Intermediate microeconomics
Professor
Yongmin Chen
Markets differ in two important dimensions: the number of sellers and the nature of product differentiation. With many firms producing a homogeneous product, we have a perfectly competitive market. With a single firm, the market becomes a monopoly. Between these two extremes are markets with a small number of firms (oligopoly), markets with a dominant firm, and markets with many differentiated-products producers (monopolistic competition).
The Cournot model is the classical model to study a market with a small number of firms competing in a homogeneous-product market.
Suppose that two firms, named A and B, are competing in choosing quantities. Suppose the market demand curve is Q = 100 - p, and each firm's marginal cost is 1. Each firm takes the other firm's output as given, and chooses its own output to maximize its profit. What is the equilibrium in this game?
Suppose A's output is q, and B's output is g, then market price would be 100 - (q+g). A's total revenue, when it produces q, given B is producing g, is
RA = q[100-(q+g)].
A's marginal revenue is
MRA = 100 - g - 2q
To be optimal for A, given B's output, A chooses its output so that marginal revenue equals marginal cost:
100 - g - 2q = 1.
Thus, A's optimal output is a function of B's output, and is given by
q(g) = (99 - g)/2
This function is called A's reaction function. Its curve is called the reaction curve.
Now firm B should set its output in a similar way. Given A's output q, B's marginal revenue is
MRB = 100 - q - 2g.
To be optimal, B also sets its output so that marginal revenue equals marginal cost, that is,
100 - q - 2g = 1.
Firm B's reaction function is thus
g(q) = (99 - q)/2.
In equilibrium, each firm should correctly anticipate what the other firm would do, and therefore should set q = q(g), and g = g(q). That is
q = (99 -g)/2
g = (99 -q)/2
The solutions to the two equations above, or the interception point of the two reaction curves, q = g = 33, are the equilibrium output of the two firms.
If firms choose their prices in stead of quantities, the model is called the Bertrand competition. (As you will see, it matters whether firms choose prices or quantities in oligopoly, while it does not matter for a monopolist.)
Comparison of outputs under perfect competition, Cournot competition, and monopoly.
Suppose again that the market demand curve is Q = 100 - p, and each firm's marginal cost is 1. The two firms independently and simultaneously name their prices. The equilibrium in this case is that both firms will choose p = 1, or price equals to marginal cost. Why?
If the market consists of a dominant firm and some fringe firms, we have a dominant firm model. Each fringe firm acts as price takers, while the dominant firm chooses its price (output). The dominant firm faces a residual demand curve, and chooses price (or quantity) so that its marginal revenue is equal to marginal cost.
See a graphical analysis in class.
In reality, firms often produce differentiated products. There can be two types of production differentiation: horizontal differentiation and vertical differentiation. For instance, two grocery stores located at two different sides of a town are differentiated, an example of horizontal product differentiation; and a French restaurant and a fast-food restaurant are differentiated, an example of vertical product differentiation.
With product differentiation, firms will have some market power and are generally able to charge prices above marginal cost.
Monopolistic Competition
Monopolistic competition is a market structure where there are a large number of firms producing differentiated products and where there are features of both monopoly and perfect competition. Since each firm's product is differentiated from other firms', each firm has some monopoly power. On the other hand, since the number of firms in the industry is sufficiently large, each firm's action has no effect on how other firms behavior.
Because each firm's product is somewhat different from other firms', each firm's demand curve is downward sloping instead of horizontal (i.e., each firm has some monopoly power). Thus, each firm's marginal revenue curve is below its demand curve, and marginal revenue is lower than price. To maximize profit, each firm sets price (or output) such that marginal revenue is equal to marginal cost.
The position of a firm's demand curve depends on the number of firms in the industry. As more firms enter the industry, each firm's demand curve shifts to the left. And as firms exit the industry, each firm's demand curve shifts to the right. In the long-run, no firm makes positive economic profit (notice that this is a feature of perfect competition), and each firm will produce at the point where its demand curve is tangent to its average cost curve.
Therefore, under monopolistic competition, firms need not produce at their minimum cost point even in the long run. The scale of each firm is too small to minimize cost. This is an inefficiency associated with monopolistic competition. On the other hand, there are certain social benefits from varieties. Compared to perfect competition, monopolist competition tends to result in higher price and lower output. Compared to monopoly, monopolist competition tends to result in lower price and higher output.
Measurement of Monopoly Power
A firm's market power is often measured by its ability to price above marginal cost. An often used measure is called Lerner index:
L = (p - MC)/p
A higher Lerner index means higher monopoly power. For firms in a purely competitive market, the Lerner index is zero.
It is often believed that the more the market is concentrated, the higher each firm's monopoly power will be. To measure the degree of market concentration, the indicators often used are:
4-firm concentration ratio: the sum of the market shares of the four largest firms in the industry.
Herfindahl index: The sum of squares of market shares of all firms.
Example 9-3: Suppose an industry consists of 14 firms and industry output is 1000. The largest four firms each produces 150. The rest 10 firms each produces 40. What are the 4-firm concentration ratio and the Herfindahl index?
It is often difficult for the government to know how much firms are pricing above marginal cost, but it is easy to know 4-firm concentration ratio or Herfindahl index. Therefore these two indicators are often used in anti-trust cases and government regulation.