Activity 3 - Managerial Economics
voyage
Baye_9e_Chapter_09.pptxBasic Oligopoly Models
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Chapter 9
Learning Objectives
Explain how beliefs and strategic interaction shape optimal decisions in oligopoly environments.
Identify the conditions under which a firm operates in a Sweezy, Cournot, Stackelberg, or Bertrand oligopoly, and the ramifications of each type of oligopoly for optimal pricing decisions, and firm profits.
Apply reaction (or best-response) functions to identify optimal decisions and likely competitor responses in oligopoly settings.
Identify the conditions for a contestable market, and explain the ramifications for market power and the sustainability of long-run profits.
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Conditions for Oligopoly
Oligopoly market structures are characterized by only a few firms, each of which is large relative to the total industry.
Typical number of firms is between 2 and 10.
Products can be identical or differentiated.
An oligopoly market composed of two firms is called a duopoly.
Oligopoly settings tend to be the most difficult to manage since managers must consider the likely impact of his or her decisions on the decisions of other firms in the market.
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Conditions for Oligopoly
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Strategic Interaction: A Firm’s Demand Depends on Actions of Rivals
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Role of Beliefs and Strategic Interaction
Output
Price
0
Demand1
Demand2
C
A
B
Demand if rivals
match price changes
Demand if rivals do not
match price changes
4
Sweezy Oligopoly
Sweezy oligopoly characteristics:
There are few firms in the market serving many consumers.
The firms produce differentiated products.
Each firm believes its rivals will cut their prices in response to a price reduction but will not raise their prices in response to a price increase.
Barriers to entry exist.
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Profit Maximization in Four Oligopoly Settings
5
Sweezy Oligopoly
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Output
Price
0
MR2
Demand2
(rival matches price change)
A
B
MC1
MR1
MC0
Demand1
(rival holds price constant)
F
E
C
MR
Sweezy Demand
Profit Maximization in Four Oligopoly Settings
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Cournot Oligopoly
Cournot oligopoly characteristics
There are few firms in the market serving many consumers.
The firms produce either differentiated or homogeneous products.
Each firm believes rivals will hold their output constant if it changes its output.
Barriers to entry exist.
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Profit Maximization in Four Oligopoly Settings
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Cournot Oligopoly: Reaction Functions
Consider a Cournot duopoly. Each firm makes an output decision under the belief that is rival will hold its output constant when the other changes its output level.
Implication: Each firm’s marginal revenue is impacted by the other firms output decision.
The relationship between each firm’s profit-maximizing output level is called a best-response or reaction function.
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Profit Maximization in Four Oligopoly Settings
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Cournot Oligopoly: Reaction Functions Formula
Given a linear (inverse) demand function
and cost functions,
the reactions functions are:
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Profit Maximization in Four Oligopoly Settings
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Cournot Reaction Functions
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Quantity2
Quantity1
Firm 2’s Reaction Function
Firm 1’s Reaction Function
Cournot equilibrium
A
B
C
D
Profit Maximization in Four Oligopoly Settings
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Cournot Oligopoly: Equilibrium
A situation in which neither firm has an incentive to change its output given the other firm’s output.
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Profit Maximization in Four Oligopoly Settings
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Cournot Oligopoly: Isoprofit Curves
A function that defines the combinations of outputs produced by all firms that yield a given firm the same level of profits.
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Profit Maximization in Four Oligopoly Settings
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Isoprofit Curves for Firm 1
Every point on a given isoprofit curve yields Firm 1 the same level of profits.
Isoprofits curves tat lie closer to Firm 1’s monopoly output are associated with higher profits for that firm.
The isoprofit curves for Firm 1 reach their peak where they intersect Firm 1’s reaction function.
The isoprofit curves do not interest one another.
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Profit Maximization in Four Oligopoly Settings
Firm 1’s Best Response to Firm 2’s Output
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Quantity2
Quantity1
A
B
Firm 1’s profit increases as isoprofit
curves move toward
(Firm 1’s reaction function)
C
Profit Maximization in Four Oligopoly Settings
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Quantity2
Quantity1
Firm 2’s profit increases as isoprofit
curves move toward
Firm 2’s Reaction Function and Isoprofit Curves
Monopoly point for firm 2
(Firm 2’s reaction function)
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Profit Maximization in Four Oligopoly Settings
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Quantity2
Quantity1
Cournot Equilibrium
Cournot Equilibrium
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Profit Maximization in Four Oligopoly Settings
Quantity2
Quantity1
Effect of Decline in Firm 2’s Marginal Cost on Cournot Equilibrium
Due to decline in
firm 2’s marginal cost
F
E
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Profit Maximization in Four Oligopoly Settings
Cournot Oligopoly: Collusion
Markets with only a few dominant firms can coordinate to restrict output to their benefit at the expense of consumers.
Restricted output leads to higher market prices.
Such acts by firms is known as collusion.
Collusion, however, is prone to cheating behavior.
Since both parties are aware of these incentives, reaching collusive agreements is often very difficult.
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Profit Maximization in Four Oligopoly Settings
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Incentive to Collude in a Cournot Oligopoly
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Quantity2
Quantity1
Collusion outcome
Profit Maximization in Four Oligopoly Settings
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Incentive to Renege on Collusive Agreements in Cournot Oligopoly
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Quantity2
Quantity1
Profit Maximization in Four Oligopoly Settings
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Stackelberg Oligopoly
Stackelberg oligopoly characteristics:
There are few firms serving many consumers.
Firms produce either differentiated or homogeneous products.
A single firm (the leader) chooses an output before all other firms choose their outputs.
All other firms (the followers) take as given the output of the leader and choose outputs that maximize profits given the leader’s output.
Barriers to entry exist.
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Profit Maximization in Four Oligopoly Settings
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Stackelberg Equilibrium
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Quantity Follower
Quantity Leader
Profit Maximization in Four Oligopoly Settings
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Stackelberg Oligopoly: Equilibrium Output Formulae
Given a linear (inverse) demand function
and cost functions and .
The follower sets output according to the reaction function
The leader’s output is
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Profit Maximization in Four Oligopoly Settings
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Stackelberg Oligopoly In Action: Problem
Suppose the inverse demand function for two firms in a homogeneous-product, Stackelberg oligopoly is given by
and their costs are $2. Firm 1 is the leader, and firm 2 is the follower.
What is firm 2’s reaction function?
What is firm 1’s output?
What is firm 2’s output?
What is the market price?
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Profit Maximization in Four Oligopoly Settings
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Stackelberg Oligopoly In Action: Answer
The follower’s reaction function is: .
The leader’s output is: .
The follower’s output is: .
The market price is: .
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Profit Maximization in Four Oligopoly Settings
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Bertrand Oligopoly
Bertrand oligopoly characteristics
There are few firms in the market serving many consumers.
Firms produce identical products at a constant marginal cost.
Firms engage in price competition and react optimally to prices charged by competitors.
Consumers have perfect information and there are no transaction costs.
Barriers to entry exist.
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Profit Maximization in Four Oligopoly Settings
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Bertrand Oligopoly: Equilibrium
The conditions for a Bertrand oligopoly imply that firms in this market will undercut one another to capture the entire market leaving the rivals with no profit. All consumers will purchase at the low-price firm.
This “price war” would come to an end when the price each firm charged equaled marginal cost.
In equilibrium, .
Socially efficient level of output.
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Profit Maximization in Four Oligopoly Settings
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Comparing Oligopoly Models
Consider the following inverse market demand function:
and the cost function for each firm in this market is identical, and given by
Under these condition, the different oligopoly outputs, prices and profits are examined.
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Comparing Oligopoly Models
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Comparing Oligopoly: Cournot
The Cournot oligopoly reaction functions are
These reaction functions can be solved for the equilibrium output. These quantities can be used to compute price and profit.
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Comparing Oligopoly Models
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Comparing Oligopoly: Stackelberg
The Stackelberg leader’s output is
The market price is:
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Comparing Oligopoly Models
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Comparing Oligopoly: Bertrand
Since , .
Total output is found by:
Solving yields:
Given symmetric firms, each firm gets half the market, or 498 units.
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Comparing Oligopoly Models
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Comparing Oligopoly: Collusion
Since the output associated with collusion is the same as monopoly output, the inverse market demand function implies that monopoly marginal revenue function is:
Setting marginal revenue equal to marginal cost yields:
Solving this: units. Each firm will produce half of these units.
Price is:
Each firm earns profits of .
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Comparing Oligopoly Models
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Contestable Markets
Contestable markets involve strategic interaction among existing firms and potential entrants into a market.
A market is contestable if:
All producers have access to the same technology.
Consumers respond quickly to price changes.
Existing firms cannot respond quickly to entry by lowering price.
There are no sunk costs.
If these conditions hold, incumbent firms have no market power over consumers.
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Contestable Markets
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