Market structure and pricing strategies: A mathematical and graphical analysis of price discrimination, accompanied by a Microsoft Excel–based tool

Abstract

The author focused on solving problems of third-degree price discrimination under a monopoly by integrating microeconomic theory and spreadsheet modeling. Price discrimination refers to a firm situation in which the same good is sold to different groups of consumers at different prices. First, the author included an introductory math background and graphical features of this type of problems. Next, he introduced a practical exercise and his own programing to solve it using Microsoft Excel. The tutorial will allow students a better understanding of the link between theory and problem solving in microeconomics.

Keywords:

• Excel spreadsheet
• microeconomics
• monopoly
• third-degree price discrimination

Notes

1 The first-, second-, and third-degree taxonomy of price discrimination was due to Pigou (1920). However, according to Ekelund (1970), price discrimination and its degrees already appeared in the writings of the French engineer-economist Jules Dupuit in the second half of the 19th century.

2 What is alleged by many textbooks as a necessary condition for profitable price discrimination might not be true. Under certain circumstances, firms could profitably price discriminate while allowing arbitrage (Marchand, Rigdon, & Roufagalas, 2000).

3 Price variations due to price discrimination do not reflect differences in marginal costs (the price difference cannot be explained by cost differences); they exist simply because the firm with market power has the ability to charge different prices for the same product.

4 In other words, a discriminating monopolist will charge a higher price to the group with the less elastic demand (Maddala & Miller, 1989).

5 It would be a linear total cost function that starts from the origin.

6 When we aggregate independent demand curves to build a market demand curve, the latter will always have at least one kink if the demand curves of each submarket are linear in price with different “reservation prices.”

7 Reservation (or reserve) price is the highest price that a buyer is willing to pay. It coincides with the ordered at the origin of the inverse demand function. In the example, 24€ and 12€, respectively.

8 If all consumers valued the good equally, there would be no rationale for the firm offering different prices to different customers.

9 To ensure that older versions of Excel can open the file, a “compatibility mode” (Excel 97-2003 Workbook) has been used.