A Peek into a Pandora's Box: Firm-Level Demand with Price Competition vs. Quantity Competition

This paper explores the impact increased competition may have on the distinction between demand and inverse demand faced by an individual firm. In the case of duopoly, inverse demand is less price elastic than demand regardless of the degree of product differentiation. (See Singh and Vives 1984). Vives (1999) and (1987) suggests why the distinction between price and quantity competition when the product is differentiated among many firms has not been addressed extensively yet. If the residual price elasticity of demand faced by a firm is unbounded with increased competition, it leads to the competitive result with no distinction. If the residual price elasticity of demand remains bounded as the number of firms is increased, it leads to monopolistic competition, but cross-price elasticities will vanish as will any difference. The distinction would remain in kind as n is increased, but only diminish in degree at most. Also, in the less technically limiting case which includes cross effects terms, inverting the demand relationship may itself be daunting with increased numbers, impeding any comparison at all. Nevertheless, Hackner (2000) explores the distinction between price and quantit