recent trade models which is more applicable to the kinds of large-scale …rm-level data sets which are increasingly becoming available. 5 Within this latter tradition, existing models impose one or other pro…le of a …rm's prices by assumption. One class of models assumes that products are symmetric on both the demand and supply sides, with the motivation for producing a range of products coming from economies of scope. As a result, all products sell in the same amount and at the same price. 6 A di¤erent approach, pioneered by Schott (2006, 2010), emphasizes asymmetries between products on the demand side. Before they decide to enter, …rms draw their overall level of productivity and also a set of product-market-speci…c demand shocks. The latter determine the …rm's scale and scope of sales in di¤erent markets, and imply that its price and output pro…les are always positively correlated. By contrast, Eckel and Neary (2010) develop a model that emphasizes asymmetries between products on the cost side and implies that price and output pro…les are always negatively correlated. 7 The present paper integrates the demand and cost approaches by assuming that costs determine the pro…le of investment in quality across di¤erent varieties, and develops a model which is more in line with recent work on models of heterogeneous …rms that engage in process and product R&D: see, for example, Bustos (2010) and Lileeva and Tre ‡er (2010) on single-product …rms, and Dhingra (2010) on multi-product …rms. It is even more closely related to those papers which allow for endogenous investment in quality, such as Antoniades (2009), including the view that quality is really perceived quality, which may be market-speci…c, so investment in quality includes spending on marketing as in Arkolakis (2007). All this work has so far focused on single-product …rms only.
This brief review of the literature on multi-product …rms highlights our main interest: how the theoretical models di¤er in the way they model the demand for and the decision to supply multiple products. The models also di¤er in other ways which are of less interest in the present application. One type of di¤erence is in the assumptions made about market structure.
In particular, most recent models assume that markets can be characterized by monopolistic competition, in which …rms produce a large number of products but are themselves in…nitesi- 5 Most models of multi-product …rms in industrial organization make one or more assumption which makes them harder to apply to large …rm-level data sets. In particular, they typically assume that products are vertically but not horizontally di¤erentiated; and/or that the number of products produced by a …rm is …xed, so the key question of interest is where in quality space it will choose to locate; and/or that the number of products produced is relatively small. For examples from a large literature, see Brander and Eaton (1984), Klemperer (1992), and Johnson and Myatt (2003). Baldwin and Ottaviano (2001) apply this kind of model in a trade context. 6 7 Arkolakis and Muendler (2009) and Mayer, Melitz and Ottaviano (2010) apply this approach to heterogeneous-…rm models of monopolistic competition with CES and quadratic preferences, respectively. mal relative to the size of the overall market. 8 By contrast, Eckel and Neary (2010) assume in their core model that markets are oligopolistic. In this paper, we know little about the market environment facing individual …rms: we do not know with which other Mexican plants in the sample they compete directly, and we have no information at all on their foreign competitors.
Hence we prefer to remain agnostic on this issue, where possible deriving predictions which will hold at the level of individual …rms irrespective of the market structure in which they operate. A further dimension of di¤erence concerns the level of analysis, whether partial or general equilibrium. Some of the trade theory papers, including Eckel and Neary (2010), highlight general-equilibrium adjustments working through factor markets as an important channel of transmission of external shocks. However, with the data set we use, it is not possible to ascertain how factor prices are a¤ected by general-equilibrium adjustments to changes in trade policy. Hence, we concentrate on testing implications of the model in partial equilibrium. Section 2 of the paper presents the model and shows how di¤erences in technology, tastes and market characteristics determine whether a multi-product …rm exhibits cost-based or qualitybased competence. Section 3 describes the data and explores the extent to which they con…rm our theoretical predictions. The Appendix shows how the results of Section 2 extend to a Cournot oligopolistic market with heterogeneous …rms, and also presents some additional robustness checks on the empirical …ndings.

The Model
As already explained, the paper extends the ‡exible-manufacturing model of Eckel and Neary (2010) to allow for the interaction of quality and cost di¤erences between the varieties produced by a multi-product …rm. To simplify ideas and notation, we focus in the text on a single monopoly …rm, but, as we show in the Appendix, all the results extend to a heterogeneous-…rms industry in which …rms engage in Cournot competition. Section 2.1 introduces our speci…cation of preferences, while Section 2.2 reviews the earlier model, which allowed for cost-based competence only, showing how a …rm chooses its product range, its total sales, and their distribution across varieties in a single market. Section 2.3 explores the additional complications which quality-based competence introduce and derives our main theoretical result, and Section 2.4 considers the model's comparative statics properties.

Preferences for Quantity and Quality
Consider a single market, in which each one of L consumers maximizes a quadratic sub-utility function de…ned over the consumption and quality levels of a set~ of di¤erentiated products: Utility is additive in a component that depends only on quantities consumed, u 1 , and one that depends on the interaction of quantity and quality, u 2 . The …rst component is a standard quadratic function, where q (i) denotes the consumption of a single variety and Q denotes total consumption. The parameter e is an inverse measure of product di¤erentiation, assumed to lie strictly between zero and one (which correspond to the extreme cases of independent demands and perfect substitutes respectively). The second component shows that additional utility accrues from consuming goods of higher quality, wherez (i) is the perceived quality level of an individual variety. We defer until Section 2.3 a detailed consideration of how the quality levelsz (i) are determined.
As discussed in the introduction, we remain agnostic in the paper about whether this subutility function is embedded in a general or partial equilibrium model: our analysis is compatible with both approaches. All we need assume is that the marginal utility of income can be set equal to one. This is ensured if the sub-utility function (1) is part of a quasi-linear upper tier utility function, with all income e¤ects concentrated on the "numéraire"good. Alternatively, as in Eckel and Neary (2010), (1) can be one of a mass of sub-utility functions without an outside good, with the marginal utility of income set equal to unity by choice of numéraire.
Maximization of (1) subject to the budget constraint R i2~ p (i) q (i) di = I (where I is individual income) generates linear demand functions for the typical consumer. These individual demand functions can then be aggregated over all L identical consumers in the market. Imposing market-clearing, so sales volume x (i) equal total demand Lq (i), gives the market inverse demand functions faced by the monopoly …rm: Here p (i) is the price that consumers are willing to pay for an extra unit of variety i. This depends negatively on a weighted average of x (i), the sales of that variety, and X, the total volume of all varieties produced and consumed in the market. Note that X is de…ned over the set of goods actually consumed, , which is a proper subset of the exogenous set of potential products~ , ~ . We will show below how is determined. Finally, the demand price also depends positively, through the intercept a (i), on the perceived quality of the individual variety, z (i).

Cost-Based Competence
Consider next the technology and behaviour of the …rm in a single market, which is segmented from the other markets in which the …rm operates. The …rm's objective is to maximize pro…ts by choosing both the scale and scope of production, as well as choosing how much to invest in enhancing the quality of individual varieties and of its overall brand. We begin by abstracting from the quality dimension in this sub-section, and recapping the results of Eckel and Neary (2010) for the case where the …rm's competence derives from di¤erences between varieties in production costs only. This is most easily done by setting equal to zero in equation (1), so utility does not depend on quality. Though it is convenient to make explicit the variety-speci…c intercepts a (i) in all equations, we do not consider the implications of di¤erences between them until the next sub-section.
With no investment in quality, the …rm's problem is to maximize its operating pro…ts only: Here t is a uniform trade cost payable by the …rm on all the varieties it sells. The marginal cost function c (i) embodies an assumption which Eckel and Neary (2010) identify as a key aspect of ‡exible manufacturing: marginal costs di¤er between varieties and rise as the …rm moves away from its "core competence" variety, the one with lowest marginal cost. 9 More precisely, 9 We assume that production costs are independent of the market served. Mayer, Melitz and Ottaviano (2009) the …rm's marginal cost of production for variety i is independent of the amount produced of that variety, is lowest for the core-competence variety indexed "0", and rises monotonically as the …rm moves away from its core competence: c 0 (i) > 0. With uniform trade costs included, this is shown by the upward-sloping locus c (i) + t in Figure 1. 10 To derive the …rm's behaviour, we …rst consider the optimal choice of output for each variety produced, i.e., for all i in the set . In choosing the output of each variety, the …rm must take account of its e¤ect on the demand for all the varieties it produces, through the demand functions (2). 11 The …rst-order conditions with respect to x (i) are: These imply that the net price-cost margin for each variety, p (i) c (i) t, equalsb times a weighted average of the output of that variety and of total output, where the weights depend on the degree of product substitutability. The presence of total output in this expression re ‡ects the "cannibalization e¤ect": an increase in the output of one variety will, from the demand function (2), reduce its sales of all varieties. Taking this into account induces the …rm to reduce its sales relative to an otherwise identical multi-divisional …rm where decisions on the output of each variety were taken independently. 12 Combining the …rst-order conditions with the demand function (2) we can solve for the output of each variety as a function of its own cost and of the …rm's total output: With a (i) independent of i, the outputs of di¤erent varieties are unambiguously ranked from larger to smaller by their distance from the …rm's core competence. Hence the problem of add an exogenous market-speci…c adaptation cost function which augments the production costs c (i). With existing data sets, this is observationally equivalent to exogenous market-speci…c taste shifts a (i), as in Bernard, Redding and Schott (2006). 1 0 Figures 1 to 2 are drawn under the assumption that the cost function c (i) is linear in i. Though a convenient special case, this assumption is not needed for any of the results. 1 1 Strictly speaking, the …rm is choosing the whole output schedule fx (i)g, which is a calculus of variations problem. However, it is helpful to think of it instead as choosing the output of each variety, one at a time. The …rstorder condition is: , the e¤ect of a small change in the output of variety i on prices (2) can be written as: @p(i) @x(i 0 ) = b e when i 6 = i 0 , and @p(i) @x(i 0 ) = b = b [(1 e) + e] when i = i 0 . Substituting gives equation (4). 1 2 Each division of such a …rm would independently set p(i) c(i) t equal tobx(i). In doing so, it would forego the gains from internalizing the externality which higher output of one variety imposes on the …rm by reducing the demand for all other varieties. Such a myopic …rm would also be indistinguishable from a set of single-product …rms which happened to have the same pro…le of marginal costs. (Thanks to Jonathan Vogel for the latter point.) choosing the set of products to produce, , reduces to the problem of choosing the product range, which we denote by . From Eckel and Neary (2010), the …rst-order condition for choice of is that the output of the marginal variety is exactly zero: x ( ) = 0. Hence the pro…le of outputs is as shown by the downward-sloping locus x (i) in Figure 1. Finally, since demands are symmetric when a (i) = a 0 , the prices which will induce this pattern of demand must be increasing in i. To induce consumers who, ceteris paribus, are indi¤erent between varieties to buy more of those closest to its core competence, the …rm must "pile 'em high and sell 'em cheap". This is con…rmed when we substitute for outputs x(i) from (5) into the …rst-order condition (4) to obtain the pro…t-maximizing pro…le of prices: Thus prices increase with costs, though less rapidly, implying that the …rm's mark-up is lower on non-core varieties. However, it makes a strictly positive mark-up on all varieties: because of the cannibalization e¤ect, it would not be pro…t-maximizing to set price equal to marginal cost on the marginal variety x( ). 13 All this is illustrated in Figure 1.

Quality-Based Competence
Consider next the case where consumers care about quality as well as quantity, so in the utility function (1) is positive. Consumers therefore perceive a quality premiumz (i) attaching to each variety, which we assume can be decomposed as follows: Here z (i) is the variety-speci…c component of quality, and Z is the quality of the …rm's brand as a whole. Note that Z is not equal to R i2~ z (i) di, the aggregate of individual varieties'quality. Here too, product di¤erentiation matters. If varieties are close to independent in demand (so e is close to zero), then the consumer perceives little bene…t from a higher quality brand in itself.
By contrast, if varieties are close substitutes (so e is close to one), then the consumer attaches more importance to the quality of the brand as a whole than to that of individual varieties. In general, the perceived quality of each individual variety is a weighted average of the variety-speci…c quality component and that of the …rm's brand as a whole, where the weights are 1 e and e respectively. 14 Next, we need to specify how the components of quality are determined. It would be possible to assume that the perceived qualities of di¤erent varieties and of the …rm's brand vary exogenously, perhaps determined by a random process as in Bernard et al. (2010). However, this would be hard to reconcile with the assumption of ‡exible manufacturing, where a …rm's products are ranked by their distance from its core competence. We assume instead that, in the absence of investment in quality, consumers are indi¤erent between all varieties. However, the …rm can invest to enhance the perceived quality of each of its individual varieties, as well as the perceived quality of its overall brand. 15 As we will see, this generates a rich framework where di¤erences between varieties are ultimately determined by costs, but where the pro…les of outputs and prices may exhibit what we call "quality-based competence" if investment in quality is su¢ ciently e¤ective.
To allow for explicit solutions, we assume that the costs of and returns to investment take simple functional forms. With k (i) denoting the …rm's investment in the quality of variety i, we assume that the cost incurred is linear in k (i), equal to k (i), while the bene…ts come in the form of higher quality, though at a diminishing rate: z (i) = 2 k (i) 0:5 . Similarly, investment in the quality of the brand incurs costs of K and raises brand quality at a diminishing rate: Z = 2 K 0:5 . Total …rm pro…ts in the market are thus given by: The …rst-order conditions for scale and scope are as before. The new feature is the …rm's optimal choice of investment in quality, which is determined by the following …rst-order conditions: The …rst equation shows that the …rm will invest in the quality of variety i up to the point where the marginal cost of investment equals its marginal return. The latter is increasing in , the weight that consumers attach to quality as a whole, and in , the e¤ectiveness of investment in raising quality. However, it is decreasing in the substitution parameter e: as goods become less di¤erentiated the incentive to invest in the quality of an individual variety falls. Exactly analogous considerations determine the optimal level of investment in the …rm's brand, with one key di¤erence: for given total output this is increasing rather than decreasing in the substitution parameter e. The more consumers view the …rm's varieties as close substitutes, the greater the pay-o¤ to investing in the brand.
The relationship between the di¤erent components of investment is highlighted by comparing total investment in the quality of individual varieties, where: Not surprisingly, investment in varieties is higher than in the overall brand the more e¤ective it is (the higher is relative to ) and the less expensive it is (the lower is relative to ).
It is also higher the less substitutable are di¤erent varieties (the lower is e). In addition, it is also higher the greater is , which Eckel and Neary (2010) de…ne as an ex post measure of the ‡exibility of technology of a multi-product …rm. Intuitively, the more ‡exible is its technology the more the …rm wants to di¤erentiate its marketing spending across di¤erent varieties; by contrast, if is low, the distribution of outputs across varieties is more even and the …rm will tend to focus on promoting its brand as a whole.
Consider next the implications of investment in quality for the pattern of the …rm's sales across varieties. The …rst-order condition (9)-(i) shows that the …rm will invest more in a variety with greater sales volume. The latter is endogenous of course, but combining this and (9)-(ii) with the expression for outputs in (5) allows us to write the output of each variety as a function of exogenous variables and of total sales only: Here, and are composite parameters which we can call, following Leahy and Neary (1997), the "marginal e¤ectiveness of investment"in the quality of individual varieties and of the …rm's brand respectively. 16 So, for example, is higher the more consumers value quality (the higher is ), the more e¤ective is investment in quality (the higher is ), and the less costly it is (the lower is ). Note that and cannot be too high: bothb (1 e) andb e must be positive from the second-order conditions for optimal choice of outputs and investment. To see the implications of (11) more clearly, evaluate it at i = and use the fact that the output of the marginal variety is zero, x ( ) = 0. The output of each variety can then be expressed in terms of the di¤erence between its own cost and that of the marginal variety: This con…rms that the pro…le of outputs across varieties is the inverse of the pro…le of costs: outputs fall monotonically as the …rm moves further away from its core competence. Moreover, it shows that the output pro…le is steeper the higher is . The greater the marginal e¢ ciency of investment in the quality of individual varieties, the more a …rm faces a di¤erential incentive to invest in the quality of its most e¢ cient varieties, those closer to its core competence, since they have the highest mark-ups in the absence of investment.
Equation (12) shows that investment in quality increases the variance of outputs but does not change their qualitative pro…le. By contrast, it can reverse the slope of the …rm's price pro…le. To see this, substitute from the expression for output (12) into the …rst-order condition (4) to solve for the equilibrium prices: The coe¢ cient of c (i) in this expression gives one of our key results. Recalling that the denominator must be positive from the second-order conditions, the slope of the price pro…le depends on the sign of the numeratorb 2 (1 e). When the direct e¤ect of an increase in i, working through a higher production cost, dominates, the numerator is positive, and the price pro…le exhibits "cost-based competence": varieties closer to the …rm's core competence must sell at a lower price to induce consumers to purchase more of them. The extreme case of this is where investment in the quality of individual varieties is totally ine¤ective, so is zero and the coef-…cient of c (i) in (13) reduces to one half as in the last sub-section. By contrast, if the indirect e¤ect of an increase in i, working through a higher value of a (i), is su¢ ciently strong, so the …rm invests disproportionately in the quality of products closer to its core competence, then it charges higher prices for them, and the price pro…le slopes downwards, as illustrated in Figure  2. We call this case one of "quality-based competence". Summarizing: The pro…le of prices across varieties increases with their distance from the …rm's core competence ifb > 2 (1 e), whereas it decreases with the distance ifb < 2 (1 e) < 2b.
Proposition 1 gives the necessary and su¢ cient condition for each outcome, but for completeness and because we will draw on them in the empirical section, it is useful to spell out its implications: Corollary 1 Quality-based competence, the case where prices of di¤ erent varieties are positively correlated with sales, is more likely to dominate: (i) when investment in quality is more e¤ ective, so is larger; (ii) when market size L is larger, sob is smaller; and (iii) when products are more di¤ erentiated, so e is smaller.
This result has been derived for the case of a single monopoly …rm, but it is independent of the extent of competition which the …rm faces. We show formally in the Appendix that it continues to hold in a heterogeneous-…rms Cournot oligopoly market, but the intuition is straightforward. With all goods symmetrically di¤erentiated, …rms compete against each other only at the level of total output, not at the level of individual varieties. Changes in the extent of competition a¤ect the scale and scope of production as well as the level of investment in quality, but do not in ‡uence the pro…le of prices across products.
It should be noted that our distinction between cost-and quality-based competence is an ex post one, based on the observable correlation between the slopes of the price and sales pro…les.
In a fundamental sense, a …rm's core competence in our model is always based on production costs, since these determine the …rm's incentives to invest in improving the quality of di¤erent varieties. It is also possible to consider how the …rm's "full marginal costs", i.e., its marginal production cost plus the average cost of investing in the quality of each variety, varies as it moves away from its core competence. Combining the …rst-order condition for investment with the expression for output in (12), the average cost of investing in the quality of each variety can be shown to equal: Hence the full marginal cost equals: Combining this with Proposition 1, we can conclude that neither marginal production costs nor full marginal costs predict the pro…le of prices across varieties. There are three cases: (i) If cost-based competence dominates, so (1 e) < 1 2b , then both prices and full marginal costs rise with i.
(ii) If quality-based competence dominates, but mildly, so 1 2b < (1 e) < 2 3b , then prices fall with i but full marginal costs rise with i.
(iii) If quality-based competence strongly dominates, so 2 3b < (1 e) <b, then both prices and full marginal costs fall with i.
Note that in case (ii), both measures of cost rise with i, despite which prices fall with i.
However, the mark-up over full marginal cost, (i), is always decreasing in i, and takes a particularly simple form: This is independent of and for given X and . Hence the relative contribution of di¤erent varieties to total pro…ts is independent of the e¤ectiveness of investment in quality: (i)

Comparative Statics
The predictions of the model for the shape of the …rm's equilibrium price pro…le given in Proposition 1 are the ones that we take to the data in the next section. It is also of interest to explore the comparative statics properties of the model. Here we note the e¤ects of exogenous shocks on the scale and scope of a single monopoly …rm, while in the Appendix we show that our results generalize to the case of a group of …rms engaged in Cournot competition.
With a continuum of …rst-order conditions for both outputs and investment levels, it might seem di¢ cult to derive the comparative statics of the equilibrium. However, we can follow the approach used in Eckel and Neary (2010) to express the equilibrium in terms of two equations which depend on total output X and …rm scope only. First, evaluate equation (11) at the marginal variety i = , recalling that x ( ) equals zero. This yields one equation in X and : Next, consider the alternative expression for individual outputs, equation (12), and integrate it over i to obtain a second equation: These two equations can now be solved for X and and the result for X plugged back into equation (11) to solve for the outputs of individual varieties. Table 1 gives the implications for the e¤ects on …rm behaviour of increases in the marginal e¤ectiveness of either kind of investment, in market access costs, and in market size.
Increase in: t L X + + + x (0) + + + + += (2010) call a "leaner and meaner" response: a rise in total output but a fall in scope. As for an increase in market access costs t, this induces a contraction in both scale and scope. The only ambiguity in the table is the e¤ect of an increase in market size L on scope. While the …rm always sells more in total in a larger market, this may or may not come with an increase in scope. The outcome depends on the relative e¤ectiveness of the two kinds of investment and on the degree of substitutability in demand between varieties: Thus, more varieties are sold in a larger market, the less products are di¤erentiated (the higher is e), and the more e¤ective is investment in brand quality relative to investment in the quality of individual varieties (the higher is relative to ).
All these results are proved in the Appendix in the general case with heterogeneous multiproduct …rms, both home and foreign-based, engaging in oligopolistic competition. We show there that the results continue to hold without quali…cation, except for the e¤ects of market size. An increase in market size raises the output of all …rms if they are identical. However, with heterogeneous …rms, the outcome exhibits a "superstar …rms"tendency as in Neary (2010).
Firms with above average total output X j and output per variety X j = j tend to grow faster with market size, while those below average grow more slowly or may even su¤er falls in output as they are squeezed by larger more pro…table …rms. As a result, the size distribution of …rms becomes more dispersed. This tendency is not peculiar to markets with multi-product …rms, but is a general feature of Cournot competition between heterogeneous …rms that invest in R&D or quality. As we show in the Appendix, even when goods are homogeneous (e = 1), so …rms are single-product, an increase in market size still implies the "superstar …rms" result. Only

Empirics
Our theoretical model makes a number of novel predictions about the behaviour of multi-product …rms. One of these in particular is unique to our model, has both theoretical and policy interest, and lends itself to empirical testing with our data. This is the prediction from Corollary 1 that the pro…le of prices across the di¤erent goods produced by a multi-product …rm is more likely to be positively correlated with the corresponding pro…le of outputs, thus exhibiting what we have called quality-based competence, when products are more di¤erentiated. In the remainder of the paper we subject this prediction to empirical testing. We …rst describe the data and document the pro…les of sales across …rms'products which it exhibits; then we explain how we operationalize the prediction about price pro…les; subsequent sub-sections present the results of testing it and consider various robustness checks.

The Data
We begin by reviewing the data set. 17 A unique characteristic of our data is the availability of plant-product level information on the value and the quantity of sales for both domestic and export markets. Our data source is the Encuesta Industrial Mensual (EIM) administered by the Instituto Nacional de Estadística Geografía e Informática (INEGI) in Mexico. The EIM is a monthly survey conducted to monitor short-term trends and dynamics in the manufacturing sector. As we are not primarily interested in short-term ‡uctuations, we aggregate the monthly EIM data into annual observations. The survey covers about 85% of Mexican industrial output, with the exception of "maquiladoras." 18 It includes information on 3,183 unique products produced by over 6,000 plants. 19 Plants are asked to report both values and quantities of total production, total sales, and export sales for each product produced, making the data set particularly valuable for our purposes. Note that the unit of observation is the plant rather than the …rm: we return to this issue in our robustness checks below.
Products in the survey are grouped into 205 clases, or activity classes, corresponding to the 6-digit level CMAP (Mexican System of Classi…cation for Productive Activities) classi…cation.
Each clase contains a list of possible products, which was developed in 1993 and remained unchanged during the entire period under observation. The classi…cation of products is similar in level of detail to the 6-digit international Harmonized System classi…cation, though with di¤erences that re ‡ect special features of the structure of Mexican industrial production. 20 Table 2 shows that the number of plants in the sample varies from 6,291 in 1994 to 4,424 in 2004. Between 1,579 and 2,137 plants were engaged in exporting. 21 The decline in the number of establishments during the period under analysis is due to exit. 22 In this paper, we refer to 1 7 For a more complete account, see Iacovone and Javorcik (2007). 1 8 Maquiladoras are mostly foreign-owned plants located close to the U.S. border, almost exclusively engaged in assembling imported inputs for export. 1 9 The classi…cation system has a total of 4,085 potential products. However, this includes headings entitled "Other unspeci…ed products" and "Other non-generic products" in each clase. Excluding the latter, 3,183 is the number of products actually produced at some point in the sample period. For comparison, the US production data at the …ve-digit SIC code level used by Bernard, Redding and Schott (2010) contain approximately 1,800 product codes, while the US export data used by Bernard, Redding and Schott (2006) contain approximately 8,000 product codes, though these include agricultural products and raw materials as well as manufactures.
2 0 For instance, the clase of Distilled Alcoholic Beverages (identi…ed by the CMAP code 313014) lists 13 products: gin, vodka, whisky, other distilled alcoholic beverages, co¤ee liqueurs, "habanero" liqueurs, "rompope", prepared cocktails, hydroalcoholic extract, and other alcoholic beverages prepared from either agave, brandy, rum, or table wine. However, it does not include tequila, which is included, along with six other related products, in a separate clase, Produccion de Tequila y Mezcal (identi…ed by the CMAP code 313011). 2 1 We exclude a very small number of plant-year observations (23 in total) which reported positive exports but no production: see Table 2. 2 2 Plants that exited after 1994 were not systematically replaced in our sample. This does not bias our results, as our main focus is on within-year rather than panel features of the data.

Sales Pro…les
As a …rst step in exploring the properties of the data through the lens of our theoretical model, The results were unsurprising. In particular, the data show that exporting plants are larger, and that larger plants produce more products. The vast majority of plants sell more products at home, and most exported products are also sold at home. Finally, the pro…le of sales across products is highly non-uniform, with a broadly similar ranking of products by sales in the home and foreign markets. These patterns are consistent with the model presented in Section 2. They are also broadly in line with the empirical patterns found in other recent studies of multi-product …rms. 23

Empirical Strategy
Consider next the theoretical prediction which is unique to our model: if and only if b L < 2 (1 e), then quality-based competence should prevail, so prices fall with distance from a …rm's core competence, or, equivalently, prices and sales values are positively correlated across a …rm's products. In our theoretical section we showed that this holds for a single …rm or (as shown in the Appendix) for a group of …rms competing against each other in an oligopolistic market. Given our large data set, it is natural to explore how this prediction fares when we consider di¤erent values of the exogenous variables, , L and e. Unfortunately, we cannot observe the marginal e¤ectiveness of investment , which is itself a composite of parameters representing the costs and bene…ts to the …rm of investment in product quality. As for market size L, the condition for quality-based competence states that it is more likely to hold the larger the market. However, we should be careful of interpreting this too literally: since we do not have data on sales in individual export markets, we cannot take for granted that the rest of the world is a larger market than the domestic Mexican market. This will be true for some …rms but not for others, depending on the foreign customers they target and on their past history of investment in marketing and product quality. This leaves only the degree of product di¤erentiation e. Fortunately, thanks to Rauch (1999), we have good information on which goods are more di¤erentiated. Hence we can test the implication of the model that more di¤erentiated products are more likely to exhibit a quality-based price pro…le.
How do we operationalize testing this prediction? The …rst issue to be addressed is how to measure the distance of each product from the …rm's core competence. In our theoretical model, with all goods symmetrically and horizontally di¤erentiated from each other, it was natural to look at products ranked by sales volume. This can be thought of as measuring volumes in terms of the true units of measurement in which all goods can be compared. However, when we come to apply the model to real data we do not observe sales volumes in terms of these underlying units of measurement. Fortunately, we can still operationalize the model by focusing on the pro…les of sales value rather then volume: s(i) = p(i)x(i). As i rises, so we consider products further from the …rm's core competence, output de…nitely falls but price may rise or fall as we have seen. However, as we show in the Appendix, Section 5.2, the output e¤ect must dominate.
Hence sales value, like sales volume, unambiguously falls as the …rm moves away from its core competence, and so can be used as an empirical proxy for the distance of a product from the …rm's core competence.
A related issue we need to address is "prices relative to what?" In the theoretical model, all goods are symmetrically di¤erentiated and so, as with outputs, their prices are directly comparable. By contrast, with real-world data, we have to compare the price of each good with the average price of an appropriate set of comparator goods. The strategy we adopt is the following. Prices are measured throughout by unit values, equal to sales value divided by sales quantity. For each product i, let J i denote the number of plants that produce a variety of that product. We measure the relative price of each variety as its own price relative to the average price of all varieties of the same product. More precisely, in all the regressions below, the dependent variable is the log of the unit value of product i from plant j at time t, relative to the weighted average unit value of all J i varieties of product i produced in or exported from Mexico at time t. We call this the price premium: Note that we are comparing the price of a particular variety of each product with di¤erent varieties of the same good, which in all cases are produced in di¤erent plants. The weights ! ijt are either 1=J i or shares in domestic sales or exports; in practice this choice makes very little di¤erence to the results.
Given our price premia, we relate them to the ranking of products produced or exported by the same plant. Thus our measure of how close a product is to its plant's core competence relies on observable production or export data, not on unobservable cost data. In all the tables below, the estimating equation is then: where D r ijt is a dummy variable, which equals one if product i is ranked r in the production or exports of plant j in year t, and zero otherwise; X is a vector of plant …xed e¤ects; and " ijt is a stochastic error term. We present results for a range of values of the number of products R, trading o¤ the improvement in the …ne detail of the price pro…le which we are able to estimate against the loss of degrees of freedom as we exclude more plants which produce or export only a small number of products.
Finally, as already mentioned, we wish to use estimates of (21) to test the prediction of Proposition 1 that a higher degree of product di¤erentiation should make …rms more likely to exhibit a price pro…le that re ‡ects quality-based rather than cost-based competence. To implement this test, we need independent observations on the degree of product di¤erentiation, and for this purpose we make use of the classi…cation developed by Rauch (1999). He grouped goods by the Standard International Trade Classi…cation (SITC), Revision 2, four-digit classi…cation into three categories, "di¤erentiated," "traded on organized exchanges" or "reference priced." We combine the latter two into a catch-all "non-di¤erentiated" category, and follow many authors in adopting the so-called "liberal" classi…cation, which maximizes the number of goods classi…ed as non-di¤erentiated. To implement this classi…cation with our Mexican data, we had to make a concordance between the clases in our data and the SITC system. Fortunately, this was possible without too much arbitrariness. 24 We are thus able to explore how the relationship 2 4 Examples of di¤erentiated clases include: 311901: Produccion de chocolate y golosinas a partir de cocoa o between the price and sales pro…les of multi-product …rms varies with the degree of product di¤erentiation. Table 3 gives the results of estimating equation (21)  The most interesting feature of the table is the pattern of the estimated coe¢ cients when we disaggregate by type of product and by destination. Looking …rst at the second and third equations, both di¤erentiated and non-di¤erentiated products sold at home exhibit the same pattern of quality-based competition. However, the coe¢ cient for di¤erentiated products is signi…cantly greater than that for non-di¤erentiated ones, exactly as our theory predicts. 27 This di¤erence between the two categories of products is repeated but to an even more striking extent in the chocolate (Production of chocolate and candy from cocoa or chocolate); 323003: Produccion de maletas, bolsas de mano y similares (Production of suitcases, handbags and similar); and 322005: Confeccion de camisas (Readyto-wear shirts). Examples of non-di¤erentiated ones include: 311201: Pasteurizacion de leche (Pasteurization of milk); 311404: Produccion de harina de trigo (Production of wheat ‡our); and 341021: Produccion de papel (Production of paper). 2 5 Except where otherwise stated, in this and all subsequent tables, ***, **, and * denote coe¢ cients that are signi…cant at the 1%, 5%, and 10% levels, respectively; all regressions have plant …xed e¤ects; and …gures in parentheses are standard errors which are clustered by plant-year. 2 6 The estimated di¤erence between the natural logarithm of the price premium for the top product and that for all other products in the …rst equation is 0.042, implying a di¤erence in the levels of 4.289%. 2 7 The di¤erence between the coe¢ cients 0.048 and 0.033 in the second and third equations is signi…cant at the 10% level, while the corresponding di¤erences in Tables 4 to 7 below are considerably more signi…cant. An alternative way of presenting the results is in terms of a single equation for all 128,493 observations, with a dummy variable for the top-selling product and a second for top-selling products that are di¤erentiated. For home sales in Table 3, this estimated equation is: ln P rice P remium = 0 + 0:033D 1 + 0:015D 1d , where the standard error of the second coe¢ cient is 0.008. This alternative format makes it easier to see the di¤erence between the coe¢ cients, but obscures their levels. export market, as the …fth and sixth equations show. The coe¢ cient for di¤erentiated exports is 0.081, implying an even higher price premium for the top-selling product in this category. By contrast, the coe¢ cient for non-di¤erentiated exports is 0:031, implying that these products exhibit cost-based rather than quality-based competence. (The coe¢ cient is signi…cantly di¤erent from zero at the 5% level, and signi…cantly lower than that on di¤erentiated exports at the 1% level.)

Results for Price Pro…les at Home and Away
It is worth summarizing the empirical …ndings from Table 3, since the same pattern is repeated, and is nearly always statistically signi…cant, in the vast majority of the equations, estimated for di¤erent groupings of the data, given below: is the estimated coe¢ cient of the dummy variable for the top-selling di¤erentiated product in the export market, etc.; the product rank r equals one in Table 3, and takes other values in later tables.) As already noted, this con…guration strongly con…rms the predictions of our model for the degree of product di¤erentiation. Firms producing more di¤erentiated products face stronger incentives to enhance their perceived quality, so the extent of qualitybased competition is greater for these products. Less consistent with our model is the e¤ect of market size, although, as already discussed, this prediction is not as clear-cut, since the identi…cation of L, the relevant market size, with raw population is problematic. In any case, our results show a systematic tendency for the coe¢ cient on di¤erentiated products to be higher abroad than at home, whereas this pattern is reversed for non-di¤erentiated products.
So far we have only considered the coe¢ cient of the dummy variable for a …rm's top-selling product. Tables 4 to 7 extend the analysis to observations in which the same plant sold at least three, four or …ve products in the one year. In each equation the residual category is all products with ranks lower than the lowest-ranking dummy variable included. For example, in the …nal equation, the four coe¢ cients give the estimated price premia on the top four products relative to the average price premium on the excluded category of all products ranked …fth or lower in production. In these tables, there is some loss of degrees of freedom as we consider plants selling more products, but nevertheless the results are qualitatively identical to those in Table 3. In addition, they show for plants selling more than two products how the pattern of dummy-variable coe¢ cients varies as we move away from the core competence product. Table 3 showed for plants selling two or more products on the home market also applies to plants selling up to …ve or more. For di¤erentiated products, Table 4 shows that the implied price premium for the top product ranges from 4.9% when all plants producing two or more products are included, to 10.0% when only those producing …ve or more are included. In Table 5 the corresponding …gures are 3.4% and 4.8%, showing once again that non-di¤erentiated products exhibit signi…cantly less quality-based competition than di¤erentiated ones. 28 Of even greater interest is that, in the second, third and fourth equations, there is clear evidence that the pro…le of prices falls with a product's rank. Not only is each coe¢ cient of the dummy variables for second-and lower-ranking products in these equations signi…cantly di¤erent from zero, almost all of them are also signi…cantly smaller than the coe¢ cient above them in the table. We can thus conclude that there is strong evidence that prices fall with a product's distance from a plant's core competence, so the price and production pro…les are negatively correlated, implying that on average the …rms in our sample compete on the basis of quality-based competence on the home market.

Tables 4 and 5 con…rm that the pattern of quality-based competition which
Tables 6 and 7 show that export sales behave even more di¤erently depending on the degree of product di¤erentiation. Consider …rst Table 6, which shows that exports of products in di¤erentiated sectors exhibit the same price pro…le away as they do at home. The evidence for a monotonically decreasing pro…le is less strong in the case of plants producing …ve or more products, although this may be due to the smaller number of observations in this sub-sample, and in any case the top three products command a signi…cant price premium over products ranked …fth or lower. Moreover, the quantitative magnitude of the e¤ects is much higher than in Table 4: the implied price premium for the top product ranges from 8.4% when all plants producing two or more products are included, to 16.1% when only those producing …ve or more are included.
By contrast, Table 7 tells a very di¤erent story for exports of non-di¤erentiated products.
Not a single coe¢ cient in this table is signi…cantly positive, most are negative, and all the coe¢ cients of the dummy variable for the top product are signi…cantly negative at the 5% level.
Unlike Tables 4, 5 and 6, this provides strong evidence against quality-based competence, and clear evidence in favour of cost-based competence for exports of non-di¤erentiated products.
Though not as overwhelmingly signi…cant as the results for di¤erentiated products, the results 2 8 As before, these premia are given by the antilogs of the corresponding entries in Tables 4 and 5. imply that the two groups of products behave very di¤erently, and exactly in the way predicted by Proposition 1. For di¤erentiated exports, prices fall with their distance from the plant's core competence, suggesting that Mexican exporters in these sectors compete on the basis of quality.
By contrast, for non-di¤erentiated exports, prices rise with their distance from the plant's core competence, suggesting that competition in such sectors is on the basis of cost rather than quality, exactly as our theory suggests.
Overall, these four tables con…rm that the coe¢ cient pattern summarized in equation (22) continues to hold when we consider plants that sell up to …ve or more products.

Robustness Checks
A possible concern with the results so far is that the sample sizes are very di¤erent in di¤erent tables, with more products produced for the home market than for exports. This is perfectly consistent with our model which predicts that higher costs of accessing a foreign market will reduce the range of products sold there. Nevertheless it might suggest a concern that the regularities we have found in our data re ‡ect behaviour very di¤erent from that predicted by our model; for example, that plants sell di¤erent products in the home and foreign markets, or that plants which select into exporting are very di¤erent from those that sell only on the home market. To address these concerns we reestimate our price pro…le equations …rst for those products that are sold on both markets, and next for the home sales of exporting plants. Tables 8 and 9 address the issue of di¤erent sample sizes directly by reestimating the equations for only those observations on products that are both exported and sold at home. The two tables present results for plants selling two or more and …ve or more products respectively. It can be seen that the conclusions drawn from the earlier tables survive this robustness check. All signi…cant coe¢ cients in the …rst …ve columns in both tables are positive, whereas the signi…cant coe¢ cient in the sixth column, the regression equation for non-di¤erentiated exports, is negative. It is true that the evidence for quality-based competence by plants in non-di¤erentiated sectors is weaker, with no signi…cant coe¢ cients in the third equation in Table 9. However, in Table 8 the coe¢ cient of the dummy variable on the top product when all observations on plants producing two or more products are included remains signi…cant and positive. We can conclude that the evidence from this smaller sample is less overwhelmingly in support of di¤erent behaviour by non-di¤erentiated product plants at home and away; but that the evidence for a di¤erence between behavior by plants in di¤erentiated and non-di¤erentiated sectors remains very strong, especially in export markets. Table 10 addresses the question of whether plants that select into exporting behave di¤erently on the home market. It gives results for home sales by export plants in both di¤erentiated and non-di¤erentiated clases, and it is clear that the two behave very similarly to the corresponding samples of all plants selling on the home market, as in Tables 4 and 5. Once again, all home sales exhibit quality-based competence, with those of di¤erentiated products signi…cantly more so. Bearing in mind that the plants in Table 10 are identical to those whose exporting behaviour is shown in Tables 6 and 7, our earlier conclusions are reinforced. Exporting plants in both di¤erentiated and non-di¤erentiated sectors exhibit quality-based competence in the home market, though the latter less strongly, so the very di¤erent behaviour of exporters in non-di¤erentiated sectors shown in Table 7 does not re ‡ect any di¤erential selection process of plants into exporting.
A di¤erent robustness check addresses the concern that our theory was developed for multiproduct …rms, whereas our data consist of observations on multi-product plants.  Tables 11 and 12 give the results of this robustness check, for single-plant …rms selling at least two and at least …ve products respectively. The evidence for quality-based competence remains overwhelming for both categories of home sales and for di¤erentiated exports. The pro…le of the sales-rank dummies is not always monotonically decreasing, and de…nitely not signi…cantly so. However, all coe¢ cients are signi…cant at the 1% level, implying that products closer to the core sell for higher prices than the non-core products in the default category of each equation. As for exports of non-di¤erentiated products, the evidence for cost-based competence is much less strong than in earlier tables. At the same time, with all coe¢ cients insigni…cant, there is no evidence for quality-based competence either. We can conclude that our earlier results are reasonably robust to excluding plants owned by multi-plant …rms in 2003.
A related concern is that our model is more applicable to Mexican-owned …rms than foreignowned ones. At least for sales in their export markets, and even in their home market too, we would expect the decisions of foreign-owned Mexican plants to be taken as part of the global operations of their parent multinational companies rather than on a stand-alone basis. It seems appropriate therefore to check that the results hold when foreign-owned plants are excluded.
Tables 13 and 14 con…rm that this is the case. All coe¢ cients of the dummy variable for the top-selling product are signi…cant and …t the pattern summarized in equation (22).
Finally, it is desirable to check that the results for price pro…les which we have uncovered do not re ‡ect features peculiar to only some years in our sample. (The Mexican economy was subjected to a number of major shocks during the early years of our data, including the coming into force of NAFTA in January 1994 and the peso devaluation of December 1994.) Table 15 gives the results of estimating the price pro…le for plants selling two or more products in each year for each of the four disaggregated categories we have considered so far. Sample sizes are now much smaller of course, especially for export markets, so not all coe¢ cients are signi…cant.
Nonetheless, the pattern of coe¢ cients is very much in line with that found already. In eight of the eleven years, it conforms exactly to that given in equation (22), and in the remaining three years there is only one departure from that pattern: in 1995, non-di¤erentiated exports exhibit quality-based competence, though less strongly than any other category; in 1996, di¤erentiated sales exhibit quality-based competence more strongly in the home market than the export market; and in 2004, di¤erentiated products exhibit slightly though not signi…cantly less qualitybased competence in the home market than non-di¤erentiated ones. It is tempting to propose ad hoc rationalizations for these departures from the norm: the improved competitiveness of Mexican exports following the peso crisis might explain the departures from the general pattern in 1995 and 1996, for example. However, it is probably better to attribute them merely to the relatively small samples available for each year, and to conclude that the patterns for individual years are not substantially out of line with those found in the sample as a whole.

Conclusion
This paper has developed a new model of multi-product production in which …rms invest to improve the quality of their products as well as the quality of their overall brand. It is thus the …rst to integrate two important strands of recent work on the behaviour of …rms in international markets. On the one hand, the growing evidence that many …rms, and especially most large exporters, are multi-product, has inspired theoretical and empirical work which focuses on the "intra-…rm extensive margin", changes in the range of products produced by …rms, distinct from the inter-…rm extensive margin which has attracted so much attention in the literature on heterogeneous single-product …rms. On the other hand, an increasing number of authors have suggested that successful …rms in international markets compete on the basis of superior quality rather than superior productivity. Our model integrates these two strands in a tractable framework. Crucially, it endogenises both the choice of product range and the choice of quality, or more speci…cally, the choice of investment in quality, thus allowing a range of issues to be explored which have so far been little studied.
The model has interesting implications for the manner in which …rms compete in international markets. In particular, it throws light on the question of whether productivity or quality is the key to successful export performance, and suggests a way of reconciling these two views. Because of ‡exible manufacturing, …rms produce more of products closer to their core competence. They also have incentives to invest more in the quality of those goods. These two e¤ects have opposite implications for the pro…le of prices. On the one hand, to the extent that consumers view all products as symmetrically di¤erentiated substitutes for each other, …rms can only sell more of their core products by charging lower prices for them. Hence, the direct e¤ect of lower production costs for core products is that …rms "pile 'em high and sell 'em cheap," implying that the pro…les of prices and sales should be negatively correlated, an outcome we call "cost-based competence". On the other hand, …rms face stronger incentives to invest in raising the perceived quality of their core products, since these are the products with the highest mark-ups. Even though investment in the quality of an individual product is subject to diminishing returns, this implies that …rms will invest more in the quality of their core products, so raising the price which consumers are willing to pay for them. This indirect e¤ect of lower production costs for core products implies that the pro…les of prices and sales should be positively correlated, an outcome we call "quality-based competence". We show that both these outcomes are possible in our model, and that which of them prevails depends on a number of exogenous factors. In particular, the greater the degree of product di¤erentiation, the more the …rm faces di¤erential incentives to invest in the quality of di¤erent products, and so the more likely is the indirect e¤ect to dominate, giving rise to quality-based competence.
This last prediction is the one we explore empirically, drawing on a unique data set on Mexican plants already used by Javorcik (2007, 2010). A great advantage of this data set is that it gives detailed information on both home and foreign sales at the same level of disaggregation, allowing us to test theoretical predictions about their relative pro…les. Our …ndings show that a two-way distinction is crucial: between home sales and exports on the one hand, and between di¤erentiated and non-di¤erentiated products on the other. In the domestic market, we …nd that both di¤erentiated and non-di¤erentiated products exhibit quality-based competence, with prices falling as sales value falls. However, this pattern is signi…cantly more pronounced for di¤erentiated products, exactly as our theory predicts. The same holds true in the export market, where the di¤erence in price behaviour between the two groups of products is considerably greater: plants in di¤erentiated-product sectors exhibit quality-based competence in export markets, but those in non-di¤erentiated-good sectors exhibit cost-based competence, with core-competence products selling for signi…cantly lower prices on average. These results turn out to be robust to a slew of alternative ways of grouping our data. We …nd very similar results whether we consider all products or only those which are sold in both home and foreign markets; and whether we consider all plants active in either market or only those active in both. They also hold when we consider only the sub-sample of single-plant …rms: con…rmation that our theory, which was developed for …rms, helps in understanding behaviour at plant level too. Finally, the patterns we have found hold in all years in our eleven-year sample, and are particularly in evidence for home-owned as opposed to foreign-owned …rms. We can thus conclude that, for this data set, quality-based competence is dominant for …rms in di¤erentiatedgood sectors, but not for the export sales of …rms in non-di¤erentiated-good sectors.
While a full consideration of the costs and bene…ts of di¤erent export promotion strategies is beyond the scope of this paper, our results have interesting implications for the design of such policies. In particular, our …nding that exporters from a middle-income country such as Mexico compete in foreign markets on either cost or quality suggests that export promotion e¤orts should focus on improving perceived product quality in di¤erentiated-good sectors and on helping producers to lower production costs in non-di¤erentiated-good sectors. The former type of intervention can take the form of marketing campaigns to stress the advantages of national products, or reductions in the costs of quality certi…cations (e.g. ISO 9000 or 14000) to improve the producer's image. The latter type of intervention can focus on stimulating investment in cost-saving technologies and worker training.
Our …ndings also have broader implications for the nature of competition in international markets. Our data set shows that within-…rm product heterogeneity is not just a rich-country phenomenon, but is also important in at least one middle-income country. Moreover, the evidence we present suggests that only …rms in di¤erentiated-product sectors compete in export markets on quality. This has a key implication for understanding how …rms compete successfully abroad. While previous studies have shown that all exporters have a productivity premium, our results suggest that those in di¤erentiated-product sectors have a quality premium too, whereas those producing non-di¤erentiated goods behave di¤erently at home and away, competing less on quality and more on price in their export markets.

Cournot Competition with Heterogeneous Firms
The model in the text considered a single monopoly …rm only, whose goal is to maximize the operating pro…ts from all the products it sells in a market. Here we show that the results on sales and price pro…les derived in the text also hold for a …rm engaged in Cournot competition, that takes as given the outputs of other …rms. We also derive the comparative statics e¤ects on such a …rm of changes in the marginal e¤ectiveness of both types of investment, in market size, and in market access costs.
To simplify notation, we consider a world of two countries only. We focus on the foreign market, in which we assume there is a …xed number of …rms, m, of which m are from the home country and m from the foreign country, each with the ‡exible manufacturing technology considered in the text. We let M , M and M denote the sets of …rms in the home and foreign countries and in the world, respectively. We allow for arbitrary di¤erences between …rms in their cost functions, with the cost function of …rm j denoted by: c j (i) ; j = 1; :::; m. The utility function is unchanged from equation (1) in the text, since, in the absence of investment in quality, consumers do not value di¤erently the goods produced by di¤erent …rms. Hence the demand function is the same as (2), except that total consumption is now Y = P j2 M X j .
Consider the behaviour of an individual …rm. The presence of competitor …rms does not a¤ect the …rst-order condition for the output of each variety in equation (4): each …rm continues to equate the price-cost margin of each variety tob times a weighted average of that variety's output and of its total output. Combining this with the demand function, the expression for outputs, equation (5), must be replaced by: where j = f0; :::; j g is the set of goods sold by …rm j, and, as in the monopoly case, the sales of each marginal product are zero: x j ( j ) = 0. Note that we write the tari¤ with …rm subscripts: t j = t for all home exporting …rms j 2 M , and t j = 0 for all foreign import-competing …rms j 2 M . As for the …rst-order conditions for investment in quality, they continue to be given by (9). 30 Substituting these into a j (i) and proceeding as in the text gives, instead of (12): This in turn leads to an equation for prices just like equation (13) in the text. Hence Proposition 1 is una¤ected: the key condition for the pro…le of a …rm's prices to rise with distance from its core competence continues to beb > j (1 e), independent of the number of …rms m and m .
Consider next the comparative statics of an initial equilibrium. We seek a set of m equations, one per …rm, which relate changes in the total output of each …rm, X j , to changes in exogenous variables = j ; j ; L; t . For simplicity we con…ne attention to the e¤ects of a change in the relative e¤ectiveness of investment for only one …rm j, assumed to be an exporter based in the home country. To eliminate the individual varieties x j (i), integrate (24) to get: To obtain a second equation linking X j and j , evaluate (23) at i = j to obtain: Finally, total market sales Y can be eliminated by recalling that it equals the sales of all m …rms.
To proceed, …rst totally di¤erentiate (25) and (26): Combining these and eliminating j gives a single equation for each …rm, which is the total di¤erential of its reaction function in fX j g space: where: and d j is a composite term summarizing the exogenous shocks to …rm j's reaction function. Solving these m reaction functions (29) allows us to derive the comparative statics e¤ects of changes in the exogenous variables.
To solve the equations in (29), we follow Dixit (1986). Multiply (29) by A j , sum the reaction functions over all m …rms, and collect terms to solve for total output Y : Next, substitute into (29) to solve for the change in the output of an individual …rm: Thus any exogenous shock a¤ects the output of …rm j directly by shifting its own reaction function, and also indirectly to the extent that it shifts di¤erentially the reaction functions of all other …rms. We can now consider the e¤ects of di¤erent shocks in turn.

E¤ects of Tari¤s
When the foreign tari¤ increases, we have: d j = dt; j 2 M and d j = 0; j 2 M . Hence from (33) the e¤ect of a foreign tari¤ on the output of a foreign import-competing …rm is: This implies that a reduction in foreign trade barriers (dt < 0) lowers the output of all foreign …rms, since it exposes them to more competition. Similarly, the change in the total output of a home exporting …rm is: Hence a reduction in foreign trade barriers raises the export sales of all home …rms. From (25), each …rm's output and scope move together for given L and j , and so the e¤ects of a tari¤ on j are qualitatively the same as its e¤ects on the corresponding X j .

E¤ects of the Marginal E¤ectiveness of Brand-Enhancing Investment
In this case we have d j 0 = 2e 2 X j d j ; j 0 = j and d j 0 = 0; j 0 6 = j. Hence from (33): As for …rm j's scope, it follows immediately from (25) that it too must rise.

E¤ects of the Marginal E¤ectiveness of Variety-Enhancing Investment
In this case we have d j 0 = 2 j (1 e) 2 X j d j ; j 0 = j and d j 0 = 0; j 0 6 = j. Hence from (33): It also follows immediately that the output of all other …rms must fall. As for the implications for scope, substituting dX j into (27) yields: Substituting for A j j from (30), this becomes: Both the fractions in parentheses are less than one, so the whole expression must be negative.
Hence product scope must fall for all …rms in this case. The …rm enjoying more e¤ective investment adopts a "leaner and meaner"pro…le, while all other …rms face tougher competition and so cut back on both scale and scope.

E¤ects of Market Size
All …rms are directly a¤ected by this shock and the outcome turns out to depend a lot on the degree of asymmetry between them. Substituting for dL from (31) into (33) gives: The second set of terms inside the square brackets on the right-hand side exhibits the "superstar …rms" tendency discussed in the text: …rms with total sales X j or sales per variety X j j above the industry average tend to grow by more, and conversely for …rms below average. In the special case where goods are homogeneous (e = 1), so …rms are single-product, equation (40) becomes: , with A 1 j =b 2 j . Though simpler than (40), this still implies the "superstar …rms"result. A di¤erent special case is where all …rms are identical, in which case the e¤ect on output is: This is greater than one provided either or is strictly positive, so …rms engage in either or both type of investment. Finally, when …rms are heterogeneous but do not invest, because j = j = 0, equation (40) reduces to d ln X j d ln L = 1. Turning to the e¤ect on scope, equation (28) can be rewritten to give: where E j j 0 is the elasticity of cost savings from ‡exible manufacturing, as in Eckel and Neary (2010), p. 201. Even for superstar …rms, scope may fall, and a high e¤ectiveness of investment in individual varieties, j , tends to encourage this outcome. When j = j = 0, so …rms do not invest, scope is independent of market size, Clearly, a higher e¤ectiveness of investment in brand quality encourages an expansion of scope, and a higher e¤ectiveness of investment in the quality of individual varieties encourages a reduction, with increased competition from more rival …rms tending to accentuate the latter.
With only one …rm, the numerator is proportional to e (1 e), the case discussed in the text.

Sales Value and Distance from Core Competence
To show that the pro…le of sales value falls with distance from core competence, totally di¤erentiate the equation de…ning s(i): The derivative of p (i) with respect to i can be found by di¤erentiating the …rst-order condition (4). Substituting this and collecting terms gives: Next, substituting for both output x (i) itself and its derivative with respect to i from equation (5) gives: Since c (i) rises with i and a (i) is either independent of i or falls with it, it follows that sales value must fall with distance from the …rm's core competence.