Oligopoly

Perloff 13.4-5; WB 19, 20.
We examine behavior in an oligopoly — a market with a small number of firms — and compare the equilibrium price markups and welfare to the market structures we studied earlier, perfect competition and monopoly.

We study two models, called Cournot and Stackelberg, in which firms choose how much to produce. In the latter, one firm “moves” first. We will use game theory to solve these models.

As emphasized earlier, firms do not only choose how much to produce, but also whether to produce or shut down. This important issue does not come up in the models considered here because there are no fixed costs; we will return to it later.

# Cournot oligopoly

When choosing how much to produce, Cournot oligopolists set MC = MR like any other firm. Like monopolists, each oligopolist faces a downward-sloping Marginal Revenue curve.

Unlike monopoly, each firm's MR curve is shifted by the other firms' output choices. In the Cournot equilibrium, every firm will take this fact into account when making its own output choice.

### Duopoly analysis

There are two firms with identical marginal costs and no fixed costs.

• Find the equilibrium quantities produced by each firm, q1C and q2C and the equilibrium price PC.

### Welfare

• Find the dead weight loss of the duopoly.

### Markup

The Lerner Index is $LI^C=\frac{P^C-MC}{P^C}$. For a Cournot oligopoly with n firms, we have $LI=1/n|\varepsilon|$, so that monopoly is the special case where n = 1; and perfect competition occurs in the limit as n goes to infinity.

• Compute the duopolists' Lerner Index.

# Stackelberg duopoly

The situation is the same as for Cournot duopoly, but now firm 1 can move first, committing to its output choice. Because it could commit to the Cournot equilibrium quantity, firm 1 is at least as well off as in Cournot.

• Find the equilibrium of the Stackelberg game q1S,q2S,PS.

# Bertrand oligopoly

Firms set prices, and the quantity each firm sells is determined by Demand. In the Bertrand equilibrium, each firm will take into account other firms' prices when setting its own price.

### Identical goods

If all firms face the same Demand, then a firm can only make a profit by under-cutting its opponents' prices. This price competition drives the price down to the marginal cost of the second-best firm. Thus, if two or more firms have identical costs, all profits are zero.

This theoretical result — low or zero profits even when there are few firms — is called the Bertrand paradox. Firms can get around it by fixing prices; or working to keep competitors out of the market.

### Differentiated goods

Economists can get around the paradox by changing an assumption. If we assume that firms have different products, then they face different Demand curves and can afford to set different prices.

This approach has been useful in empirical work, and proceeds as follows. First, we estimate the Demand curve for each good, by running a regression on the prices of all goods and allowing for product differentiation. From Demand, we find Marginal Revenue for each firm. And finally, setting MC = MR for each firm, we find the firms' optimal price/quantity.

The first step, estimating Demand, requires some strong assumptions on consumer preferences. Typically, we assume that consumers buy goods for their observable characteristics. For example, a car with one more horsepower is worth \$500 more dollars to the consumer. This is a hedonic approach to Demand.

An alternative empirical approach to the hedonic-Demand-with-Bertrand-Supply model is the Monopolistic Competition model. Competitive Monopoly differs in that (i) there is free entry, so it is not an oligopoly model, and (ii) there are different but equally strong assumptions on Demand (“preference for variety” and a constant “elasticity of substitution”).

# Market power and market concentration

(This section is based on the FTC discussion paper linked below.) Antitrust authorities want to protect consumers and small firms from the market power of large firms. There are several problems with the LI as a tool for achieving this.

It may be difficult to measure firms' marginal costs (and sometimes even to measure the prices the firm charges); as a result, calculating the markup/LI is also hard. A high markups by a small firm does not harm consumers as much as a high markup by a large firm, but the LI does not distinguish between these two cases. And finally, high markups may reflect a high-quality product and not a lack of competition.

The Dead Weight Loss may seem like an attractive alternative, but it requires even more careful measurement — not just of marginal costs and prices but of the entire MC and Demand curves.

In practice, antitrust authorities often measure a firm's market power by comparing its share of total industry sales to other firms' shares. Unlike marginal costs, sales data are available to government agencies. Two common measures are the k-firm concentration ratio, which is the combined share of sales for the k largest firms; and the Hirschman-Herfindahl Index (HHI) which is calculated as the sum of each firm's share squared.