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Article Excerpt
THE DIXIT-STIGLITZ (1977) model of monopolistic competition has become a workhorse model in many literatures that examine product differentiation in general equilibrium, including literatures on international trade, macroeconomics, and growth and development (see Gordon 1990 and Matsuyama 1995 for literature reviews). The model is widely used because it is tractable. In its most commonly used form the model assumes constant elasticity of substitution (CES) demand so that varieties are not assigned to any particular "address" and product space is effectively infinite. This implies that the elasticity of demand, markups, and prices are invariant to market size and firm entry.
We examine an alternative model of horizontal product differentiation with richer implications for pricing. Lancaster (1979) originally developed a model of trade in ideal varieties in which variety space is finite, and varieties have unique addresses in product space. Firm entry causes "crowding"--varieties become more substitutable as more enter the market so that the own price elasticity of demand increases with market size, and prices fall.
We generalize the preferences in the ideal variety framework. Lancaster (1979) assumes that the equilibrium choice of variety is independent of consumption quantities, so that consumers get no closer to their ideal regardless of expenditures. We allow the opportunity cost of the ideal variety to depend on consumers' individual consumption levels. When incomes rise, consumers increase the quantity consumed but also place greater value on proximity to the ideal variety. The price elasticity of demand drops and prices rise. In equilibrium, the market responds by supplying more varieties, with lower output per variety. Essentially, economies of scale forsaken are compensated for by the higher markups that consumers are now willing to pay.
We examine, and confirm, these implications in two exercises focusing on cross-country variation in trade goods prices and in the own-price elasticity of demand. We use Eurostats trade data for 1990-2003 that report bilateral export prices for 11 EU exporters selling to all importers worldwide in roughly 11,000 products. Unlike many cross-country price studies that rely on domestic price data, our border prices are not contaminated by distribution markups within each country. We have many price observations for the same exporter-product over time, and this allows us to control for unobservables such as product quality that are outside of the model. We control for price levels that are specific to an importer-product and price changes that are specific to an exporter-product. We can then relate over-time changes in prices for an importer/exporter-product to changes in importer characteristics. We find that price changes covary negatively with GDP growth and covary positively with growth in GDP per capita (conditioning on GDP growth), consistent with model predictions.
The generalized IV model implies that variation in the elasticity of demand generates cross-importer price differences. We use the TRAINS database on bilateral trade and trade costs to identify the own-price elasticity of demand and examine its covariation with importer characteristics. We find that the own-price elasticity of demand is increasing in importer GDP and decreasing in importer GDP per capita, consistent with model predictions. The data reveal substantial variation in these elasticities across importers.
This paper relates, and adds, to several literatures. First, we contribute to a literature in which market entry affects the elasticity of demand facing a firm. Most of the trade theory literature with this feature has emphasized oligopoly and homogeneous goods as in Brander and Krugman (1982). (1) The more sparse empirical literature has focused on plausibly homogeneous goods within a single country, such as the markets for gasoline (Barron, Taylor, and Umbeck 2004) and concrete (Syverson 2004). In contrast, our model emphasizes free-entry monopolistic competition in a general equilibrium with multiple countries and differentiated goods. (2)
The model's predictions for import market size and the elasticity of demand are similar to quadratic utility models as in Ottaviano, Tabuchi, and Thisse (2002) and Melitz and Ottaviano (2008). We are unaware of other papers that directly test this implication, and so to the extent that model predictions are similar, our empirical findings are consistent with the broader idea of market entry increasing substitutability across goods. However, we also allow for income effects operating through an intensity of preference for the ideal variety that can potentially counteract pure market size effects. (3) These income effects significantly improve our ability to fit the model to the data.
Second, this paper adds to the literature on price variation across markets. The literature on Balassa-Samuelson effects emphasizes the importance of nontraded goods prices in explaining why price levels are higher in richer countries. We provide a theoretical explanation and empirical evidence supporting the idea that prices of traded goods are also higher in richer countries. A similar prediction using a different channel can be found in Alessandria and Kaboski (2004) who link larger markups in high-income importers to consumers' opportunity cost of search.
The literature on pricing-to-market (see Goldberg and Knetter 1997 for an extensive review) has shown that the same goods are priced with different markups and thus have different price elasticities of demand across importing markets. We differ from, and add to, this literature in two ways. First, we show how markups systematically vary across importers depending on market characteristics. Second, we provide a complementary explanation for the variation in markups. The pricing-to-market literature focuses on movements along the same, non-CES, demand curves (e.g., Feenstra 1989, Knetter 1993) so that variation in quantities caused by tariff or exchange rate shocks yields variation in the elasticity of demand. We show that variation in market characteristics (size, income per capita), yields different demand curves and thus different price elasticities of demand across countries.
Third, we contribute to a relatively new but growing literature providing empirical evidence on models of product differentiation in trade. Most of these papers employ cross-exporter facts to understand Armington- versus Krugman-style horizontal differentiation as in Head and Ries (2001) and Acemoglu and Ventura (2002), or the importance of quality differentiation as in Schott (2004), Hallak (2006), and Hummels and Skiba (2004), or some combination of the two, as in Hummels and Klenow (2002, 2005). We emphasize cross-importer facts and depart from the CES utility framework that dominates this literature.
In particular, our model provides a partial resolution to a puzzle about the rate of variety expansion. Hummels and Klenow (2002) use cross-country data to examine how the variety and quantity per variety of imports covary with market size. They show that while the number of imported varieties is greater in larger markets, variety differences are less than proportional to market size. That is, larger countries import more varieties but also import higher quantity per variety. (4) The generalized ideal variety model generates this implication but the standard CES model does not. If entry does not "crowd" variety space, the own-price (and cross-price) elasticity of demand is the same regardless of market size. This implies that price and quantity per variety are the same in the two markets, and so there is a strict proportionality between number of varieties and market size.
The rest of the paper is organized as follows. Section 1 uses a simplified closed-economy setting to motivate the generalization of Lancaster compensation function and to concentrate on the comparative statics in the model with a single differentiated product. Appendix B demonstrates that the key empirical predictions can also be derived in an open-economy model. Sections 2 and 3 provide empirical examinations of model implications for prices and the own-price elasticity of demand. Section 4 concludes.
1. MODEL
1.1 Demand Functions
Preferences of a consumer are defined over a differentiated product q, which is defined by a continuum of varieties indexed by [omega] [member of] [OMEGA]. Varieties can be distinguished by a single attribute. We assume that all varieties can be represented by points on the circumference of a circle, with the circumference being of unit length.
Each point of the circumference represents a different variety. Each consumer has his most preferred type, which we call his "ideal" variety, and which we denote as [??]. It is ideal in the sense that given a choice between equal amounts of his ideal variety [??] and any other variety co consumer will always choose [??]. Moreover, utility is decreasing in distance from [??]: the further is the product from the ideal variety the less preferable it is for the consumer. These assumptions are usually incorporated in the formal model with a help of Lancaster's compensation function h([v.sub.[omega]], [??]), defined for [less than equal to] [v.sub.[omega]], [less than or equal to] 1. Lancaster's compensation function is defined such that the consumer is indifferent between q units of his ideal variety [??] and h([v.sub.[[omega], [??])q units of some other variety co, where [v.sub.[omega],[??]] is the shortest arc distance between [??] and [omega]. It is assumed that:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (1)
The subutility of variety co for consumer whose ideal variety is [??] is usually assumed to have the following separable form (e.g., Lancaster 1979, 1984, Helpman and Krugman 1985):
u([q.sub.[omega]], [omega] [??]) = [q.sub[omega]]/h([v.sub.[omega],[??]]).
The utility function, which includes all varieties [omega] [member of] [OMEGA], can then be formulated as
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (2)
The budget constraint is:
[[integral].sub.[omega][member of][OMEGA]] [q.sub.[omega]] [p.sub.[omega]] = I, (3)
where [p.sub.[omega]] are the prices of the varieties being produced and I is income. We can maximize the utility subject to the budget constraint, I, and given the prices of differentiated varieties, [p.sub.[omega]]. The solution to this problem is:
[q.sub.[omega]'] = I/[p.sub.[omega]'], [q.sub.[omega]] = for [omega] [not equal to] [omega]' ,
where [omega]' = arg min [[p.sub.[omega]]h([v.sub.[omega]], [??])|[omega] [member of][OMEGA]]. (4)
In (4), the utility-maximizing variety is independent of expenditures. For example, imagine that the consumer's ideal beverage is apple juice, the price of which is five times higher than the price of water: [p.sub.AJ] = 5[p.sub.W]. Equation (4) suggests that the consumer will buy I/[p.sub.W] units of water if 5 >h([v.sub.W,AJ]). This answer holds whether income allows him to buy five cups or 50 gallons of water.
Consider a more general formulation in which the strength of preference for the ideal variety depends on quantities consumed. Formally, we define a generalized compensation function, h([q.sub.[omega]], [v.sub.w],[??]; [gamma]), having the following properties:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (5)
h([q.sub.[omega]], 0; [gamma]) = 1, [h.sub.2] ([q.sub.[omega]], 0; [gamma]) = 0, (6)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (7)
h([q.sub.[omega]], [v.sub.[omega],[??]]; 0) = h([v.sub.[omega],[??]], (8)
where the parameter [gamma] [greater than or equal to] defines the degree to which the consumer is "finicky," or willing to forego consumption to get closer to the ideal.
The standard properties associated with the distance from the ideal variety are represented by (5) and (6). By (7) we assume that the consumer is not finicky at all at a zero consumption level, but when his consumption of a differentiated good increases he becomes increasingly finicky. Finally, (8) nests Lancaster's compensation function: if [gamma] = 0, the compensation function does not depend on consumption volumes. An additional condition needs to be introduced to address the fact that in the generalized compensation function, the quantity of the chosen variety appears both in the nominator and in the denominator of the subutility function (2). Consequently, while the quantity consumed increases, the cost of being distanced from the ideal variety might increase so fast that it outweighs utility gains from the higher consumption level of this variety. This would contradict the standard assumption of the nondecreasing (in quantity) utility function. It is easy to show that the necessary and sufficient condition for utility to be increasing in the quantity consumed is:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (9)
[FIGURE 1 OMITTED]
The difference between the Lancaster and generalized compensation functions is illustrated by Figure 1.
In order to derive a closed form solution of the model, we chose a specific functional form of the generalized compensation function:
h([q.sup.[gamma].sub.[omega]], [v.sub.[omega],[??]]) = 1 + [q.sup.[gamma].sub.[omega]] [v.sup.[beta].sub.[omega],[??]] [beta] > 1, [less than or equal to] [gamma] [less than or equal to] 1. (10)
It is easy to verify that the restrictions imposed on the parameters [beta] and [gamma] in (10) are necessary and sufficient for properties (5)-(9) to hold. The corresponding utility function is then
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (11)
Consumption of a differentiated variety [omega]' is found by maximizing the utility (11) subject to budget constraint (3):
q[omega]' = I/[p.sub.[omega]'], [q.sub.[omega]] = for [omega] [not equal to] [omega]'. (12)
where...
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