Market Expansion in Duopoly∗ Andrei Hagiu1 and Wei Sun2 August 30, 2016 Abstract We study the eect of market expansion due to exogenous factors on a duopoly's equilibrium prices and prots. The total eect on each rm's prots consists of a direct eect, proportional to the demand derived from the new market segment, and a competitive eect, proportional to the change in the rival rm's equilibrium price. We show that the sign of the total eect on prots depends only on rst-order and second-order demand elasticities, and on the ratio between how important the new market segment is relative to the existing segments for the two rms. In particular, this sign can be independent of the magnitude of the (positive) direct eect. The total eect on each rm's price consists of a non-strategic eect (the adjustment induced by the demand from the new market segment) and a strategic eect (the response to the price adjustment by the rival rm). Due to the strategic eect, market expansion to a more price elastic segment for both rms can lead to a higher equilibrium price for one rm. We also derive implications for empirical estimations of the eects of market expansion. JEL classication: L13, M21 Keywords: market expansion, duopoly. ∗We thank Julian Wright and seminar participants at the National University of Singapore for their helpful comments. 1 MIT Sloan School Of Management, Cambridge MA 02142, [email protected] 2 Harvard Business School, Boston, MA 02163, [email protected] 1 1 Introduction Oligopolies can see their relevant markets expand unexpectedly due to exogenous factors, such as decreases in the price (or increases in the quality) of an underlying platform or a complementary technology, the appearance of new information or cultural trends that change customer perceptions, etc. For example, as videogames gradually entered the cultural mainstream, the addressable market for makers of home videogame consoles (Microsoft, Nintendo, Sega, Sony) expanded from teenage boys in the late 1980s, to older males throughout the 1990s, and nally to just about everyone else after the release of the Nintendo Wii in 2005. Similarly, the cloud infrastructure and computing services oered by Amazon, Google, IBM and Microsoft initially only appealed to start-ups and small companies. Due to the emergence of virtualization and other complementary technologies that helped alleviate security and reliability concerns for cloud services, the relevant market has signicantly expanded to also include large corporations. What is the eect on rm prots of an exogenous market expansion in the absence of new entry? Whereas market expansion always increases monopoly prots, the eect on oligopoly prots can go either way. At a high level, market expansion has both a direct eect and a competitive eect on each rm's prot. The direct eect is always positive (more customers to sell to), while the competitive eect is negative (respectively, positive) if the competitor's new equilibrium price is lower (respectively, higher). If the competitive eect is negative and outweighs the direct eect, market expansion decreases equilibrium protswe derive precise conditions under which this occurs. Although we focus on a competitive duopoly, our formal analysis and insights also apply when the two rms are complementors (e.g. Microsoft and Intel in the market for personal computers). In our model, there is a (continuous) set of existing market segments and we conceptualize market expansion as the addition of a new (innitesimal) market segment. In this set-up, whether market expansion increases or decreases equilibrium prices and prots depends only on the rst- order and second-order demand elasticities, and on the ratio between how important the new market segment is relative to the existing segments for the two rms. An important and novel result of our analysis is that the sign of the total eect on prots can be independent of the 2 magnitude of the direct eect, which is proportional to the size of the new market segment and is always positive. For instance, for two symmetric rms, the size of the new market segment has no bearing on whether market expansion decreases or increases equilibrium prots. In fact, if the sign of the prot change is negative, then increasing the new market segment's size exacerbates the negative impact on prots. Market expansion can also have a counter-intuitive total eect on equilibrium prices. On the one hand, if the new market segment is more price elastic for the two rms, then, assuming no price discrimination, each rm is inclined to decrease its price for the entire marketthis is the non-strategic eect. However, there is also a strategic eect: each rm's price decrease aects the competitor's demand elasticity, prompting the competitor to further adjust its pricedownward if the two prices are strategic complements, and upward if they are strategic substitutes. Thus, if the prices exhibit suciently strong strategic substitutability, the strategic eect may overturn the non-strategic eect, leading to a counter-intuitive result for one of the two rms, i.e. market expansion to a more price elastic segment leads to a price increase. Our analysis has important implications for empirical studies. In particular, both rst-order and second-order price elasticities must be accurately estimated for the existing market in order to correctly predict the sign of the total eects of market expansion on prices and prots. Furthermore, we show that dierent sources of consumer heterogeneity aect the outcome dierently. Thus, empirical models that accomodate only one type of consumer heterogeneity can yield qualitatively wrong preditions regarding the eect of market expansion. The next section discusses the related literature. Section 3 sets up our model and derives the expressions for the total eects of market expansion on equilibrium prices and prots. To build intuition for interpreting these expressions, Section 4 analyzes and interprets a simpler version of our model, by shutting down the strategic eect. Section 5 returns to the full equilibrium, interprets the expressions obtained in Section 3, and derives additional results. Section 6 briey shows that our analysis also applies to complementors. Section 7 illustrates our main results with simple examples based on linear demand. Section 8 discusses the implications of our theoretical analysis for empirical estimations. Finally, Section 9 concludes. 3 2 Related literature The idea that seemingly benecial exogenous shocks (i.e. those that would unambiguously raise prots for a monopoly rm) may decrease the equilibrium prots of oligopoly rms even in the absence of entry dates back to at least Bulow et al. (1985). Specically, Bulow et al. (1985) showed that an exogenous cost decrease in one market for a rm that benets from economies of scale across two markets can hurt that rm's overall protability if it induces a suciently aggressive competitive response by its rival in the second market. This counter-intuitive phenomenon can only occur if the strategic eecti.e. the change in prots due to the induced change in the choice of strategic variable (price or quantity) by the competitor in the second marketis negative and outweighs the positive direct eect of the cost decrease in the rst market. The sign of the strategic eect is determined by whether the two rms' products are strategic complements or substitutes. In contrast, a key contribution of our analysis is to show that the strategic eect is not essential for obtaining the counter-intuitive result that market expansion can decrease equilibrium prots. The reason is that the exogenous shock in our framework (market expansion) aects both rms directly. This implies that both rms experience a direct eect and a competitive eect, the latter of which can be further decomposed in a strategic eect and a non-strategic eect. The non-strategic eect can deliver the counter-intuitive result on its own. Meanwhile, in Bulow et al. (1985) the exogenous shock is unilateral, i.e. only one rm experiences a direct eect. This implies that the competitive eect is reduced to the strategic eect, which then becomes crucial to the result. Furthermore, Bulow et al. (1985) informally suggest that for the cost decrease to lower total prots, the (positive) direct eect has to be small relative to the strategic eect.3 By contrast, we completely characterize the necessary and sucient conditions for market expansion to lower prots and show that in our framework, the sign of the total eect of market expansion on prots can be independent of the magnitude of the (positive) direct eect. In particular, it is possible that increasing the magnitude of the direct eect exacerbates the negative total eect. Also related is Seade (1985), who shows that in an oligopolistic setting with no entry, an increase in marginal cost common to all competitors (e.g. tax increase) can sometimes lead to higher prot 3 Specically, sales in the market where the focal rm experiences the cost decrease must be suciently small relative to sales in the oligopolistic market. 4 for all competitors. While in this set-up all rms face a direct eect, a non-strategic competitive eect and a strategic competitive eect, the mechanism with cost shocks is quite dierent from the one with market expansion that we study. Furthermore, Seade (1985) relies on a Cournot quantity competition model, whereas we use a general Bertrand competition model, which yields more tractable conditions and is easier to interpret. Finally, at a high level, our paper is also reminiscent of an earlier literature, which points out that increased competition in an oligopolistic setting (i.e. a higher number of competitors), can result in higher equilibrium pricessee, for example, Salop (1979), Satterthwaite (1979), Rosenthal (1980). We obtain a somewhat similar result, namely that market expansion to a more elastic segment can result in a price increase for one of the competitors, but the underlying mechanisms are very dierent.