Multiproduct Oligopoly and Bertrand Supertraps

We study oligopoly price competition between multiproduct firms, firms whose products interact in the pro¯t function. Specifically, we focus on the impact of intra firm product interactions on the level of equilibrium prices and pro¯ts. This impact is divided into two effects: a direct effect and a strategic effect (i.e., through the competitors' actions). We derive conditions such that, if intra-firm product interactions cause prices to decrease (increase) while holding competitors' prices fixed, then the strategic effect hurts (benefits) the ¯rm. We also show that, under reasonable general assumptions, the strategic effect more than outweighs the direct effect, so that equilibrium pro¯ts vary in the direction opposite of the direct effect (Bertrand supertrap). Several instances of Bertrand supertraps are developed. For example, stronger demand complementarity or economies of scope lead to tougher price competition to an extent that may decrease profitability (even when the direct profit effect is positive). We present a number of applications of the general results, including learning curves, network effects, systems competition, bundling, switching costs, and internet cross-referencing

Multiproduct Oligopoly and Bertrand Supertraps

We study oligopoly price competition between multiproduct firms, firms whose products interact in the pro¯t function. Specifically, we focus on the impact of intra firm product interactions on the level of equilibrium prices and pro¯ts. This impact is divided into two effects: a direct effect and a strategic effect (i.e., through the competitors' actions). We derive conditions such that, if intra-firm product interactions cause prices to decrease (increase) while holding competitors' prices fixed, then the strategic effect hurts (benefits) the ¯rm. We also show that, under reasonable general assumptions, the strategic effect more than outweighs the direct effect, so that equilibrium pro¯ts vary in the direction opposite of the direct effect (Bertrand supertrap). Several instances of Bertrand supertraps are developed. For example, stronger demand complementarity or economies of scope lead to tougher price competition to an extent that may decrease profitability (even when the direct profit effect is positive). We present a number of applications of the general results, including learning curves, network effects, systems competition, bundling, switching costs, and internet cross-referencing

Oligopoly Dynamics

The present notes summarise the oligopoly dynamics lectures professor Lu\'is Cabral gave at the Bank of Portugal in September and October 2017. The lectures discuss a set industrial organisation problems in a dynamic environment, namely learning by doing, switching costs, price wars, networks and platforms, and ladder models of innovation. Methodologically, the materials cover analytical solutions of known points (e.g., $\delta = 0$), the discussion of firms' strategies based on intuitions derived directly from their value functions with no model solving, and the combination of analytical and numerical procedures to reach model solutions. State space analysis is done for both continuous and discrete cases. All errors are my own

Why Are Firms Sometimes Unwilling to Reduce Costs?

This paper establishes three new results for multiproduct oligopolies: 1) it presents the first explicit expression of Nash equilibria for asymmetric multiproduct oligopolies; 2) it shows that reducing a multiproduct firms cost in Bertrand oligopolies will reduce its profits if the cost-reducing unit is sufficiently small; and 3) it demonstrates that a multiproduct firm has no incentive to eliminate a product whose sales are zero. Because a single-product firm whose sales are zero is indifferent between exiting and staying, and its cost reductions always increase its profits, our results are unique to the multiproduct firm, and they suggest that extending oligopoly studies from a single product to multi-products could be as significant as the extension of calculus from a single variable to multi-variables.Effect of cost reduction, multiproduct oligopoly, price competition, quantity competition

Aftermarket Power and Basic Market Competition

I revisit the relation between aftermarket power and basic market competition. I consider an infinite period model with overlapping consumers: in each period, one consumer is born and joins one of the existing installed bases, then aftermarket payoffs are received by sellers and consumers, then finally one consumer dies. I derive the unique symmetric Markov equilibrium of this game and the resulting stationary distribution over states (each firm’s installed base). I show that an increase in aftermarket power increases the extent of increasing dominance (i.e., a large firm is increasingly more likely to capture a new consumer than a small firm). This in turn leads to several implications of aftermarket power. First, the stationary distribution places greater weight on asymmetric states. Second, social welfare is greater. Third, under some conditions consumer welfare is also greater. Fourth, the value of a firm with zero installed base is lower, and so barriers to entry are higher

Exchange-rate exposure in a “Rule of Three” Model

We examine exchange-rate exposure in an international Bertrand model of differentiated goods using a “Rule of Three” (RoT) market structure that allows both within and between countries competition. We construct two versions of our model, a static and a dynamic one. In the latter, we explore how the intertemporal effects of exchange rates on the optimal prices of a firm’s domestic and international rivals will affect a firm’s long-run exposure in relation to its short-run exposure. We find that in the static version, the addition of a domestic competitor increases the firm’s exposure, while the effect on its foreign competitor is ambiguous. In the dynamic case, we find that the gap in exposure between the RoT model and the international duopoly case is larger in the long run than in the short run for the company facing a domestic rival, while the exposure for that firm can be either smaller or larger in the long run relative to the short run. Finally, the firm that remains a monopolist in its domestic market has a smaller exposure in the long run as compared to the short run

Switching Costs and Equilibrium Prices

In a competitive environment, switching costs have two eects. First, they increase the market power of a seller with locked-in customers. Second, they increase competition for new customers. I provide conditions under which switching costs decrease or increase equilibrium prices. Taken together, the suggest that, if markets are very competitive to begin with, then switching costs make them even more competitive; whereas if markets are not very competitive to begin with, then switching costs make them even less competitive. In the above statements, by "competitive" I mean a market that is close to a symmetric duopoly or one where the sellers' discount factor is very high

Aftermarket Power and Basic Market Competition

I revisit the relation between aftermarket power and basic market competition. I consider an infinite period model with overlapping consumers: in each period, one consumer is born and joins one of the existing installed bases, then aftermarket payoffs are received by sellers and consumers, then finally one consumer dies. I derive the unique symmetric Markov equilibrium of this game and the resulting stationary distribution over states (each firm’s installed base). I show that an increase in aftermarket power increases the extent of increasing dominance (i.e., a large firm is increasingly more likely to capture a new consumer than a small firm). This in turn leads to several implications of aftermarket power. First, the stationary distribution places greater weight on asymmetric states. Second, social welfare is greater. Third, under some conditions consumer welfare is also greater. Fourth, the value of a firm with zero installed base is lower, and so barriers to entry are higher

Advertising in a Competitive Market: The Role of Product Standards, Customer Learning, and Switching Costs

Standard models of competition predict that firms will sell less when competitors target their customers with advertising. This is particularly true in mature markets with many competitors that sell relatively undifferentiated products. However, the authors present findings from a large-scale randomized field experiment that contrast sharply with this prediction. The field experiment measures the impact of competitors' advertising on sales at a private label apparel retailer. Surprisingly, for a substantial segment of customers, the competitors' advertisements increased sales at this retailer. This robust effect was obtained through experimental manipulation and by measuring actual purchases from large samples of randomly assigned customers. The effect size is also large, with customers ordering more than 4% more items in some categories in the treatment condition (vs. the control). The authors examine how these positive spillovers vary across product categories to illustrate the importance of product standards, customer learning, and switching costs. The findings have the potential to change our understanding of competition in mature markets