MicroEconomics 5e by besanko braeutigam chapter 13

Definition: The relationship between the price charged by firm i and the demand firm i faces is firm is residual demand In other words, the residual demand of firm i is the market demand

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Chapter Thirteen Overview

1. Introduction: Cola Wars

2. A Taxonomy of Market Structures

3. Monopolistic Competition

4. Oligopoly – Interdependence of Strategic Decisions

5. The Effect of a Change in the Strategic Variable

6. The Effect of a Change in Timing: Stackelberg Equilibrium

1. Introduction: Cola Wars

2. A Taxonomy of Market Structures

3. Monopolistic Competition

4. Oligopoly – Interdependence of Strategic Decisions

• Bertrand with Homogeneous and Differentiated Products

5. The Effect of a Change in the Strategic Variable

• Theory vs Observation

• Cournot Equilibrium (homogeneous)

• Comparison to Bertrand, Monopoly

• Reconciling Bertrand, and Cournot

6. The Effect of a Change in Timing: Stackelberg Equilibrium

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Market Structures

• The number of sellers

• The number of buyers

• Entry conditions

• The number of sellers

• The number of buyers

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Product Differentiation

Definition: Product Differentiation between two or more products

exists when the products possess attributes that, in the minds of consumers, set the products apart from one another and make them less than perfect substitutes.

Examples: Pepsi is sweeter than Coke, Brand Name batteries last longer than "generic" batteries.

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Product Differentiation

• "Superiority" (Vertical Product Differentiation) i.e one product is viewed as unambiguously better than another so that, at the same price, all consumers would buy the better product

• "Substitutability" (Horizontal Product Differentiation) i.e at the same price, some consumers would prefer the characteristics of product A while other consumers would prefer the characteristics of product B.

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Types of Market Structures

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Assumptions:

• Many Buyers and Few Sellers

• Each firm faces downward-sloping demand because each is a large producer compared to the total market size

• There is no one dominant model of oligopoly We will review

several.

Assumptions:

• Many Buyers and Few Sellers

• Each firm faces downward-sloping demand because each is a large producer compared to the total market size

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Price adjusts according to demand.

Residual Demand: Firm i's guess about its rival's output determines its residual demand.

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Simultaneously vs Non-cooperatively

Definition : Firms act simultaneously if each firm makes its strategic

decision at the same time, without prior observation of the other firm's decision.

Definition: Firms act non-cooperatively if they set strategy independently,

without colluding with the other firm in any way

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Definition: The relationship between the price charged by firm i and

the demand firm i faces is firm is residual demand

In other words, the residual demand of firm i is the market demand

minus the amount of demand fulfilled by other firms in the market:

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Residual Demand when q2 = 10

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Best Response Function:

The point where (residual) marginal revenue equals marginal cost gives the best response of firm i to its rival's

(rivals') actions

For every possible output of the rival(s), we can determine firm i's best response The sum of all these points

makes up the best response (reaction) function of firm i

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Reaction Function of Firm 1

Reaction Function of Firm 2

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What is the equation of firm 1's reaction function?

Firm 1's residual demand:

• P = (100 - Q2) - Q1

• MRr = 100 - Q2 - 2Q1

• MRr = MC  100 - Q2 - 2Q1 = 10

• Q1r = 45 - Q2/2 firm 1's reaction function

• Similarly, one can compute that

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Bertrand Oligopoly (homogeneous)

*Definition: In a Bertrand oligopoly, each firm sets

its price, taking as given the price(s) set by other firm(s), so as to maximize profits.

*Definition: In a Bertrand oligopoly, each firm sets its price, taking as given the price(s) set by other firm(s), so as to maximize profits.

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• Homogeneity implies that consumers will buy from the low-price seller.

• Further, each firm realizes that the demand that it faces depends both on

its own price and on the price set by other firms

• Specifically, any firm charging a higher price than its rivals will sell no output.

• Any firm charging a lower price than its rivals will obtain the entire market

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Residual Demand Curve – Price Setting

• Assume firm always meets its residual demand (no capacity constraints)

• Assume that marginal cost is constant at c per unit.

• Hence, any price at least equal to c ensures non-negative profits.

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Best Response Function

Each firm's profit maximizing response to the other firm's price is to undercut (as long as P >

MC)

Definition: The firm's profit maximizing action as a function of the action by the rival firm is

the firm's best response (or reaction) function

Example:

2 firmsBertrand competitors

Firm 1's best response function is P1=P2- eFirm 2's best response function is P2=P1- e

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Where does this stop? P = MC (!)

If we assume no capacity constraints and that all firms have the same constant average and marginal cost of c then:

For each firm's response to be a best response to the other's each firm must undercut the other as long as P> MC

Where does this stop? P = MC (!)

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1 Firms price at marginal cost

2 Firms make zero profits

3 The number of firms is irrelevant to the price level as long as more than one firm is present: two firms is enough to replicate the perfectly competitive outcome.

Essentially, the assumption of no capacity constraints combined with a constant average and marginal cost takes the place of free entry.

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Stackelberg model of oligopoly is a situation in which one firm acts as a quantity leader, choosing its quantity first, with all

other firms acting as followers.

Call the first mover the “leader” and the second mover the “follower”

The second firm is in the same situation as a Cournot firm: it takes the leader’s output as given and maximizes profits accordingly, using its residual demand.

The second firm’s behavior can, then, be summarized by a Cournot reaction function.

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A single company with an overwhelming market share (a dominant firm) competes against many small producers (competitive fringe), each of whom has a small market share.

Limit Pricing – a strategy whereby the dominant firm

keeps its price below the level that maximizes its current profit in order to reduce the rate of expansion by the fringe.

Dominant Firm Markets

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Bertrand Competition – Differentiated

Assumptions:

Firms set price*

Differentiated product Simultaneous

Non-cooperative

*Differentiation means that lowering price below your rivals' will not result in capturing the entire market, nor will raising price mean losing the entire market so that residual demand decreases smoothly

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Coke’s Price

MR0

Pepsi’s price = $0 for D0 and $10 for D10

100

Residual Demand, Price Setting, Differentiated Products

Each firm maximizes profits based on its residual demand by setting MR (based on residual demand) =

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100

D0 D10

Key Concepts

MCCoke’s Price

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MCCoke’s Price

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D10 MR10

110

100

Key Concepts

MCCoke’s Price

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MCCoke’s Price

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Key Concepts

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Key Concepts

Each firm maximizes profits based on its residual demand by setting MR (based on

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And, using the demand curve, we have:

• P1 = 50 + P2/2 - 45/2 - P2/4 or

• P1 = 27.5 + P2/4 the reaction function

And, using the demand curve, we have:

• P1 = 50 + P2/2 - 45/2 - P2/4 or

• P1 = 27.5 + P2/4 the reaction function

Key Concepts

Each firm maximizes profits based on its residual demand by setting MR (based on

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Pepsi’sPrice (P2)

Coke’s Price (P1)

P2 = 27.5 + P1/4 (Pepsi’s R.F.)

27.5

Equilibrium and Reaction Functions

Price Setting and Differentiated Products

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P2 =

Bertrand Equilibrium

27.5

Pepsi’sPrice (P2)

Coke’s Price (P1)

P2 = 27.5 + P1/4

(Pepsi’s R.F.)

P1 = 27.5 + P2/4

(Coke’s R.F.)

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Equilibrium occurs when all firms simultaneously choose their best response to each others' actions

Graphically, this amounts to the point where the best response functions cross.

Equilibrium occurs when all firms simultaneously choose their best response to each others' actions

Graphically, this amounts to the point where the best response functions cross.

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Example: Firm 1 and Firm 2, continued

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Profits are positive in equilibrium since both prices are above marginal cost!

Even if we have no capacity constraints, and constant marginal cost, a firm cannot capture all demand by cutting price

This blunts price-cutting incentives and means that the firms' own behavior does

Profits are positive in equilibrium since both prices are above marginal cost!

Even if we have no capacity constraints, and constant marginal cost, a firm cannot capture all demand by cutting price

This blunts price-cutting incentives and means that the firms' own behavior does

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The reaction functions slope upward: "aggression =>

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Cournot, Bertrand, and Monopoly Equilibriums

P > MC for Cournot competitors, but P < PM:

If the firms were to act as a monopolist (perfectly collude), they would set market MR equal

to MC:

• P = 100 - Q

• MC = AC = 10

• MR = MC => 100 - 2Q = 10 => QM = 45

• PM = 55

• ΠM= 45(45) = 2025

P > MC for Cournot competitors, but P < PM:

If the firms were to act as a monopolist (perfectly collude), they would set market MR equal

to MC:

• P = 100 - Q

• MC = AC = 10

• MR = MC => 100 - 2Q = 10 => QM = 45

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A perfectly collusive industry takes into account that an increase in output by one firm depresses the profits of the other

firm(s) in the industry A Cournot competitor takes into account the effect of the increase in output on its own profits only

Therefore, Cournot competitors "overproduce" relative to the collusive (monopoly) point Further, this problem gets

"worse" as the number of competitors grows because the market share of each individual firm falls, increasing the

difference between the private gain from increasing production and the profit destruction effect on rivals

Therefore, the more concentrated the industry in the Cournot case, the higher the price-cost margin

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Homogeneous product Bertrand resulted in zero profits, whereas the Cournot case resulted in positive profits Why?

The best response functions in the Cournot model slope downward In other

words, the more aggressive a rival (in terms of output), the more passive the Cournot firm's response

The best response functions in the Bertrand model slope upward In other

words, the more aggressive a rival (in terms of price) the more aggressive the Bertrand firm's response

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Cournot: Suppose firm j raises its output…the price at which firm i can

sell output falls This means that the incentive to increase output falls as the output of the competitor rises.

Bertrand: Suppose firm j raises price the price at which firm i can sell

output rises As long as firm's price is less than firm's, the incentive to

increase price will depend on the (market) marginal revenue.

Cournot: Suppose firm j raises its output…the price at which firm i can

sell output falls This means that the incentive to increase output falls as the output of the competitor rises.

Bertrand: Suppose firm j raises price the price at which firm i can sell

output rises As long as firm's price is less than firm's, the incentive to

increase price will depend on the (market) marginal revenue.

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Chamberlinian Monopolistic Competition

Market Structure

• Many Buyers

• Many Sellers

• Free entry and Exit

• (Horizontal) Product Differentiation

When firms have horizontally differentiated products, they each face downward-sloping demand for their product

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1 Each firm is small each takes the observed "market price" as given in its production decisions.

2 Since market price may not stay given, the firm's perceived demand may differ from its actual demand.

3.If all firms' prices fall the same amount, no customers switch supplier but the total market consumption grows

4 If only one firm's price falls, it steals customers from other firms as well as

increases total market consumption

Monopolistic Competition – Short Run

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Perceived vs Actual Demand

Demand assuming no price matching

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Market Equilibrium

The market is in equilibrium if:

• Each firm maximizes profit taking the average

market price as given

• Each firm can sell the quantity it desires at the

actual average market price that prevails

The market is in equilibrium if:

• Each firm maximizes profit taking the average

market price as given

• Each firm can sell the quantity it desires at the

actual average market price that prevails

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d (PA=50)

Demand (assuming price matching by all firms P=PA)

Demand assuming no price matching

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d (PA=50)

Demand (assuming price matching by all firms P=PA)

Demand assuming no price matching

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Short Run Monopolistically Competitive Equilibrium

Computing Short Run Monopolistically Competitive Equilibrium

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A What is the equation of d40? What is the equation of D?

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Inverse Perceived Demand

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D What is the short run equilibrium price in this industry?

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Monopolistic Competition in the Long Run

At the short run equilibrium P > AC so that each firm may make positive profit

Entry shifts d and D left until average industry price equals average cost

At the short run equilibrium P > AC so that each firm may make positive profit

Entry shifts d and D left until average industry price equals average cost

This is long run equilibrium is represented graphically by:

MR = MC for each firm

D = d at the average market price

d and AC are tangent at average market price W

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