This paper presents a general analysis of the effects of monopolistic third-degree price discrimination on welfare and output when all markets are served. Sufficient conditions — involving straightforward comparisons of the curvatures of the direct and inverse demand functions in the different markets — are presented for discrimination to have negative or positive effects on social welfare and output. (JEL D42)
The welfare effects of third-degree price discrimination are analyzed when demand in one market is an additively shifted version of demand in the other market and both markets are served with uniform pricing. Social welfare is lower with discrimination if the slope of demand is log concave or the convexity of demand is nondecreasing in the price. The demand functions commonly used in models of imperfect competition satisfy at least one of these sufficient conditions. * University of Oxford; simon.cowan@economics.ox.ac.uk. I am grateful to Igal Hendel, Katy Graddy, Tom Holmes, David Myatt, John Thanassoulis, John Vickers and two anonymous referees for helpful comments on earlier versions of this paper.Copyright © 2007, RAND. 419 420 / THE RAND JOURNAL OF ECONOMICS a, might represent the effect of the external temperature on demand. An alternative interpretation involves geographical discrimination. Suppose that a single firm, say a supermarket, restaurant or cinema chain, sells in different towns. In a given town, there are a committed consumers who always buy the product and b price-sensitive consumers, each with demand of q( p). The demographic composition of each town is defined by the ratio of committed to price-sensitive customers, a/b. Discrimination is not feasible within a town, maybe because of arbitrage possibilities, but it is feasible to discriminate across towns and a profit-maximizing firm will want to do so if a/b varies across towns. The UK's Competition Commission investigated supermarket pricing and found that "pricing might also respond to local demographics" in addition to local competitive pressures (Competition Commission, 2000). For simplicity, the analysis is presented with a alone varying, but all the results also hold when b also varies across markets.The main result is that discrimination lowers welfare for all underlying demand functions typically used in theoretical and econometric models of imperfect competition, as long as all markets are served. With this demand structure, social welfare with discrimination is lower than that with uniform pricing if welfare with discrimination is a concave function of a/b. Two sufficient conditions for concavity of the welfare function are presented. An important role is played by the ratio of the curvature of the slope of the demand function to the curvature of the demand function itself. If this ratio is at most 1, which is equivalent to the slope of demand being log concave, then welfare falls with discrimination. Many demand functions have log-concave slopes. Some demand functions, though, such as those in the isoelastic class, do not satisfy this condition. Nevertheless, welfare is also lower with discrimination for a general class of such functions, which are characterized by a curvature that does not decrease with the price. Welfare can rise with discrimination when a large concentration of low-value consumers induces the firm to cut price substantially when discrimination is allowed and two examples are given. In general, though, welfare onl...
This paper considers the effects of monopoly third‐degree price discrimination on aggregate consumer surplus. Discrimination is likely to reduce surplus (relative to that obtained with a uniform price), but surplus can rise under reasonable conditions. If the ratio of the pass‐through coefficient to the price elasticity at the uniform price is higher in the market with the higher price elasticity then surplus is larger with discrimination (for a large set of demand functions). The relatively high pass‐through coefficient implies a large price reduction in this market. With logit demand functions surplus is higher with discrimination if pass‐through is above 0.5.
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