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About the article
Published Online: 2013-07-30
See Cowling and Mueller (1978, 728) for a summary of the criticism of Harberger’s approach.
It can be argued that lack of market coverage cannot occur once entry is allowed in the model. At this stage, however, we want to concentrate the analysis on markets with an established oligopoly in the short run, leaving the issue of entry for future research.
Following Economides (1984), we use term “touching” for an equilibrium in which the markets just touch and there is no tangency of demand.
Economides (1984) studied the case of a “not-too-high” reservation price where consumers at the edges of the market prefer not to purchase the differentiated good.
PWL could be calculated, if the reservation price was observed. The latter is usually thought to be private information but, in some cases, it can be elicited by the mechanism of Becker, DeGroot, and Marschak (1964). For the limitations of this mechanism, see Horowitz (2006) and the references there.
Knowledge of demand elasticity cannot be used to break the indeterminacy of PWL, since PWL is independent of demand elasticities (own and cross) and markups. This is explained by the fact that as demand is totally inelastic, a high price, unless it induces not buying the good, does not cause welfare losses. This makes a difference with models in which consumers may buy several goods where demand elasticities and markups can be used to find PWL, even though their impact is sometimes counterintuitive (see Corchón and Zudenkova 2009).
See Economides (1989) where this assumption emerges in equilibrium in a model which generalizes Salop model but in which transportation costs are quadratic. This is the case we consider here.
Results for linear transportation costs or positive fixed costs are available upon request.
These results generalize Wauthy’s (1996) findings for the case of zero costs.
Alternatively, only one firm may produce the whole output at the maximum quality.
Tirole (1988) made the observation that non-optimal locations or quality choices lead to distortions. Our contribution formally analyzes and quantifies these distortions.
It is important to stress that here, as well as in other equilibrium configurations in the models of horizontal and vertical differentiation, an equilibrium is unique up to a permutation of firms.