In monopolistic competition, each firm supplies a small part of the market this occurs because

4.1 The fourth wave of the increasing returns revolution in economics

The first monopolistic competition revolution was triggered by the works of Chamberlin [1933] and Robinson [1933], but its impact on mainstream economics has been rather small. Johnson [1967] writes that

… what is required at this stage [viz. after Chamberlin and Robinson's work on monopolistic competition] is to convert the theory from an analysis of the static equilibrium conditions of a monopolistically competitive industry…into an operationally relevant analytical tool capable of facilitating the quantification of those aspects of real-life competition so elegantly comprehended and analysed by Chamberlin but excluded by assumption from the mainstream of contemporary trade theory. [Johnson, 1967, p. 218]

For many economists the D-S model provides precisely that “operationally relevant analytical tool.” Its workability and analytical flexibility allows its application to a number of different areas of inquiry. Although the D-S model was originally conceived as a contribution to the literature on product differentiation, it was later applied to phenomena of international trade, growth, development and geography, all of which are taken to be the result of the presence of increasing returns. These new applications resulted in the development of “new trade theory” [Krugman, 1979; Dixit and Norman, 1980], “new growth theory” [Romer, 1987; Lucas, 1988; Grossman and Helpman, 1991] and GeoEcon. The impact of the “second monopolistic competition revolution” has therefore been much greater than that of its predecessor.

The application of the D-S model to phenomena of growth and trade largely follows a similar path. In both cases, the neoclassical variant was incapable of addressing some stylized facts and the presence of increasing returns was regarded as a possible explanation. Krugman describes the situation of trade theory around the 1970s as “a collection of highly disparate and messy approaches, standing both in contrast and in opposition to the impressive unity and clarity of the constantreturns, perfect competition trade theory” [Krugman, 1995, p. 1244]. It was thanks to the introduction of the D-S model that theories of growth and trade phenomena based on increasing returns became serious alternatives to the neoclassical ones. The result has been the development of new growth and new trade theory, which were treated as complementary to their neoclassical predecessors and in fact were later integrated with the latter.

The new trade theory enjoys a special role in the path towards unification of GeoEcon. In a sense, GeoEcon has developed out of a sequence of progressive extensions of new trade theory models. Witness the role of Paul Krugman as founding father of both new trade theory and GeoEcon. As observed by a commentator, “in stressing the relevance to regional issues of models derived from trade theory, Krugman has not so much created a new-subfield as extended the applicability of an old one” [Neary, 2001, p. 28]. Krugman [1979] shares with GeoEcon the presence of increasing returns and the D-S monopolistic competition framework, but it does not include transportation costs, an essential ingredient of the GeoEcon models. Krugman [1980], still a new trade theory model, includes transportation costs and differences in market size: together these assumptions imply that a country will produce those varieties for which the home demand is higher (market-size effect). In both Krugman [1979] and Krugman [1980] the distribution of economic activity is assumed to be even and fixed (agglomeration therefore cannot emerge). In a later work, Krugman and Venables [1990], uneven distribution of economic activity is introduced and thereby agglomeration can be shown to emerge. Yet, firms and factors of production are assumed to be immobile across countries, and differences in market size are given, not determined by the locational choices of the agents. It is the inclusion of factor mobility, which in turn endogenously determines market size, which generates the first GeoEcon model, namely Krugman [1991].

GeoEcon appears to provide a unified framework for the study of trade and location phenomena. Recent modeling efforts have also been made to integrate growth into the spatial models of GeoEcon. That geography is relevant for economic growth was clear before GeoEcon, and new growth models do allow for agglomeration of economic activity. Yet, differently from GeoEcon, “the role of location does not follow from the model itself and …it is stipulated either theoretically or empirically that a country's rate of technological progress depends on the location of that country” [Brakman et al., 2001, p. 52]. Instead, GeoEcon models of growth aim to make the role of geography endogenous.9 Not only is GeoEcon one of the fields partaking in the increasing returns revolution, but it can also be seen as its culmination, as it holds out the promise to unify the most prominent theories engendered by the revolution.

7.6.3 Heterogenization and Monopolistic Competition

The concept of monopolistic competition was introduced by Chamberlin in 1933 (Chamberlin, 1933), and in parallel by Robinson (Robinson, 1933). Observing market structures, he concluded that the available models of perfect competition and monopoly, respectively, were only incomplete approximations of real markets, where advertising and product differentiation played a significant role. Commonly observed market structures, rather, allow firms some degree of market power, without enjoying full or “pure” monopoly power, though. At the outset of his concept, thus, stand firms that can behave like monopolists in their particular market segments. They do, however, face competition from firms offering imperfect substitutes to their products—if price differences get too pronounced, customers will seek a variety that may be less suitable for their needs but that they are willing to except in exchange for the money saved in the purchase in comparison to the preferred option. The reasoning is that in order to avoid price competition that may reduce their profits, firms could divide markets and create market segments through product differentiation. As a result, they are assumed to face downward-sloping demand curves, albeit more elastic ones than a pure monopolist would. The basic reasoning applied to monopoly markets as explained earlier applies here as well—the degree of pricing power depends on the elasticity of substitution, as seen in the Amoroso–Robinson relation in Eq. (7.1).

More specifically, two separate demand curves are introduced to illustrate a company’s problem structure (see Figure 7.8). One gives a demand schedule for the situation in which all its competitors keep their prices constant, this is relatively elastic (dd). The other refers to a situation in which all firms set the same price. This one is assumed to be relatively inelastic (DD). Note that the reasoning corresponds to that of the kinked demand curve that Sweezy formulated. To the left of the intersection between the dd and DD curves, Sweezy’s kinked demand curve corresponds to the dd curve, to the right it corresponds to the DD curve.

As long as free entry is assumed, eventually a situation with many companies in the market realizing zero profit would result (see also the formalization of this setting at the end of this chapter). This connects the idea of a monopolistic component to the competitive market. If companies realize profits, more competitors enter the market. As companies face downward-sloping demand curves, the resulting price would in the end correspond to their average costs, i.e., zero profits per unit, while still lying above their marginal cost, though. The situation is reversed if the original setup is characterized by losses. In that case, firms leave the market until zero profits are realized.

If entry barriers can be erected, the companies in a market may be smaller in number, and we will observe an oligopoly with heterogeneous products (heterogeneous oligopoly). We will return to this point in Section 7.7. For a simple illustration of entry deterrence, see Box 7.2. Even though the market structure is described as monopolistically competitive, and continuing entry would eventually drive profits down to zero unless countermeasures were taken, such heterogeneous oligopolies, i.e., including barriers to entry, in fact appears closer to what Chamberlin (and Robinson and Sweezy as well) had in mind. The importance of product differentiation that he noted and the fact that real competition includes a number of nonprice variables (including such aspects as imperfect information regarding alternative products and specific product details on the customer side), which allow companies to create market niches in which they can exercise market power, point in this direction.

Box 7.2

A Simple Entry Deterrence Game—Illustration

The game with entry (entry deterrence fails) (incredible threat)

Incumbent I may play soft (S): He does not expand supply, thus no price deterioration. Thus, Entrant E has a chance to make profit after entry.

I may also play tough (T): He expands supply, thus price will decline (also at his own expense), with no profit opportunity for E.

The normal-form game resulting in the game matrix is shown in Figure 7.9.

The announcement of I to fight would be an incredible threat, given the incentive structure. One Nash equilibrium will result: E will enter.

As a three-stage game in extensive form (1.5 interactions, a pre- and a post-entry decision of the incumbent), this is depicted in Figure 7.10.

The game when entry deterrence succeeds (credible threat)

I now makes a credible threat through self-commitment: He makes a large investment in capacity (production, R&D, advertising) as sunk costs. Thus, it pays better for him to expand his production and sales, thus utilizing his extended capacities. Now T pays better, +Δ1, S yields −Δ1. The new normal form is shown in Figure 7.11.

Now T yields +1 (full capacity utilization), while S yields −1 for the incumbent. A new Nash equilibrium (still two Pareto optimal) results: The newcomer will not enter!

This is shown as a three-stage game with sunk costs and with entry deterrence in Figure 7.12.

An example of entry deterrence/defending one’s monopoly over time

Assume that T (a price war) takes place for 1 interaction only, at first (while E is already in). Thereafter, I decides on his permanent strategy, and E decides on staying in or exiting as shown in Figure 7.13.

How large must the monopoly profit b for I be at the minimum (bmin) in order to make him play T forever? (Assume δ=0.9.) (Note: Apply the single-shot solution as explained in Chapter 3. Use I’s T/in-payoff for the first interaction, then b for an infinite geometric series, then deduct b once for the first interaction.)

Solution key:

−15+b1−0.9−b>!101−0.9→Solve forb!

Alternatively, determine the discount factor δ (future expectation). How large must δ be at the minimum (δmin) for T to become the superior strategy for I, i.e., to make E exit? In other words, when does it pay for I to defend his monopoly position? (Assume b=12).

Solution key:

−15+121−δ−12>!→Solve forδ!

6.3.2.5 Does the model have adequate convexity?

It is well known that monopolistic competition models do not necessarily have a general equilibrium. Arrow and Hahn (1971) have shown, however, that in an economy with both perfectly competitive and monopolistically competitive sectors, a general equilibrium can be guaranteed if the perfectly competitive sectors have enough resources available to support the expansion of the imperfectly competitive sectors.24 Since we use models as a basis of policy discussions with governments who take assessments of industry output change seriously, we have a more binding constraint than the existence of an equilibrium – we must assure that the sector results are reasonable. For example, in a developmental stage of the model of Russia, we had a counterfactual equilibrium in which one sector essentially became the whole economy – an implausible result for a policy change such as WTO accession in an economy as diverse as the Russian. These issues imply that it is necessary to develop a model structure that limits potentially explosive expansions of the imperfectly competitive sectors. The following are four ways to introduce convexity in the model that we have employed in various applications. We have chosen to employ the first two in this model.

3.1. A monopolistically competitive firm selling a service

In virtually all characterizations of physicians in economics journals and textbooks, the physician is portrayed as having some market power. Monopolistic competition is a versatile structure for representing market power, and is the expressed favorite of many writers [Frech and Ginsburg (1975), Pauly and Satterthwaite (1981), McGuire (1983), Klevorick and McGuire (1987), Dranove (1988), Dranove and Satterthwaite (1991, 1992, 1999), Getzen (1984), Zuckerman and Holahan (1991), Pauly (1979, 1991), Phelps (1997), Frech (1996), Newhouse (1978), Folland et al. (1997), Gaynor (1994)]. Monopolistic competition includes an element of monopoly (downward-sloping demand) and an element of competition (large number of competitors – each firm ignoring strategic interactions). Because of location, specialty, quality, or some other element of taste, patients do not regard physicians as perfect substitutes. Information imperfections could also generate a monopolistically competitive structure. There may in fact be good substitutes for a given physician, but if the patient doesn't know who these are, the patient may be willing to pay more for the services of the familiar doctor, an idea proposed by Pauly and Satterthwaite (1981). For now, however, we will keep informational issues in the background and simply assume that the structure is monopolistically competitive because of recognizable differences among physicians.

A point in favor of monopolistic competition is that it is an appealing alternative to models that rely on collusion among physician to explain some observed patterns of price and quantity. Consider Fuchs’ (1974, p. 71) story of the “surgeon surplus:” “A comprehensive, detailed study of general surgeons in one suburban community in the New York metropolitan area revealed that the surgical workload of the typical surgeon was only about one-third of what experts deemed a reasonably full schedule.” Fuchs further characterized the market as follows: “For most types of surgery, the quantity physicians would like to supply at the going price is far greater than the quantity demanded.” How can this excess supply persist? Why does competition fail to reduce price and increase demand and workload? A conspiracy is the explanation that Kessel might have proposed. Surgeons might be colluding to keep prices high, to maximize their joint profits. But more plausibly, as Fuchs notes (p. 73), “Many surgeons believe, perhaps rightly, that demand would not increase appreciably in response to a price cut …,” in other words, each physician faces a downward-sloping demand. Collusion is not required to observe price above marginal cost and for there to be “excess supply.”14

The classic evidence for a monopolistically competitive structure is a demand curve with a negative slope [Haas-Wilson (1990), Klevorick and McGuire (1987), McCarthy (1985), McLean (1980)]. If the instrument for competing for patients is quality [Gaynor and Gertler (1995)] or even the aggressiveness in “inducing demand” [Dranove (1988)], evidence that such a decision variable influences demand supports the monopolistically competitive assumption. Many other empirical features of the market are also consistent with monopolistic competition. Studies of physician practice costs conclude that physicians operate on a downward-sloping portion of their average cost curve [PPRC (1992), Escarce and Pauly (1998)]. Firm-level advertising only pays if there is imperfect competition [Feldman and Begun (1978), Haas-Wilson (1986), Rizzo and Zeckhauser (1990)]. Wong (1996) found that physicians respond to factor price changes in a manner consistent with monopolistic competition.

The basic conception of the physician–patient relationship embodied by monopolistic competition is that physicians are imperfect substitutes in the eyes of patients. A patient has a demand for the services of a particular physician, as opposed to demand for “physicians’ services” in general. Although some observers have written about the “demise” of the physician–patient relationship [see Sloan et al. (1993, p. 51) for one discussion], surveys continue to show that a clear majority of patients have what they regard as a “regular source of care” [Moy et al. (1998)]. Even without a primary care provider, patients may rely on physicians to supervise their care during an episode of illness. The demand curve a patient has for a physician is not the same as the demand the patient has for physicians’ services, a distinction, despite the general enthusiasm for the monopolistically competitive structure that has not been given much attention in the literature.15 Many papers motivate their model with words associated with monopolistic competition, and then analyze a single firm.

Although interaction is not strategic in monopolistic competition, actions of one physician, such as a price change, affect demand for other physicians. In what follows, we present a model of monopolistic competition in which the physician has some market power but the patient has some alternatives. We will model the patient's alternatives as simply as possible in order to enable us to focus on the behavior of a representative physician.

Another important feature of the market will also be taken into account. Physicians sell a service; a diagnosis or treatment provided to one patient cannot be resold by that patient to some other customer. As Gaynor (1994, p. 224) observes in his review, “services are by their nature inherently heterogeneous and nonretradable.” The nonretradability of physician services has important implications for price discrimination and more generally for price and quantity setting. Farley (1986) called attention to the connection between non-retradability and price discrimination in physician markets, but the implications of nonretradability have not been fully appreciated in the context of physician markets.16

We can now proceed to set up a model of patients and physicians that we will build on throughout this chapter. The quantity of physician services is x. The patient benefits from services according to B(x), denoted in dollars. The marginal benefit function is b(x) = B′(x). b(0) > 0; b’(x) < 0. We employ a benefit function rather than a demand curve since profit maximization implies price-quantity pairs that may not be “on” the demand curve. The B(x) function captures any health shocks implicitly, so that B(0) may be negative. Time costs, inconvenience, and other costs and benefits of using medical care experienced by the individual are incorporated in B(x).17 By assuming that the benefit function depends only on the quantity of x, we abstract from the role of other goods, including income, influencing the valuation of services. Physician services are produced at constant cost per unit c.18 If p is the price of physician services (insurance will be introduced shortly), physician profit is π = px – cx, and patient net benefit can be written NB(x) = B(x) – px. Define x* as the solution to b(x) = c, the efficient level of x. Let NB* = B(x*) – cx*, the maximum possible patient net benefit. Also, for purposes of reference define xm, the level of x that maximizes B(x), or, the solution to b(xm) = 0. See Figure 2.19

In monopolistic competition, the patient has substitutes. In general, a patient could consume services of many physicians at the same time, and benefits from physicians’ services would be a function of the set of services consumed. We simplify this by forcing the patient to choose a physician from whom to receive care. With this interpretation, the benefit function used here is consistent with the idea of “residual demand” in models of imperfect competition and product differentiation. We will recognize that a market gives a patient alternatives, and say that if the patient leaves this physician, he can receive net benefit NB0 from an alternative physician. The patient then uses the current physician if and only if the net benefit he receives is no less than NB0. By altering NB0, this model includes perfect competition and monopoly as extremes. If NB0 = 0, the patient has no alternative to this physician and the physician is a monopolist. If NB0 = NB*, the market is perfectly competitive, and the physician has no market power. In general, 0 < NB0 < NB*.

The price and quantity of physician services are found by maximizing the physician's profit, subject to the constraint on patient net benefit imposed by competition with alternative physicians. We can set this up as a constrained maximization problem in Program I.

Program I:

(3.1)L=px−cx−λ(B(x)−px−NB0).

Maximizing L with respect to p, x, and λ, the first-order conditions (assuming an interior solution) for Program I are:

(3.3)Lx:p−x+λ(b( x)−p)=0,

The three first-order conditions can be solved sequentially for the three variables, λ, x and p. From (3.2), λ = 1, reflecting the fact that the seller gains all the surplus above NB0, and any relaxation of the surplus constraint goes to profits. Normally, one thinks that a two-part tariff is necessary for a seller to extract all the surplus, but here, both p and x are chosen by the physician, and two-part pricing is not required to extract surplus. Then, from (3.3), x is such that b(x) = c, or, as we have defined above, x is set efficiently, x = x*. Finally, rewriting (3.4) as (3.4'), price is determined so as to extract all surplus above NB0

Figure 3 illustrates the solution. NB0, a given, is equal to the lightly shaded region. The combination (p, x*) chosen by the doctor gives her profits (p – c)x* = NB(x*) – NB0, the entire available surplus. The doctor has only to match the surplus available elsewhere to keep the patient. Quantity is always x*, that which maximizes total surplus available. Note that the patient is not a price taker. At the price of p, the patient would prefer to consume fewer services than x* but nonretradability lets the doctor set quantity. One can think of the consumer surplus gained above NB0 by consuming up to the point where b(x) = p (the moderately shaded region in Figure 3) as just being offset by the consumer surplus lost from consuming beyond this point to x* (the dark region).20 In effect, the physician makes an all-or-nothing offer to the patient, extracting all available consumer surplus. This is not surprising, since with market power and the nonretradability feature, the physician possesses the prerequisites for the exercise of first-degree (or perfect) price discrimination [Varian (1989)].

In Kessel's world of the 1950s, physicians could set prices (and quantities) without contending with third-party regulations. Price discrimination across patients emerges naturally from the model in Program I. Consider different patients with different benefit functions. Suppose one patient has a higher willingness to pay indicated by a higher B(x). Equation (3.4′) tells us immediately that the higher willingness-to-pay patient will pay more for the same services. Nonretradability shelters the price discrimination. The poor paid less simply because they had a lower willingness to pay (not because they had a more elastic demand).

The model in Program I also features quantity setting by the physician. An immediate implication of profit maximization in monopolistic competition is that the physician takes advantage of the nonretradability of her services and sets both price and quantity. This quantity setting, according well with direct observation of patient–doctor interactions, emerges from the most simple model of the process of quantity determination, with (and this is worth emphasizing) perfectly rigid patient preferences not subject to manipulation by the physician. It is the first form of physician quantity setting previewed in Table 1.

Consider the effect of price regulation in this model. Suppose p is not under the control of the physician but is set by the payer. Program I could be solved again in this case dropping condition (3.2) and regarding price as fixed (one fewer unknown, one fewer equation). The net benefit constraint (3.4) still holds, and indeed, when price is fixed, it is (3.4) that can be solved for quantity, x. Note that (3.4) implies that:

In words, if price is fixed by the payer, a decrease in price will be cause an increase in quantity. The reason is straightforward. The physician need not give the patient any more than a fixed level of net benefit. If a payer restricts how much surplus a physician can extract by setting price, the physician can counter by extracting surplus by setting quantity higher. This yields the physician more surplus since price is fixed above cost. The patient accepts this because the price limitation increases surplus on the previously purchased units. Note that the implication of a negative derivative of quantity on price in (3.5) emerges from the very simplest model of physician quantity setting, without appeal to induced demand or target income motivation.

We now proceed to add some institutional elements to this simple model. Third-party payers insure patients against health care costs, reducing price paid by the patient at the time of service delivery to below cost. In the course of this, payers have found it necessary to constrain physicians’ ability to set prices by adopting fee schedules.

2.3.1 Trade Models with Heterogeneous Firms

In the early 1980s, new trade theory included heterogeneity in the trade model to explain the phenomenon of interindustry trade but the heterogeneity was mainly reflected in product differences and monopolistic competition and no attention was paid to the differences between firms in productivity. Therefore, it is assumed that firms in the same industry are symmetrical and at the same technological level, all firms have the same productivity level, and all other firms will also export if one firm exports. However, more and more empirical studies have proved that the symmetry assumption of new trade theory has major limitations. In the 1990s, a large number of empirical studies on firms showed that only some firms export products to other countries and exporting firms are better than nonexporting firms in terms of size and productivity.

Melitz (2003) combines the monopolistic competition model of new trade theory with the firm heterogeneity assumption and constructs a model of intraindustry dynamics with heterogeneous firms. The model builds the general-equilibrium monopolistic competition model with industry dynamics of Hopenhayn (1992), expands the trade model of Krugman (1980), and introduces firms’ differences in productivity. Melitz examines the relationship between international trade and intraindustry resource allocation and proves that firms with higher productivity take the initiative to enter the export market while firms with lower productivity are forced to exit from the market so that the productivity level of the entire industry is raised and that trade brings development opportunities for some firms and great challenges to others. The predictions made based on this model basically go with those of empirical studies so it is widely acknowledged that the research into firm heterogeneity and the basic framework of international trade and investment has great significance of theoretical foundation.5,6

Many theoretical models introduced after Melitz (2003) can well explain the relationship between heterogeneous firms and their internationalization moves. Building on the Melitz model, Helpman et al. (2004) include heterogeneous firms, export and FDI in the same analytical framework, construct a multicountry, multisector, general-equilibrium model to examine firms’ export and FDI activities, and prove that firms’ productivity difference is an important factor affecting their export and FDI. Yeaple (2005) attempts to explain the systematic differences between exporting and nonexporting firms and effectively explains why skill premium has been growing by connecting trade costs with firms’ decision-making in four aspects, that is, entry, technology, export, and worker type. Melitz and Ottaviano (2008) construct a variable markup model in analyzing the relations among market size, productivity, and trade, and prove that market size and trade will affect the intensity of competition and heterogeneous firms’ production decision. Bernard et al. (2007) successfully explain the causes of intraindustry trade and find factors that influence firms’ entry into the export market by introducing firm heterogeneity in a standard trade model. Helpman et al. (2007) create a theoretical model for analyzing MNCs’ choice of integration strategy by combining firm heterogeneity with two types of FDI (vertical FDI and horizontal FDI). Manova (2008) integrates credit constraint in the model of Melitz (2003) and finds that firms with higher productivity enjoy advantages in winning export credit support and firms in financially developed countries have easier access to the export market and export more products, particularly in sectors that rely on external financing.

2 The Baseline Model of Aggregate Supply

We start with a model of monopolistic competition in general equilibrium, which is now standard in the study of monetary policy.2

6.4 Monopolistic competition

6.4.1 Equilibrium of an imperfectly competitive company

Edward Chamberlin (1933) coined the term “monopolistic competition” to include all the market forms between perfect competition and monopoly. Joan Robinson (1933) preferred instead the expression “imperfect competition” for the same markets. The market structure in question has the following characteristics:

•

competition between companies, each of which ignores other companies' reactions to its own actions;

•

freedom of market entry and exit;

•

the goods produced by different companies are heterogeneous but perfectly interchangeable.

The first two characteristics show the competitive aspect of this market form; the third shows its monopolistic aspect. Indeed, due to product differentiation each company succeeds in winning over a market segment in which it can exercise some market power. It is thus a price-setter rather than a price-taker, as happens in perfect competition. However, its discretion in setting prices is not unlimited, as happens in a monopoly, since each company must always take into account the competition from close substitutes offered by rival companies.

It is now easy to derive the equilibrium conditions of a company in monopolistic competition.

Consider Fig. 6.2A regarding the price p and output y of the short-run equilibrium for a representative firm (R″ is the marginal revenue, ATC is the average total cost, y∗ and p∗ are the equilibrium output and price, and D is the demand curve for an individual company).

Fig. 6.2. Monopolistic competition: (A) short-run equilibrium; (B) long-run equilibrium.

The necessary condition for maximum profit is that R″ = C″, where the marginal revenue is less than the price, as in the case of a monopolist. In the case of Fig. 6.2A this condition is satisfied at y∗. Price p∗ corresponds to that quantity on the demand curve. In this situation the company earns an extra profit represented by the dashed area in Fig. 6.2A (recall that normal profit is already included in the ATC curve).

The presence of extra profits will attract new companies into the sector. This in turn will influence the revenue of companies already operating in it, for the obvious reason that each firm sells less at each price level when new brands are marketed; consequently, the demand curve for an individual company will shift to the left, as the same number of buyers must now be divided up among a higher number of companies. That will clearly reduce the extra profits of the existing companies. The process of new companies entering the market will continue until a company's expected demand curve becomes tangent to its average long-run cost curve. As shown in Fig. 6.2B, in this situation extra profits are zero since the price equals the average cost.

23.2.2 Krugman trade

Krugman (1980) proposed a trade model with monopolistic competition based on a Dixit and Stiglitz (1977) aggregation of firm-level varieties. Applying this model is an alternative method of dealing with the data challenges faced by Armington (1969). Intraindustry trade, for example, is a natural feature of the Krugman structure. As in the Armington structure, varieties are aggregated at constant elasticity of substitution, but we now need to track the number of firms in each region, Nkr and note that there is a scale effect associated with increases in variety. Firms are assumed to be relatively small, symmetric and produce under a simple linear increasing-returns technology. Furthermore, we assume that entry is costless so profits are driven to zero as the product space becomes saturated with varieties.

Let pkrs be the gross (of trade cost) price set by a region r firm selling in market s and let σk > 1 indicate the elasticity of substitution. The dual Dixit–Stiglitz price index in region s is then given by:

(23.6)Pks=[∑rNkrpkrs1−σk]1/(1−σk),

and the corresponding bilateral firm-level demands are given by:

(23.7)qkrs =Qks(Pkspkrs )σk.

Note that qkrs is the (net) import quantity delivered to s by a firm from region r. Under the iceberg cost assumption the supporting export quantity is τkrsqkrs.

Firms are assumed small enough such that their pricing decisions have negligible impacts on the Pks, but they do have market power over their unique variety. Faced with constant elasticity demand (where Pks is assumed constant) firms maximize profits by charging their optimal markup over marginal cost:

(23.8)pkrs=τkrsckr1−1/σk,

where the marginal cost of delivering product on the r–s link is τkrsckr. This is consistent with our definition of pkrs as gross of trade costs. In addition to marginal cost, firms incur a fixed cost, denoted fk (measured in composite input units). The free-entry assumption indicates that the number of firms will adjusts such that nominal fixed-cost payments equal profits:

(23.9) ckrfk=∑spkrsqkrsσk.

With the industrial organization well specified we proceed with a condition for market clearance for the composite input:

(23.10)Yk r=Nkr(fk+∑sτkrs qkrs).

Again the τkrs term must be included to reflect the real resource cost of delivering qkrs units in the foreign market. Combining the downstream demand equation (23.1) and the upstream supply equation (23.2) with the Krugman-specific equations (23.6)–(23.10) we have a square system of dimension [(5×R×K)+(2×R×R×K)]. The partial equilibrium Krugman trade equilibrium is fully specified. To illustrate the operation of the trade equilibrium in a numeric setting we provide the GAMS code in Section A.2 of the Appendix.

3.1 The market structure problem

In his review of Chamberlin's (1933) book, Kaldor (1935) claims that a firm affects the sales of its neighboring firms, but not distant ones. The impact of its price reduction is, therefore, not symmetric across all locations. In other words, there are good reasons to believe that competition across locations is inherently oligopolistic [Eaton and Lipsey (1977), Gabszewicz and Thisse (1986)]. Unfortunately, models of spatial competition are plagued by the frequent nonexistence of an equilibrium in pure strategies [Gabszewicz and Thisse (1992)]. Thus, research has faced a modeling trade-off: to appeal to mixed strategies, or to use monopolistic competition in which interactions between firms are weak. For the sake of simplicity, Krugman and most of the economics profession have retained the second option, which is not unreasonable once we address spatial issues at a macro-level. In addition, models of monopolistic competition have shown a rare ability to deal with a large variety of issues related to economic geography, which are otherwise unsatisfactorily treated by the competitive paradigm [Matsuyama (1995)]. However, it should be kept in mind that spatial competition should not be missed at the micro-level.

In the Dixit and Stiglitz (1977) setting, monopolistic competition emerges as a market structure determined by consumers’ heterogeneous tastes and firms’ fixed requirements for limited productive resources. On the demand side, the set of consumers with different tastes are aggregated into a representative consumer whose preferences exhibit love for variety: her utility is an increasing function not only of the amount of each variety of a horizontally differentiated good, but also of the total number of varieties available.15 On the supply side, production exhibits economies of scale within varieties but no economies of scope across varieties, thus implying a one-to-one relationship between firms and varieties. Consequently, each firm supplies one and only one variety (monopolistic). However, there are no entry or exit barriers so that prices are just enough to cover average cost (competition). Finally, firms are so many that they do not interact directly but only indirectly through aggregate demand effects. Formally, we assume that there is a continuum of firms.

The continuum approach does not imply the absence of interactions among firms. Indeed, each firm must figure out what will be the total output (or, alternatively, the average price index) in equilibrium when choosing its own quantity or price, or when deciding whether to enter the market. This is not what we encounter in a differentiated oligopolistic market when individual decisions made by competitors are needed by each firm. Here, we have a setting in which each firm must know only a global statistics about the market but not its details. We believe that using a statistics of the market is a particularly appealing way to capture the idea of monopolistic competition because it saves the essence of competition by forcing each firm to account for the aggregate behavior of its competitors.

Furthermore, the continuum assumption is probably the most natural way to capture Chamberlin's intuition regarding the working of a ‘large group’ industry, while allowing us to get rid of the ‘integer problem’ which often leads to inelegant results and cumbersome developments. Note also that, unlike oligopoly theory, which is plagued by the differences between the Bertrand and Cournot settings, the distinction between price competition and quantity competition becomes immaterial in monopolistic competition. Indeed, being negligible to the market, each firm behaves as a monopolist on the residual demand, which makes it indifferent between using price or quantity as a strategy. Last, this modeling strategy allows one to respect the indivisibility of an agent's location (her ‘address’) while avoiding to appeal to the existence of strong nonconvexities associated with large agents. At the same time, it leads to a description of the regional shares of economic and demographic magnitudes by means of continuous variables.

Although we consider only specific models of monopolistic competition such as the CES and the linear models, we expect the results obtained in these two different settings to be representative of general tendencies.

3.1 Measuring access to markets

We employ the Dixit–Stiglitz–Krugman model of monopolistic competition and trade in a multi-region setting. Let μiYi denote expenditures by region i on the representative industry. In theoretical models it is standard to make industry-level expenditure be exogenous by assuming an upper-level utility function that is Cobb–Douglas with expenditure parameter μi, thus giving rise to fixed expenditure shares out of income, Yi. The sub-utility is a constant elasticity of substitution (CES) aggregate of differentiated varieties produced in the considered industry, with σ representing an inverse index of product differentiation.4 In this model, σ plays several “roles”, being in particular an inverse measure of the markup and available economies of scale. This parsimony is useful in theory but dangerous in applications.

The amount spent by consumers from region i for a representative variety produced in region j is given by

(1)pijq ij=pij1−σ∑knkpik1−σμiYi,

where pij is the delivered price faced by consumers in i for products from j. It is the product of the mill price pj and the ad valorem trade cost, τij, paid by consumers. Trade costs include all transaction costs associated with moving goods across space and national borders. We can see from (1) that trade costs influence demand more when there is a high elasticity of substitution, σ. Indeed many results in Dixit–Stiglitz-based models depend on the term φij≡τij1−σ, that Baldwin et al. (2003) punningly refers to as the “phi-ness” of trade.

The total value of imports (including trade costs) from all nj firms based in region j will be denoted mij:

(2)mij=njpijqij=njpj1−σφijμiYiPiσ−1,

where Pi=( ∑knkpk1−σφik)1/(1−σ). Fujita, Krugman and Venables (1999) refer to Pi as the “price index” in each location. It is a generalized mean of the delivered costs of all the suppliers to location i that assigns increasing weight to sources that have a large number of suppliers, nk, or good access to market i, measured by a high φik. Thus a location that is served by a large number of nearby and low-price sources will have a low Pi and will therefore be a market where it is difficult to obtain a high market share.

Equation (2) can be manipulated to obtain an estimate of φij. First, divide mij by mii, the region i's imports from itself. The μiYiPiσ−1 cancel since they apply to i's imports from all sources. The remaining expressions involve relative numbers of firms and relative costs in i and j. These ratios can be eliminated by multiplying by the corresponding ratio for region j: mji/mjj. The result is

(3)mijmjimiimij=φijφjiφiiφjj.

The standard practice in NEG models is to assume free trade within regions, i.e., φii = φjj = 1 and symmetric bilateral barriers φji = φij. These assumptions lead to a very simple estimator for φij:

(4)φˆij=mijmjimiimjj.

The numerator requires only trade flow data expressed according to industry classifications. The denominator factors are each region's “imports from self” (or, equivalently, “exports to self”). They are calculated as the value of all shipments of the industry minus the sum of shipments to all other regions (exports).

It therefore is fairly easy to give a feeling of the extent of current trade freeness among the biggest industrialized countries for which bilateral trade flows and production figures are readily available. We use here the database recently made available by the World Bank5 combined with the OECD STAN database (the Appendix gives details about this data) in order to calculate values of trade flows and φij for distinctive pairs of countries in 1999. We opt for the United States–Canada and France–Germany as our pairs of countries.

Recalling that 0<φˆij<1 with 0 denoting prohibitive trade costs, the overall level of trade costs in Table 1 seems to be very high. We can obtain from φˆ an estimate of the ad valorem equivalent of all impediments to trade between the United States and Canada. The calculation requires an estimate of the price elasticity σ. Using the lowest Head and Ries (2001) estimate of σ for U.S.–Canada trade in manufactured goods (8), trade costs have an ad valorem equivalent ranging from τ – 1 = 0.717−1/7 – 1 = 4.9% for Canada–U.S. auto trade to just over 36% for Canada–U.S. trade in clothing and Germany–France trade in autos. With the exception of North American auto trade, the level of trade freeness appears to be quite low, even though we have chosen pairs of countries known for their high levels of formal trade integration.

Table 1. The ϕ-ness of trade in 1999 for North America and Europe, selected industries, import values in millions of US$

The starkest predictions of NEG models deal with the possibly dramatic consequences of trade liberalization on agglomeration. It is often assumed that we live in an era of trade integration and that would here translate into a trend of rising φˆ over time. Do we actually observe this trend in the φˆ data?

We consider, in Figure 1, the evolution of trade freeness for three distinctive country pairs. We can indeed see that international trade is getting easier over the recent period. The rate of progress is not the same for all country pairs, with North America being the fastest integrating region since the end of the eighties. The pace of trade integration also seems to be more important since the late eighties in the European Union, as can be seen from the France–Italy combination for which a longer time period is available.6 It is noteworthy that the change in the pace of integration for the median industry seems to correspond in both regions to the starting date of implementation of a major trade liberalization agreement (the U.S.–Canada Free Trade Agreement in January 1989 and the Single European Act in January 1987). This observed rise in φˆ is a sort of pre-requisite for any test of the main predictions of NEG models: although remaining at surprisingly low levels, the integration of the world economy is rising, which corresponds to the typical thought experiment of NEG theoretical predictions.