Comparing welfare and profit in quantity and price competition within Stackelberg mixed duopolies

Abstract

We compare welfare and profits under price and quantity competition in mixed duopolies, wherein a state-owned public firm competes against a private firm. It has been shown that price competition yields larger profit for the private firm and greater welfare if the two firms move simultaneously, regardless of whether the private firm is domestic or foreign. We investigate welfare and profit rankings under Stackelberg competition. Under public leadership, the profit and welfare rankings have common features with the simultaneous-move game, regardless of the nationality of private firms. By contrast, under private leadership, the result depends on the nationality of the private firm. When the private firm is domestic, welfare is greater under quantity competition, while the result is reversed when the private firm is foreign. However, regardless of nationality, private firms earn more under price competition. Introducing the nonnegative profit constraint in the public firm improves welfare and increases the private firm's profit, and price competition yields a higher profit for private firms regardless of nationality and which firm is the leader. However, this constraint affects the welfare ranking. Under private leadership, quantity competition yields greater welfare regardless of the nationality of the private firm. These results indicate that profit ranking is fairly robust to the time structure in mixed Stackelberg duopolies, but welfare ranking is not.

Cost‐reduction innovation under mixed economy

“…Otherwise, the (semi‐) public firm obtains more profits in the competition. Differently, Hirose and Matsumura (2019) found that private firms always earn more in mixed economy. Notice that the research conducted by Hirose and Matsumura focused on price competition, and the model of this paper emphasized on quantity competition.…”

Cournot vs. Bertrand in mixed markets with R&D

“…3 Motivated by the recent trends in R&D in mixed markets, we consider a mixed market where both public and private firms invest in cost-reducing R&D. First, we show that choosing price contract is the dominant strategy for both firms. Next, we argue that the findings that Cournot profit is strictly higher than Bertrand in standard oligopoly (Singh and Vives, 1984) 4 and that the Bertrand profit is strictly higher than Cournot in mixed oligopoly (Ghosh and Mitra, 2010;Matsumura and Ogawa, 2012;Hirose and Matsumura, 2018), both hold if the welfare maximising public firm and profit maximising private firm engage in cost reducing R&D.…”

Bertrand versus Cournot competition in a downstream mixed oligopoly with foreign ownership

“…The other stream of extension of Cournot‐Bertrand debate focuses on mixed markets, wherein state‐owned public firms compete against private firms (De Fraja & Delbono, ; Ghosh & Mitra, ; Haraguchi & Matsumura, ; Hirose & Matsumura, ; Matsumura & Ogawa, ; Scrimitore, ). Ghosh and Mitra () have reexamined the comparison between Cournot and Bertrand competition in a differentiated duopoly in which a welfare‐maximizing public firm competes against a profit‐maximizing private firm.…”

“…Taking optimal privatization policy of the government into account in the mixed oligopoly model, Scrimitore () has shown that Cournot‐Bertrand profit ranking can restore to that in the study of Singh and Vives (), that is, Cournot profit is more profitable and less efficient in welfare than Bertrand competition. Hirose and Matusmura () have shown that price competition always yields greater welfare than quantity competition under public leadership while quantity competition can yield greater welfare than price competition under private leadership.…”