Issues in Price Discrimination: A Comment on and Addendum to 'Teaching Price Discrimination,' by Carroll and Coates.

• Author: Jeitschko, Thomas D.
• Position: Brief Article

Thomas D. Jeitschko [*]

1. Introduction

   There is a large variety of treatments of the topic of price discrimination in the most widely used undergraduate principles and intermediate microeconomic textbooks as well as industrial organization texts. In a recent Southern Economic Journal article, Carroll and Coates (1999) set out to bring into focus the issues that ought to be discussed and made clear when teaching price discrimination to undergraduates. Their paper concludes with a list of six points that instructors should follow to spark students' interest and create as little confusion as possible when covering the topic.

   While in several ways their article is an improvement over many a textbook discussion, I think their contribution can also be improved upon, as it contains some misconceptions and mistakes. Specifically, there are two concerns regarding the coverage of price discrimination in general and both of these affect the paper by Carroll and Coates in particular. The first is mostly technical, but has led to widespread misconceptions about the relationship between the price elasticity of demand and third-degree price discrimination. The other is mainly pedagogical and concerns what can (or should) actually be taken away from the classroom after a discussion of price discrimination, especially regarding implications of price discrimination on economic efficiency.

2. Price Elasticity of Demand

   Point (ii) on Carroll and Coates' list intended to prevent students' confusion on price discrimination states that one should cover the three necessary conditions for price discrimination to occur. These are: (i) The firm must have some market power; (ii) there can at best be imperfect arbitrage opportunities for consumers; and (iii) "consumers have different price elasticities of demand" (p. 471).

   The third point (repeated again on p. 472, where it is stated that price discrimination would not be possible "if buyers' price elasticities were identical"), however, needs some qualification. First of all, a difference in the price sensitivity of the quantity demanded is not a necessary condition for either first- or second-degree price discrimination--and there is no confusion about this in the most common textbook treatments on price discrimination. Second, when it comes to third-degree price discrimination, the role of the price elasticity of demand is frequently mischaracterized. [1] In particular, the common (and seemingly intuitive) statement that "if the firm knows that elasticity is related to some identifiable group characteristic, then it can use third-degree price discrimination to induce the price-insensitive buyers to pay a high price and price-sensitive buyers to pay a low price" (p. 471) is hard to verify in practice, and is indeed frequently misleading or false. The reason for this is that what constitutes a "price-insensitive buyer" can only be determined by comparing the demands of two consumers, whereas an elasticity criterion is often only applied to a particular quantity demanded.

   The following example (taken from Jeitschko and Thon 1999) illustrates this point.

   Example 1 A firm with zero cost can price discriminate between the two following demands.

   [Q.sub.1] = [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

   and [Q.sub.2] = [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

   The inverse demands for the firm's product in the two markets are given by

   [P.sub.1] = [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

   and [P.sub.2] = [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

   resulting in

   [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

   [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

   In both submarkets there are two critical points, (P, Q), where [MR.sub.i] = MC(=0). In market 1 these are (50, 10) and (15, 30); in market 2 these are (52.5, 10.5) and (17.5, 35). Since AC = 0, the firm maximizes revenue. Hence, in market 1, the optimum is at [[P.sup.*].sub.1] = 50, whereas in market 2 it is at [[P.sup.*].sub.2] = 17.5. Thus, the price in market 1 is higher than in market 2, that is, [[P.sup.*].sub.1] [greater than] [[P.sup.*].sub.2].

   Consider now the elasticity in the two respective markets. Given that the firm has zero cost, at the two distinct optimal prices the two respective price elasticities must...