On the Optimal Number of Firms in the Commons: Cournot vs Bertrand

Efficient regulation of the commons requires information about the regulated firms that is rarely available to regulators (e.g., cost of pollution abatement). This paper proposes a simple mechanism that implements the first-best for any number of firms: a uniform price, sealed-bid auction of an endogenous number of (transferable) licenses with a fraction of the auction revenues given back to firms. Paybacks, which rapidly decrease with the number of firms, are such that truth-telling is a dominant strategy regardless of whether firms behave non-cooperatively or collusively. The mechanism also provides firms with incentives to invest in socially optimal R&D. (JEL D44, L51, Q21)

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Welfare-Improving Effect of a Small Number of Followers in a Stackelberg Model

The B E Journal of Theoretical Economics ◽

10.1515/bejte-2015-0045 ◽

2016 ◽

Vol 16 (1) ◽

pp. 243-265 ◽

Cited By ~ 10

Author(s):

Hiroaki Ino ◽

Toshihiro Matsumura

Keyword(s):

Optimal Number ◽

Welfare Effect ◽

Cournot Model ◽

Oligopoly Model ◽

Stackelberg Model ◽

Number Of Firms

AbstractWe investigate a Stackelberg oligopoly model in which m leaders and $N - m$ followers compete. We find an important welfare effect that relates to anti-monopoly policies when we move from the Cournot model ($m = N$) to the Stackelberg model: Exchanging a small number of Cournot firms for Stackelberg followers always improves welfare under moderate conditions. This contrasts with the welfare effect that can reduce welfare when a small number of Cournot firms are exchanged for Stackelberg leaders. The key result behind this asymmetry is the contrasting limit results in the cases where m converges to N and m converges to 0. We also discuss the optimal number of leaders and the integer constraint for the number of firms.

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The Optimal Number of Firms With an Application to Professional Sports Leagues

Journal of Sports Economics ◽

10.1177/1527002505279764 ◽

2007 ◽

Vol 8 (1) ◽

pp. 99-108 ◽

Cited By ~ 4

Author(s):

Sanghoo Bae ◽

Jay Pil Choi

Keyword(s):

Professional Sports ◽

Optimal Number ◽

Sports Leagues ◽

Professional Sports Leagues ◽

Number Of Firms

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Competitive Entry In Ontarios Deregulated Power Generation Industry

Journal of Business & Economics Research (JBER) ◽

10.19030/jber.v10i2.6791 ◽

2012 ◽

Vol 10 (2) ◽

pp. 111

Author(s):

Xiaoting Wang ◽

Jun Yang

Keyword(s):

Electricity Market ◽

Optimal Number ◽

Social Optimum ◽

Market Demand ◽

Equilibrium Outcome ◽

Efficient Outcome ◽

The Social ◽

The Relationship ◽

Equilibrium Number ◽

Number Of Firms

In this paper we investigate the issues involved in the deregulation of an electricity market. The paper focuses on efficiency considerations, comparing the gap between the socially efficient outcome and that achievable by a market. We model this problem with two-sided uncertainty: the uncertain market demand and the uncertain cost of production. In each case, we find the social optimum and the equilibrium outcome of the deregulated market. Conditions when deregulated industry cannot generate the socially optimal number of firms are identified. The relationship between market demand, the degree of risk-aversion of private firms, and the equilibrium number of firms is investigated.

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