Comparing Bertrand and Cournot in mixed markets

Social Welfare under Quantity Competition and Price Competition in a Mixed Duopoly with Network Effects: An Analysis

“…These effects reflected a simple mechanism where the surplus obtained by a firm's client increases directly with the number of other clients of this firm. In this study, we show that when the strength of such network effects is sufficiently high, the equilibrium social welfare is higher in a quantity-setting competition than in a price-setting competition; this finding is strikingly different from those in the existing literature in this field including Ghosh and Mitra [5] and Matsumura and Ogawa [6].…”

“…Thus, when takes some sort of positive value, firm 0's price level is strictly higher in price-setting competition than in quantity-setting competition. Therefore, in particular when the strength of network effects is sufficiently low, since the ranking order of the equilibrium market outcomes seldom changes against the introduction of network effects, the equilibrium social welfare is higher in price competition than in quantity competition owing to the large difference of the equilibrium producer surplus relative to that of the equilibrium consumer surplus, which is similar to Ghosh and Mitra [5] and Matsumura and Ogawa [6].…”

“…0 n  From Lemma 1, even if network effects are introduced, the ranking orders of equilibrium outcomes except for the price level of firm 1 are the same as those obtained in Ghosh and Mitra [5]. The introduction of network effects widens the difference in the price level of firm 0 between price-setting competition and quantity-setting competition, implying that such a low level of 0 creates a strong downward pressure on firm 1's price level.…”

“…In Ghosh and Mitra [5] and Matsumura and Ogawa [6], where network effect is not considered, it was shown that the equilibrium social welfare is always higher in pricesetting competition than in quantity competition 6 . However, in this paper, when the strength of network effects is sufficiently high, we found that the ranking order of the equilibrium social welfare between price-setting competition and quantity-setting competition is totally reversed.…”

“…Surprisingly, Proposition 1 implies that when the strength of network effects is sufficiently high, the result on the ranking order of the equilibrium social welfare between a price-setting competition and a quantity-setting competition obtained in Ghosh and Mitra [5] and Matsumura and Ogawa [6] is totally reversed; hence, the equilibrium social welfare can be higher in quantity-setting competition than in pricesetting competition. The intuition behind this result is given by using the following lemma:…”