Monopoly Behavior
 10 minutes read  2116 wordsContext
 Many market structures examined in economics assume that the market has a single price. Both perfect competition and monopoly, which we have previously studied, are single price market structures.
 However, in practice prices for similar, and in some cases even identical products, can be different from seller to seller.
 Why do we observe price dispersion in real markets?
 How is this related to the firms' choices?
 How does this affect the total market welfare?
Course Structure Overview
Lecture Structure and Learning Objectives
Structure
 Marseille and Ancona Fish Market (Case Study)
 Basic Concepts
 An Example of Group Pricing
 Welfare Analysis of Price Discrimination
 Current Field Developments
Learning Objectives
 Describe the pricing strategies available to the monopolist.
 Explain the difference between price discrimination and price dispersion.
 Illustrate price discrimination by a group pricing example.
 Analyze the welfare effects of price discrimination.
 Describe product differentiation and monopolistic competition.
Marseille and Ancona Fish Markets
 Price differences might arise due to various reasons.
 A potential reason is price discrimination. But…
 Price dispersion is not necessarily due to price discrimination.
Market Structure Matters
 Marseille:
 Sellers have stands.
 Buyers approach the stands.
 Prices are pairwise agreed.
 Ancona:
 Fish crates go down a conveyor belt.
 A screen displays the initial price. An auctioneer decides the initial price.
 The price declines incrementally until a buyer pushes a button to buy.
 Gallegati et al. (2011) studied prices in these two markets.
Price discrimination in Marseille
 Individual vendors vary prices of the same kind of fish to different buyers by up to \(30\%\).
 Some buyers are loyal to certain sellers, while others circulate.
 More loyal customers pay slightly higher prices than their less loyal counterparts.
 Sellers prioritize the demand of more loyal customers.
 This market structure leads to higher profits for sellers and higher payoffs (counting demand satisfaction) for \(90\%\) of loyal customers.
Price dispersion in Ancona
 Individual buyers in the market have very atypical pricequantity relationships.
 Even without facetoface interaction, buyer loyalty is present.
 Many loyal customers pay lower prices than their less loyal counterparts.
Market power
 Market power refers to the ability of a firm to influence the price at which it sells the product or service it offers.
 Monopolies tend to have market power, which they can use to increase their profits.
Reservation values
 A reservation value is the least favorable price point at which an economic agent is willing to engage in trade.
 Examples:
 A buyer’s reservation value is the maximum price she is willing to pay in exchange for a commodity or service.
 A seller’s reservation value is the minimum price she is willing to sell a commodity or service.
Price Discrimination
 Conventional Definition: Price discrimination is present when a producer sells the same commodity at different prices to different consumers.
 But this could be due to differences in shipping costs etc.
 Preferred Definition by Stigler (1987): Price discrimination occurs when a producer sells two or more similar goods at prices that have different markups.
 Example: A book that sells in hardcover for \(15\) € and paperback for \(5\) €.
Types of Price Discrimination
 The classic typology from Pigou (1920), distinguishes three price discrimination classes.
 Their names are not very helpful: first, second, and third price discrimination degree.
 We follow the naming convention of Belleflamme and Peitz (2010).
 Group Pricing (aka thirddegree price discrimination)
 Personalized pricing (aka firstdegree or perfect price discrimination)
 Menu Pricing (aka seconddegree price discrimination, or nonlinear pricing)
Group Pricing
 Group pricing occurs when a seller offers different markups to different groups of consumers.
 This is perhaps the most common form of price discrimination.
 Example: Student discounts.
Menu Pricing
 Menu pricing occurs when a seller offers different markups depending on the characteristics of the enclosing package bought, but not across consumers.
 For instance, packages (or menus) may differ in the number of units of the good they contain.
 Quantity discounts or premia are the most prominent examples, but there are also other cases…
 Some airlines add surcharges for oneway tickets.
Personalized Pricing
 Personalized pricing occurs when a seller sets the price of each sold unit equal to the maximum amount that the consumer who is buying it is willing to pay for that unit.
 The reservation value of each purchased unit must be known to the seller.
 In reality, impractical due to the enormous amount of required information.
 It can be thought of as an extreme case of group pricing.
A Group Pricing Example
 Under uniform pricing, the monopolist can charge a single price.
 Under price discrimination, the monopolist can charge two different prices.
 Let demand be (piecewise) affine and cost be linear (no fixed cost).
Low uniform pricing
 At \(p_{l} = 8\), all customers are buying
 \(q_{l} = 100\)
 \(\pi_{l} = q_{l} \left(p_{l}  c\right) = 500\)
 \(W^{c}_{l} = \frac{50 \times 19}{2} + \frac{50 \times 2}{2} = 525\)
 \(W_{l} = \pi_{l} + W^{c}_{l} = 1025\)
High uniform pricing
 At \(p_{h} = 15\), only high spenders are buying
 \(q_{h} = 50\)
 \(\pi_{h} = q_{h} \left(p_{h}  c\right) = 600\)
 \(W^{c}_{h} = \frac{50 \times 5}{2} = 125\)
 \(W_{h} = \pi_{h} + W^{c}_{h} = 725\)
Price Discrimination

The firm charges \(p_{g,h} = 15\) to high spenders and \(p_{g,l} = 8\) to low spenders

\(q_{g,h} = 50\) and \(q_{g,l} = 50\)

Profit
\begin{aligned} \pi_{g} &= q_{g,h} \left(p_{g,h}  c\right) + q_{g,l} \left(p_{g,l}  c\right) \\ &= 600 + 250 = 850 \end{aligned}

\(W^{c}_{g} = \frac{50 \times 5}{2} + \frac{50 \times 2}{2} = 175\)

\(W_{g} = \pi_{g} + W^{c}_{g} = 1025\)
Product Differentiation
 Another potential strategy for a firm to gain market power is to attempt to make its product distinct.
 Product differentiation refers to firm strategies aiming to distinguish its product from similar products produced by competitors. Product differentiation can be present either due to branding or product quality differences.
 Consumers who perceive a product as being different from competitive products are less likely to substitute it with alternatives.
 Essentially, this makes demand more inelastic, which increases the firms' market power.
Monopolistic Competition
 Monopolistic competition is a market structure with multiple competing firms selling products that are differentiated from one another.
 The market does not suffer from any other market failure (imperfect information, externalities, etc.).
 There are no entry barriers in the market.
 Consumers are price takers, but firms are setting prices.
 Consumers try to maximize their utility.
 The differentiated products are not perfect substitutes.
 Firms try to maximize their profits.
Current Field Developments
 Firm strategies like product differentiation and price discrimination are actively examined in specific market contents by economics (e.g., Gallegati et al. 2011).
 Policy makers are also interested in market models involving such strategies because competition regulation prevents some forms of price discrimination.
 Personalized pricing becomes even more relevant in digital economies where data accumulation about consumers is feasible.
 The recent EU privacy Law affects the availability of pricing strategies of firms operating on the web (Borgesius and Poort 2017).
 Dynamic extensions of market models indicate that firms can also profit by intertemporal price discrimination strategies.
Concise Summary
 Price dispersion is not necessarily price discrimination.
 Firms can employ price discrimination strategies to increase their profits.
 This can increase the total welfare of the market.
 The consumers in the market, however, do not necessarily do better.
 Firms can use product differentiation strategies to increase their market power.
 Monopolistic competition is a market structure that borrows elements from both perfect competition and monopoly.
Further Reading
 Varian (2010, chap. 26)
 CORE Team (2017, sec. 11.2)
 Gallegati et al. (2011)
 Borgesius and Poort (2017)
 Belleflamme and Peitz (2010, chaps. 8, 9)
Mathematical Details
Personalized Pricing
Perfect price discrimination can increase the total welfare in cases of monopolies. Not everyone is doing better, though. The monopoly extracts the whole welfare and consumers nothing.
Demand and cost
Suppose that demand is given by
\begin{align*} d(p) = \left\{ \begin{matrix} \frac{p_{0}}{p_{1}} + \frac{1}{p_{1}} p, & 0 \le p < p_{0} \\ 0, &\neq \end{matrix}\right., \end{align*}
where \(p_{0} >0, p_{1} < 0\). Let the cost function be \[c(q) = c_{1} q,\] with \(c_{1} > 0\).
Uniform Monopoly Pricing
Under uniform pricing the monopolist’s objective is \[\max_{p} \left\{ p d(p)  c(d(p)) \right\} = \max_{p} \left\{ d(p) (p  c_{1}) \right\}.\] We obtain the first order condition \[p_{0}  2 p_{m} + c_{1} = 0,\] which gives the optimal price \[p_{m} = \frac{p_{0} + c_{1}}{2} \implies q_{m} = \frac{p_{0}  c_{1}}{2 p_{1}}\] We can calculate the welfare in this case by adding the consumer’s and producer’s surpluses. The producer’s surplus is equal to profit because the cost function does not have a fixed cost component. We have \[\pi_{m} = \frac{\left(p_{0}  c_{1}\right)^2}{4 p_{1}}.\] The consumer’s surplus is \[W^{c}_{m} = \frac{\left(p_{0}  p_{m}\right) q_{m}}{2} = \frac{\left(p_{0}  c_{1}\right)^2}{8 p_{1}}.\] Therefore, the total welfare is \[W_{m} =  \frac{3\left(p_{0}  c_{1}\right)^2}{8 p_{1}}\]
Perfect Competition
Profit is zero in perfect competition because the market price is equal to the firms' marginal cost. We have \(p_{c} = c_{1}\), which implies that \[q_{c} = \frac{p_{0}  c_{1}}{p_{1}}.\] The total welfare is equal to the consumer’s surplus \[W_{c} = W^{c}_{c} = \frac{\left(p_{0}  p_{c}\right) q_{c}}{2} = \frac{\left(p_{0}  c_{1}\right)^2}{2 p_{1}}\]
Personalized pricing
In the case of personalized pricing, the situation is completely reversed. The consumer’s surplus is zero, and the total welfare is equal to the profit of the firm, namely \[W^{s}_{p} = \pi_{p} = W^{c}_{c} = \frac{\left(p_{0}  c_{1}\right)^2}{2 p_{1}}\]
Comparison
Monopoly  Competition  Personalized Pricing  

Profit  \(\frac{\left(p_{0}  c_{1}\right)^2}{4 p_{1}}\)  \(0\)  \(\frac{\left(p_{0}  c_{1}\right)^2}{2 p_{1}}\) 
Consumer Welfare  \(\frac{\left(p_{0}  c_{1}\right)^2}{8 p_{1}}\)  \(\frac{\left(p_{0}  c_{1}\right)^2}{2 p_{1}}\)  \(0\) 
Total Welfare  \(\frac{3\left(p_{0}  c_{1}\right)^2}{8 p_{1}}\)  \(\frac{\left(p_{0}  c_{1}\right)^2}{2 p_{1}}\)  \(\frac{\left(p_{0}  c_{1}\right)^2}{2 p_{1}}\) 
Monopolistic competition
Monopolistic competition is a structure describing a market with many firms offering similar, but not perfectly identical, commodities or services. Firms can affect prices but not as effectively as a monopolist.
A symmetric, affine demand, and liner cost example
Suppose \(\bar p\) is the average price of the differentiated products. The firm’s demand depends on the difference of its price from the average price. That is,
\begin{align*} d(p) = q_{0} \left( \frac{1}{n} + q_{1} (p  \bar{p}) \right) = \underbrace{\frac{q_{0}}{n}  q_{0} q_{1} \bar{p}}_{:= \frac{p_{0}}{p_{1}}} + \underbrace{q_{0} q_{1}}_{:=\frac{1}{p_{1}}} p , \end{align*}
where \(q_{0}, \bar{p} > 0, q_{1} < 0\). The production costs of all firms have the form \[c(q) = c_{1} q,\] with \(c_{1}>0\).
Profit for a fixed number of firms in the market
For interior solutions, each firm sets
\begin{align*} p &= \frac{q_{1}c  \frac{1}{n} + q_{1} \bar{p}}{2 q_{1}} , \\ q &= q_{0}\frac{q_{1}c + \frac{1}{n}  q_{1}\bar{p}}{2} . \end{align*}
For symmetric solutions, these are simplified to
\begin{align*} p &= \frac{q_{1}c  \frac{1}{n}}{q_{1}}, \\ q &= \frac{q_{0}}{n}. \end{align*}
What happens when the number of firms increases?
The market power of each individual firm decreases with \(n\). The limiting case gives prices coinciding with the perfect competition price, namely \(p \xrightarrow[n\to\infty]{} c\). Limiting quantities become irrelevant as the number of firms in the market increases, i.e., \(q \xrightarrow[n\to\infty]{} 0\).
Exercises
Group A

Suppose that a monopolist can adopt a group pricing strategy in a market with two groups. Both groups' demands have constant price elasticities correspondingly equal to \(e_{d,1}\) and \(e_{d,2}\). The marginal production cost is constant at \(c_{1}\), and there are no fixed cost. What price does the monopolist charge to each group?
The monopolist solves \[ \max_{p_{1}, p_{2}} \left\{ p_{1} d_{1}(p_{1}) + p_{2} d_{2}(p_{2})  c_{1}\left(d_{1}(p_{1}) + d_{2}(p_{2})\right) \right\}. \] The optimality conditions for this problem are
\begin{align*} d_{i}(p_{i}) + p_{i} d_{i}'(p_{i})  c_{1} d_{i}'(p_{i}) &= 0 \qquad (i=1,2). \end{align*}
From them, we deduce that
\begin{align*} p_{i} = \frac{c}{\frac{1}{e_{d,i}} + 1} \qquad (i=1,2). \end{align*}
References
References
Topic's Concepts
 monopolistic competition
 product differentiation
 personalized pricing
 menu pricing
 group pricing
 price discrimination
 sellers reservation value
 buyers reservation value
 reservation value
 market power