Endogenous Role in Mixed Markets: A Two‐Production‐Period Model

Abstract

In this paper, I investigate endogenous roles in a mixed duopoly, where private and state‐owned public turns compete, by allowing two production periods. I find that many equilibria exist, including the Coumot‐type equilibrium and one Stackelberg‐type equilibrium where the public firm becomes the follower. However, another Stackelberg‐type equilibrium where the public firm becomes the leader does not exist. If small inventory costs are introduced, the unique equilibrium outcome becomes the Stackelberg type where the public firm is the follower.

What role should public firms play in the upstream market?

“…We find that multiple equilibria may exist, including the Cournot‐type and Stackelberg‐type. This is ipso facto consistent with Ono (1978), Robson (1990), and Matsumura (2003) when the marginal cost of the public firm is relatively high, even though in a vertically related market involving partial privatization of the upstream public firm.…”

“…When θ = 0 and c c > 2 meaning the public firm is purely state-owned and the marginal cost of the public firm is relatively high, the public leadership competition is an equilibrium. In some ways, this is coherent with Pal (1998) and Matsumura (2003) when the number of upstream private firms is less than two.…”

“…Proof See the appendix. □ Matsumura (2003) has shown that in a traditional downstream mixed duopoly model with multiperiod production and constant‐marginal cost, the public leadership is never optimal. They further state in a footnote that if each firm can only produce once, then both Stackelberg outcomes are sustainable as equilibria if the cost of the public firm is high relative to that of the private firm.…”

Stable market structures from merger activities in mixed oligopoly with asymmetric costs

“…Thus, this merged firm m must consider both profit as well as social welfare. Let s ∈ [0, 1] denote the public sector's 5 There are studies on a mixed oligopoly with the constant marginal cost setting such as Mujumdar and Pal (1998), Pal (1998), Matsumura (2003) and Lu (2006).…”

“…Then, following Matsumura (1998) and other studies related to partial privatization, 7 we assume that firm m maximizes…”