Chap 11: Oligopoly - An Introductory Course in Economics PDF

# An Introductory Course in Economics: Oligopoly ## Chapter 11: Oligopoly **In this chapter, we will learn:** * Understand the basic application of game theory to markets with large firms * Understand how the Cournot equilibrium is constructed * Describe the properties of the Cournot equilibrium...

# An Introductory Course in Economics: Oligopoly ## Chapter 11: Oligopoly **In this chapter, we will learn:** * Understand the basic application of game theory to markets with large firms * Understand how the Cournot equilibrium is constructed * Describe the properties of the Cournot equilibrium * Describe the properties of the Bertrand equilibrium * Understand simple game theoretic models of product differentiation ## 11.1 Motivation American industry is highly concentrated; now more than 50 years ago. You might get the impression by walking into your favorite store that there is a lot of choice and tons of competition. However, this impression exists in grocery stores, clothing stores, liquor stores, home improvement stores, and even more. You will be blown away by the plethora of choices, but this does not spell competition. **The table below (from Eeckhout 2021) highlights some examples of highly concentrated markets:** | Industry | Market Share (%) | Number of Firms | |-------------------|-------------------|-----------------| | Pacemakers | 89 | 3 | | Baby Formula | 69 | 2 | | Dry Cat Food | 57 | 1 | | Mayonnaise | 87 | 2 | | Home Improvements | 81 | 2 | | Coffins | 82 | 2 | ## 11.2 Cournot Equilibrium **Key facts:** * We are studying the simplest case of an oligopoly, a duopoly, which has two firms. * These firms produce an identical product. * The cases of heterogeneous products will be considered later. **The Cournot model builds from a monopoly model:** * **Demand:** $P = 20 - Q$ (where $Q$ is the market quantity and $q_1$ is the firm quantity). * **Marginal cost:** $MC = 9$. * **Profit:** $MB = MC$ where $MB$ is Marginal Benefit **Cournot model assumptions:** * Firms compete in quantities, not prices. * They simultaneously choose their output levels. * Both firms have the same cost function. **We can find the Cournot equilibrium by using a process of iteration:** 1. We start with the assumption that firms are price-takers and we calculate the market supply, which is the horizontal sum of the firm's MC curves. 2. This will give us a market price at any particular level of output. 3. Then, consider firm 1. Firm 1 knows what firm 2's output will be, and it can calculate its own profit-maximizing output. 4. This will lead to firm 1's profit maximization at 5 units, as a result, Firm 2 will maximize its profit at 4 units. 5. This process will continue until we reach a point where neither firm has an incentive to change its output. 6. The Nash Equilibrium is reached when both firms produce 4 units. **Key takeaways from the Cournot Model:** * As the number of firms increases from a monopoly to a duopoly: * Each individual firm produces less. * Total industry output increases. * Price decreases. * Profit for each firm decreases. * Overall industry profit decreases. * This model predicts that the larger the number of firms is in the market, the more likely it is that the equilibrium will approach the competitive outcome - where all firms produce at a price equal to marginal cost. * This type of Nash Equilibrium is named after Antoine Augustin Cournot and is commonly referred to as Cournot Nash Equilibrium or just Cournot Equilibrium. ## 11.3 Bertrand Equilibrium The Bertrand Equilibrium assumes firms compete on price, not quantity. **Key assumptions:** * Firms produce homogenous goods. * Firms have the same cost function. * Firms set their prices simultaneously. **In this model. firms have a strong incentive to undercut one another:** * If one firm sets its price lower than the other firm, it will capture all of the market. * This leads to a process of price-cutting that continues until the price falls to marginal cost. * In the Nash equilibrium, both firms set their prices equal to marginal cost. **Key takeaways from the Bertrand Model:** * The Bertrand equilibrium is much more competitive than the Cournot equilibrium. * Because of the strong incentive to undercut, prices will be driven down to marginal cost, leading to zero profits in the long run. **The Bertrand model is a good example of how competition can drive prices down to the point where all firms are making zero profits. However, it's not very realistic in many real-world situations.** ## 11.4 Mergers: Intro and Some Theory * Mergers are frequently observed in industries, particularly in industries with high market concentration. * There are three main types of mergers: * **Conglomerate mergers:** Two firms in totally unrelated markets. * **Horizontal mergers:** Two firms operate in the same industry (think of a merger between two restaurants). * **Vertical mergers:** One firm merges with the supplier or customer of another firm. * **Economic theory suggests that mergers can have a variety of effects, including both positive and negative consequences:** * **Potential increases in efficiency:** Reducing waste, improving production processes, or taking advantage of economies of scale. * **Increasing market power and potentially leading to higher prices:** Increasing market power through mergers can benefit companies, but consumers may pay higher prices because competition is reduced. **There is compelling evidence to indicate that mergers DO lead to increased markups in the US Manufacturing sector.** This is because mergers allow firms to lower costs and increase market power. **The health care sector presents an interesting case study of the effects of mergers:** * In 2007, two large hospital chains merged, creating a large increase in market power. * This resulted in increased costs for both patients and insurance companies. * Some research suggests that mergers may also have negative effects on health care quality. * There is a wide range of opinions about the extent to which mergers are harmful or beneficial. ## 11.5 Product Differentiation **This section focuses on product differentiation, where firms attempt to make their products unique and distinguishable from competitors in order to: ** * **Gain market share.** * **Charge higher prices.** * **For example:** * If two vendors sell hotdogs on a one-mile stretch of Main Street, they will position themselves strategically to capture the most customers. * A customer will purchase from the vendor closest to them. * The Nash equilibrium is reached when both vendors are located in the middle of the street. * If one vendor moves away from the middle, they will lose customers and their profits will decrease. ## 11.6 More Firms! * The Nash Equilibrium is not an easy thing to find. * It can be challenging to determine the best location for a company when there are multiple firms in the market. * "Mixed strategies" are sometimes necessary to reach a Nash Equilibrium. * This is where firms don't have a fixed location – they are constantly moving (think of a soccer player taking a penalty kick) * In the case of 4 firms, each firm will be located at 1/4 1/2, 3/4 and 1. ## 11.7 Glossary of Terms * **Bertrand Equilibrium:** The equilibrium in an oligopoly when all firms have price as the strategic variable. * **Cournot Equilibrium:** The equilibrium in an oligopoly when all firms have quantity as the strategic variable. * **Heterogeneous Goods:** These are goods differ in some way by taste, color, location, durability, or any other characteristic. * **Homogeneous Goods:** These are goods that are the same by taste, color, location, strength, and any other relevant characteristic. * **Horizontal Differentiation:** This refers to different types of goods such as different degrees of sweetness in iced teas. There is no sense that one variant is better than the other, they are just different, and different customers prefer different variants. * **Location Game:** A game where a relatively small number of firms strategically choose a location. * **Market Concentration:** This is a measure of how many or how few firms are in a particular market. * **Rational expectations:** Expectations formed by agents in a model that turn out to be true in the model, at least in an expected value sense. * **Vertical Differentiation:** This refers to different levels of quality, where most consumers agree that some goods are better than others, such as the durability of a pair of jeans, or the gas mileage of a car, internet speed. ## 11.8 Practice Questions **Discussion:** 1. **Efficiency in locations** - Using the 2 player game, is the location at 1/2 an efficient location? Should we consider "transportation costs" for customers. 2. **Efficient Location** - Using the 2 firm location game, what is the most efficient location for the two firms? 3. **4 Firms - Nash Equilibrium** - In a location game with 4 firms, what is the Nash equilibrium location? 4. **4 Firms - Efficient Location** - In the 4 firms location game, what is the most efficient location? **Multiple Choice:** 1. **Cournot:** If a firm increases output, how will the other firm react (Think about the Cournot Nash Game)? 2. **3 Firms:** Imagine a three-firm oligopoly; firm 1 increases output, and firm 2 keeps the output constant. What will the rational response for firm 3 be in this example? 3. **3 Firms - Same Output Decrement:** Imagine a three-firm oligopoly; firm 1 increases output, and firm 2 decreases output by the same amount. What will the rational response for firm 3 be in this example? 4. **Bertrand:** In a duopoly (2-firm oligopoly) where firms sell an identical product, and one increases its price, will the other firm follow suit, or lower its price? 5. **3 Firms - Bertrand:** Imagine a three-firm oligopoly; firm 2 raises its price; what would be the rational response for firm 1? 6. **Bertrand-Nash** - In a Bertrand-Nash price game (20 rounds), where the demand function is $P = 10 - Q$, where $Q$ is total industry output, what can we expect to observe? 7. **Circular Location - Firms:** Imagine that 2 firms choose locations on a circle (not the disk). They know each other's prices and choose locations simultaneously. What is the most likely Nash Equilibrium (think about the market share)? 8. **Mergers - Homogeneous Goods:** When firms selling homogenous goods merge, what happens to prices, quantity, and profit? 9. **Mergers - Differentiated Goods:** What is the most likely outcome for prices, quantity, and profit when companies selling differentiated goods merge? 10. **Zoning Law - Relocation:** Imagining two vendors of a consumer product on a one-mile-long street, one is at 1/4, and the other at 3/4. The city passes a zoning law requiring both vendors to relocate closer to the center of the street. How will this impact competition, and thus, prices?