Abstract
In this paper, we provide a welfare ranking for the equilibria of the supply function and quantity competitions in a differentiated product duopoly with demand uncertainty. We prove that the expected consumer surplus is always higher under the supply function competition. By numerical simulations, we also show that if the degree of product substitution is extremely low, then the supply function competition can become a superior form of competition for the duopolistic producers, as well. However, if the degree of product substitution is not extremely low, then the expected producer profits under the supply function competition can be lower than under the quantity competition in situations where the size of the demand uncertainty is below a critical level. We find that this critical level is non-decreasing in the degree of product substitution, while non-increasing both in the marginal cost of producing a unit output and in the own-price sensitivity of each inverse demand curve. Our results imply that in electricity markets with differentiated products, the regulators should not intervene to impose the quantity competition in favor of the supply function competition unless the degree of product substitution is sufficiently high and the predicted demand fluctuations are sufficiently small.
Highlights
The supply function competition that was originally developed by Grossman (1981) could find applications in oligopolistic industries only after Klemperer and Meyer (1989), who eliminated the problems with the multiplicity of supply function equilibria by introducing an exogenous uncertainty about the demand functions faced by oligopolists
We have presented in Propositions 1 and 2 the characterizations of the symmetric equilibrium obtained under each form of competition, and calculating the expected welfares of the producers and consumers at each of these equilibria, we have first studied how they would respond to changes in various model parameters
These parameters are the size of the demand uncertainty measured by the coefficient of variation (η), the own-price sensitivity of the demand faced by each duopolist (β), the degree of substitution between the products of the duopolists (γ), and the marginal cost faced by each duopolist to produce a unit output (c)
Summary
The supply function competition that was originally developed by Grossman (1981) could find applications in oligopolistic industries only after Klemperer and Meyer (1989), who eliminated the problems with the multiplicity of supply function equilibria by introducing an exogenous uncertainty about the demand functions faced by oligopolists. Saglam (2018) found that if the demand uncertainty in the industry is sufficiently large with respect to the number of firms, the size of the product markets, and the marginal cost of the unit output, the supply function competition can be ex-ante more desirable for the producers, as well. If the degree of product substitution is not extremely low, the expected producer profits under the supply function competition can be lower than under the quantity competition in situations where the size of the demand uncertainty is below a critical level We find that this critical level is non-decreasing in the degree of product substitution, while non-increasing both in the marginal cost of producing a unit output and in the own-price sensitivity of each inverse demand curve. It is assumed that the form of the cost, demand and inverse demand curves, the parameters c, β, γ, b, and g, the density f (α) and its support are commonly known by both firms
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