Cartel sustainability with vertical product differentiation: Price versus quantity competition

In the context of a vertically differentiated duopoly, we analyse the influence of the degree of differentiation on cartel sustainability, under both price and quantity competition. We find that, under both Bertrand and Cournot competition, the effect of vertical product differentiation on sustainability of the collusive equilibrium is unclear. It is shown that, given a degree of differentiation, price collusion is more sustainable than quantity collusion.     

Price and quantity competition under free entry

This paper complements that of Cellini et al. (Cellini, R., Lambertini, L., Ottaviano, G. I. P., 2004. Welfare in a differentiated oligopoly with free entry: A cautionary note. Research in Economics, 58:125–33.), which shows that Cournot competition may generate higher welfare compared to Bertrand competition in an economy with free entry. Unlike them, we provide a more general proof for this result and show that Cournot competition generates higher welfare compared to Bertrand competition when the products are sufficiently differentiated. If the products are close substitutes, welfare is higher under Bertrand competition. We show that these qualitative results hold whether or not number of varieties increases market size. We also show when the active firms earn higher profits under Bertrand competition compared to Cournot competition.     

Corporate social responsibility,vertical product differentiation and international competition

Would a foreign firm’s consumer‐oriented corporate social responsibility (CSR) activities be rewarded by an importing country’s voluntary tariff reduction? The current paper addresses this question in an import‐competing duopoly model with vertical product differentiation. It is shown that the tariff will decrease if the foreign firm switches from a purely profit‐driven firm to a CSR firm. A consumer‐oriented CSR strategy will always hurt the domestic firm’s profit, whereas the relationship between the foreign firm’s profit and CSR sensitivity (the degree to which a firm cares about consumer welfare) is invertedly U‐shaped. When firms’ decisions to switch to CSR are endogeneized, only the foreign firm will become a CSR firm.     

Nonexclusionary input prices under quantity competition: vertical integration,foreclosure and sabotage

A vertically integrated provider is a monopoly supplier of an input essential for its rival to produce downstream output. Market exclusion in the form of inefficient foreclosure or sabotage can arise when input prices are, respectively, ‘too high’ or ‘too low’ relative to the downstream price. The range of nonexclusionary input prices within which neither form of market exclusion arises is determined by displacement ratios. The safe harbour range of downstream-to-upstream ‘price-cost’ margin ratios is decreasing in the degree of product homogeneity and approaches a single ratio in the limit as the products become perfectly homogeneous. The bounds of nonexclusionary input prices are markedly wider under Bertrand–Nash competition than they are under Stackelberg competition.     

Price versus quantity in a duopoly of vertical differentiation with loss-averse consumers

In a model à la Mussa and Rosen (1978) in which consumers are loss-averse, I check the robustness of the result obtained by Tanaka (2001). As he did, I find that the quantity contract is a dominant strategy for both firms. Thus, Cournot is the outcome in equilibrium. Finally, I find that loss aversion in general intensifies competition.     

Monopolistic third-degree price discrimination under vertical product differentiation

This paper shows in a vertical product differentiation model with variable costs of quality that monopolistic third-degree price discrimination always reduces welfare regardless of whether the quality is fixed or is endogenous. The results provide rich implications for antitrust policy.     

Profitability of price and quantity strategies in a duopoly with vertical product differentiation

Using a model according to Mussa and Rosen (1978) and Bonanno and Haworth (1998) we consider a sub-game perfect equilibrium of a two-stage game in a duopolistic industry in which the products of the firms are vertically differentiated. In the industry, there are a high quality firm and a low quality firm. In the first stage of the game, the firms choose their strategic variables, price or quantity. In the second stage, they determine the levels of their strategic variables. We will show that, under an assumption about distribution of consumers' preference, we obtain the result that is similar to Singh and Vives (1984)' proposition (their Proposition 3) in the case of substitutes with nonlinear demand functions. That is, in the first stage of the game, a quantity strategy dominates a price strategy for both firms. Received: April 23, 1999; revised version: May 31, 2000     

Innovation,licensing, and price vs. quantity competition

In this paper, we develop a differentiated duopoly model with endogenous cost-reducing R&D and review the argument on welfare effect of price and quantity competition in the presence of technology licensing. We show that, with licensing, the standard conclusion on duopoly (Singh and Vives, 1984) is completely reversed. Cournot competition induces lower R&D investment than Bertrand competition does. Moreover, Cournot competition leads to lower prices, lower industry profit, higher consumer surplus and higher social welfare than Bertrand competition.     

Two-sided competition with vertical differentiation

This paper studies duopoly in which two-sided platforms compete in differentiated products in a two-sided market. Direct competition on both sides leads to results that depart from much of the current literature. Under some conditions the unique equilibrium in pure strategies can be computed. It features discounts on one side and muted differentiation as the cross-market externality intensifies competition. Less standard, that equilibrium fails to exist when the externality is too powerful (that side becomes too lucrative). A mixed-strategy equilibrium always exists and is characterized. These results are robust to variations in the extensive form. The model may find applications in the media, internet trading platforms, search engine competition, social media or even health insurance (HMO/PPO).     

Licensing cost-reducing innovations under supply function competition

In this paper, we study the licensing of cost-reducing innovations in a duopoly under supply function competition. We show that the innovator prefers fixed-fee licensing to no licensing if its cost advantage is not extremely large. Moreover, if its cost advantage is not extremely small, the innovator prefers fixed-fee licensing and mixed licensing to revenue-royalty licensing. This second result arises only because of our assumption that the cost functions are quadratic. We show that if the cost functions are linear and royalty payments are per unit of output, the innovator strictly prefers royalty licensing to fixed-fee licensing. We also show that in our model, consumer surplus is remarkably higher under any type of licensing than under no licensing. However, revenue-royalty licensing is slightly superior for consumers to the other two types of licensing and only so if the cost advantage of the innovator is sufficiently large.     

Perfect competition and optimal product differentiation

This paper considers whether a competitive economy will achieve an optimal allocation when firms produce differentiated products.In the model studied, firms market those products which maximize profit given the demand curves facing them. Markets are assumed to be open only for goods actually traded. Competitive conditions are achieved by replicating the consumer sector. It is shown that market equilibrium may be suboptimal if those products not being produced are highly complementary in consumption. Sufficient conditions on preferences and production sets for the market equilibrium to be optimal are given.     

Price normalization under imperfect competition

In general equilibrium models of imperfect competition the equilibria depend on how prices are normalized. This note shows that a price normalization preserves convexity properties if and only if prices are measured in terms of a fixed commodity bundle. I am grateful to an anonymous referee for helpful comments, inspiring a simplification in the proof of the main result, and the argument in the Remark.     

Remarks on good vs. bad characteristics in vertical differentiation

In a recent paper, Garella and Lambertini [Economic Letters 65 (1999) 245] claim that we should distinguish between good and bad characteristics in analysing the incentives for a duopoly to vertically differentiate their products. We prove here that the results obtained by the authors are false and we show that in the context of their model, maximum differentiation should appear whether characteristic is good or bad.     

Profits and competition under alternative technologies in a unionized duopoly with product differentiation

This paper aims at investigating if the conventional wisdom (i.e. an increase of competition linked to a decrease in the degree of product differentiation always reduces firms׳ profits) can be reversed in a unionized duopoly model. We show that a decrease in the degree of product differentiation may affect wages, hence profits, differently, depending on both the firms׳ production technology and the mode of competition in the product market. Specifically, under constant returns to labour, the “reversal result” can apply under both Cournot and Bertrand competition, but it is more likely when firms compete in quantities. By contrast, under decreasing returns, profits can increase with competition but only if firms compete in prices.     

Price vs quantity in a duopoly supergame with Nash punishments

We examine the endogenous choice between price and quantity behaviour in a duopoly supergame with product differentiation. We find that (i) if cartel profits are evenly split between firms, then only symmetric equilibria s obtained; (i) if instead the additional profits available through collusion are split according to the Nash bargaining solution, there are parameter regions where all subgame perfect equilibria are asymmetric, with firms colluding in price–quantity supergames.     

Price competition and quality differentiation with multiproduct firms

This paper examines a two-stage competition where firms simultaneously choose the number of products and qualities in the first stage, and then compete in prices. It is shown that a monopolist must sell a single product. In addition, in any equilibrium of multiproduct duopoly, there are segmented patterns of quality differentiation. Entangled configurations never emerge because each firm has an incentive to reduce the number of products facing direct competition with its rival. This result contrasts sharply with the equilibrium of non-segmented quality differentiation when firms compete in quantities. Furthermore, we find that the high-quality firm never offers more products than the low-quality firm, and quality differentiation between firms is greater than that within a firm.     

Quantity competition vs. price competition under optimal subsidy in a mixed oligopoly

This paper reconsiders the literature on the irrelevance of privatization in mixed markets within which both quantity and price competition are investigated under product differentiation. By allowing for partially privatization of a state-controlled firm, we explore competition under different timings of firms' moves and derive the conditions under which an optimal subsidy allows to achieve maximum efficiency. We show that, irrespective of the mode of competition, while the ownership of the controlled firm is irrelevant when firms play simultaneously, it matters when firms compete sequentially, requiring the leader to be publicly-owned for an optimal subsidy to restore the first-best. The paper also focuses on the extent to which a subsidy is needed to attain the social optimum in the considered scenarios, providing an ordering which highlights the subsidy equivalence between Cournot (Bertrand) private leadership and simultaneous Bertrand (Cournot) under duopoly, and the dominance of the former in oligopoly.     

Complementarity of willingness to pay and cost heterogeneity under vertical product differentiation: A welfare analysis

Due to the fact that a consumer’s willingness to pay differs between segments, many unregulated industries are price constrained, although the specific costs of market segments also differ. If the product quality is endogenously chosen, we find that third-degree price discrimination increases welfare if a sufficiently pronounced complementarity between the willingness to pay and variable cost heterogeneity is given. This is due to the fact that the monopolist’s incentive for employing a pronounced price dispersion strategy is directly influenced by the consumers’ willingness to pay for the quality of a product. With endogenous product quality, the paper shows that the standard welfare result of third-degree price discrimination compared to uniform monopoly pricing (e.g. that total welfare and consumer surplus both fall if total output does not rise) can be only reversed given the complementarity is sufficiently pronounced.     

Price equilibrium in address models of product differentiation: unit-elastic demand

Summary. I present a class of address models of product differentiation with unit-elastic individual demand and show the existence of Nash equilibrium in prices under assumptions on utility functions and the taste and income heterogeneity across consumers. This paper complements the work by Caplin and Nalebuff (1991, Econometrica), who analyze unit demand models of product differentiation. Received: December 28, 1998; revised version: September 5, 2001