©2005, Southwestern

Slides by Pamela L. Hall

Western Washington University

Industrial Organization

Chapter 15

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Introduction Firms with some degree of monopoly power can control their

product price and influence their output by advertising and differentiating their product Resulting enhanced profit is not necessarily caused by advertising and

product differentiation• Profits may be high because product coincidentally was offered in right

place at right time However, in general, improvements in effective marketing can boost profit

significantly

Marketing efficiency of a firm may be characterized in terms of attempting to satisfy customer preferences by Acquiring information on these preferences Determining competing firms’ strategies Efficiently allocating marketing resources

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Introduction Applied economists are actively working

Either within firms or As consultants to provide empirical analysis on marketing efficiency

• For example, economists provide Market share movement analysis Mapping of alternative marketing strategies Sales force size and productivity determination Advertising expenses and mix optimization Sales analysis and targeting

Economic consulting firms will develop a quantitative measure of alternative marketing strategies Provide scores indicating which strategy action yields most profit

enhancement• Scores can be used by a firm’s management to allocate resources where largest

payoff in terms of profits will occur Management will then attempt to equate marginal revenue with marginal cost in

marketing its output

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Introduction Degree of monopoly power and how firms interact determine strategies

offered by applied economists Alternative economic models for developing strategies are employed

• Based on degree of monopoly power and firm interactions

For determining economic efficiency, we contrast imperfectly competitive models of firm behavior with perfectly competitive and monopoly models Standard for judging imperfectly competitive markets is perfect competition

• Which is Pareto efficient Equilibrium occurs where price equals marginal cost

Firms operate at full capacity

However, there are some desirable features of imperfect competition• Consumers may desire firms to product differentiate, advertise, and innovate

All of which have limits under perfect competition

Under perfect competition, characteristics of homogeneous products and perfect knowledge preclude firms from advertising and innovating

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Introduction Aim in this chapter

Investigate how price, output, sales promotion, and product differentiation are determined under various market conditions

We begin with product differentiation Present a model to determine optimal level of product differentiation and advertising (selling

expenses) Assess advertising for its information versus persuasive characteristics We examine classical models of monopolistic competition and oligopolies

Cournot model assumes firms do not realize that their individual output decisions affect output decisions of their competitors

Stackelberg model--one firm realizes interdependence of output decisions and determines its optimal output decision based on this

• Also consider Stackelberg disequilibrium Each firm realizes output interdependence but believes other firms do not

Bertrand model assumes firms compete in terms of price rather than through output• We contrast these with Cournot conditions

We investigate economics of collusion in oligopoly markets We briefly discuss formal cartel arrangements and legal provisions

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Product Differentiation Wide range of product differentiation offers consumers a great deal of choice

in determining their optimal selection For example, toothbrushes

Demand for product differentiation is derived by consumers receiving some level of utility for having products differentiated Firms respond to this demand by differentiating their products

• Possibly by quality and style, guarantees and warranties, services provided, location of sales

Product differentiation by firms may be either real or imaginary• How differentiated a product is in the eyes of the beholder

Heterogeneous nature of products due to differentiation provides firms with some degree of monopoly power Individual firms face a downward-sloping demand curve for their product No longer a market with firms producing identical products

• A group of firms are producing a number of closely-related but not identical products Law of One Price for a market no longer exists

Replaced with each firm having a partial monopoly and setting its own price

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Advertising (Selling Cost) Selling costs (also called information differentiation) are marketing

expenditures Include advertising, merchandising, sales promotion, and public relations

• Designed to adapt buyer to product

Distinguishes them from production costs• Designed to adapt product to buyer

Firms advertise to shift market demand for their commodity upward Increases market share and short-run pure profits

A firm’s advertising objective Convince consumers that its product is not sharply different from competing

products • Yet is somehow superior

When deciding on optimal strategy to pursue, a firm will weigh Additional revenues generated by shifts in demand curve against cost of

differentiating its product

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Maximizing Profit Assume costs and revenue depend on

Đdollar measure of extent of product differentiation Ameasure of advertising expenditures qoutput

Objective of firm is to maximize profit

F.O.C.s are

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Maximizing Profit For profit maximization, marginal revenue from each activity must equal marginal

cost for that activity For example, a firm will produce additional advertising messages up to point at which

the marginal revenue from additional demand generated by a message is equal to message’s marginal cost

• Messages that spark greatest reaction from consumers will receive a larger share of expenditures

Firms generally engage in both product differentiation and advertising Indicates at least some positive increment to profit for these two activities Advertising services is a major industry within U.S.

• Accounts for 2% to 3% of GNP

Determining marginal revenue for each activity is difficult Market for advertising messages is not separate from market for commodity

• For example, beer is a joint product where beer and advertising for beer are both produced

Firms that do not account for joint production and contribute all of any increase in revenue to advertising will overinvest in advertising Must remember that commodity itself has some value

• Some individuals will consume product regardless of level of advertising

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Maximizing Profit Marginal revenue being generated by advertising reflects consumers’

willingness-to-pay for Commodities being purchased Information provided by advertising

In terms of product differentiation, firms will differentiate their products to soften price competition By differentiating their products firms can possibly satisfy a market niche and

create monopoly power with potential of increasing profit However, firms generally do not seek maximum level of product

differentiation Instead, they offer products that are not too different from their competitors’

products yet have some unique features• Idea of not maximizing product differentiation is related to Law of the Obvious

Better to be a half-step ahead and understood than a whole step ahead and ignored

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Assessing Advertising In general, it is not possible to determine overall social value or

loss associated with advertising Advertising is not a composite commodity where prices associated

with all forms of advertising move together Empirical evidence on precise effect of advertising in general is not available

An economic assessment is only undertaken when advertising is disaggregated across types and commodities Such disaggregation has yielded some general implications

• Advertising can affect consumer choices among commodities that are close substitutes

But it may or may not have any effect on overall consumption choices For example, cigarette advertising can have a major effect on consumers’ choice

of brands However, there is little evidence that cigarette advertising has increased demand

for cigarettes among adults

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Assessing Advertising Two major types of advertising

Informational Persuasive

Informational advertising educates consumers Provides information on product price, location, and characteristics Can make markets more efficient by

• Reducing consumers’ search costs

• Enabling them to make rational choices

Informational advertising is generally found in newspapers Such as weekly grocery ads

• By familiarizing consumers with products, this type of advertising broadens market for commodities

Results in economies of scale and more efficient markets

Advertising also encourages competition by Exposing consumers to competing products Enabling firms to gain market acceptance for new products more rapidly than they

could without advertising

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Assessing Advertising Persuasive advertising

Firm is attempting to modify consumers’ preferences by creating wants • Little information concerning product is generally provided

Television advertising is generally persuasive Can encourage artificial product differentiation among

commodities that are physically similar Persuasive advertising among competing firms tends to have a

canceling effect (examples are colas and detergents)• Duplication of effort results in wasted resources, inefficiencies, higher

production costs, and higher prices

Also facilitates concentration of monopoly power Large firms can usually afford continuous heavy advertising whereas

new or smaller firms cannot

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Assessing Advertising National Advertising Division of the Council of Better Business Bureaus was created

by advertising industry in 1971 to Provide a system of voluntary self-regulation Minimize government intervention Foster public confidence in credibility of advertising

Advertisers, advertising agencies, and consumers rely on this division to maintain high standards of principles in advertising By 2001, over 3200 advertising cases had been successfully handled through this self-

regulatory process• Has reduced inefficiencies associated with advertising

• Mitigated pressure for government regulation

A problem with any type of regulation is determining what is true and false in advertising and who should determine it Documentation supporting advertising claims and litigation costs associated with

regulation may increase product price Laws governing regulation must be enforced

Requires government appropriations

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Monopolistic Competition Monopolistic competition (first described by Edward H. Chamberlin in 1933) is a

market structure characterized by Product differentiation Relatively large number of firms Easy entry into market

• Examples include service stations, convenience stores, and fast-food franchises

Key difference between perfect competition and monopolistic competition Product differentiation is in the eye of the beholder (buyer)

Monopolistically competitive firms produce similar but not identical products with relatively easy entry into industry Products may be differentiated only by brand name, color of package, location of the

seller, customer service, or credit conditions• Results in each firm having a partial monopoly of its own differentiated product

Possible to have wide differences among firms in price, output, and firm profit

• Because each firm has a partial monopoly, each firm has its own output demand curve Demand curves are downward sloping

Indicates a seller can increase its price without losing all of its sales

• No industry supply curve

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Monopolistic Competition Concept of an industry becomes somewhat clouded and vague in

monopolistic competition as a result of product differentiation Instead a product group exists

• Products of competitors are close but not perfect substitutes

Elasticity will vary inversely with degree of product differentiation The smaller the degree of product differentiation and greater the number

of sellers Closer market will be to perfect competition

In contrast to perfect competition, sellers under monopolistic competition can Vary nature of their product Employ product promotion Change their output to influence profit

• Makes monopolistic-competition model very useful for describing decentralized allocations in presence of producing with excess capacity

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Monopolistic Competition

A monopoly produces with excess capacity but, unlike monopolistic competition, allocation decisions are centralized into one firm In contrast, perfectly competitive allocation decisions are

decentralized into many firms However, perfectly competitive firms are operating at

minimum point of long-run average cost • Are at full (rather than excess) capacity

Monopolistic competition focuses market implications of operating with excess capacity without worry of strategic interactions among firms

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Short- and Long-Run Equilibrium under Monopolistic Competition Long-run equilibrium position for a monopolistically

competitive firm is illustrated in Figure 15.1 Given large number of firms, effect from a firm’s change in

output on price of any particular competitor is negligible Firm acts as if its actions have no effect upon its competitors

• Results in Qd demand curve Competitors’ prices remain fixed

However, a firm’s individual profit-maximizing decisions will be replicated by all other firms within this market Causing a change in total output beyond its small output change

• Effective demand curve is QD

Firm’s competitors’ prices do change

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Figure 15.1 Long-run equilibrium for a monopolistically competitive firm

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Short- and Long-Run Equilibrium under Monopolistic Competition With all other firms changing their output

At a particular price firm will not sell expected level of output based on Qd demand curve

Instead, firm will sell lesser output associated with QD curve Since response of price to an output change by one firm will be less

when all other prices are fixed QD demand curve will be more inelastic than Qd curve

For profit maximization, firm will equate MR associated with Qd demand curve to marginal cost Long-run equilibrium will result where

• Long-run average cost curve, LAC, is tangent to Qd curve and

• Qd and QD curves intersect Results in equilibrium output qe and price pe

• At this tangency point, firm cannot vary output to enhance its profit

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Short- and Long-Run Equilibrium under Monopolistic Competition Long-run pure profit for monopolistically competitive firms will be zero In short-run, monopolistically competitive firms earning pure profits will attract new firms

supplying similar products Consumers will perceive these new products as possible substitutes

• Demand curves for original firms will shift downward and eventually squeeze out any pure profits

In long-run, costs will also adjust and squeeze profits However, as indicated in Figure 15.1, production is not at minimum of LAC, p > LMC

• There is deadweight loss in consumer and producer surplus

However, because firms only have a partial monopoly, their aggregate level of output will be greater than that for a pure monopoly

In Figure 15.1, QD demand curve cuts above short-run average total cost curve Creates an area where a monopoly can earn a short-run pure profit by reducing output to within

this area Thus, monopolistically competitive firms’ level of resource misallocation is less than if a monopoly

was sole supplier in industry Consumers may view greater degree of product differentiation (more choices) as a

desirable characteristic Which mitigates this inefficiency

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Oligopoly A major market characterized as an oligopoly in U.S. is the media

landscape Dominated by giant firms such as Bertelsmann, Disney, General Electric,

Liberty Media, Rupert Murdoch’s News, Seagram, Sony, Time-Warner, and Viacom

To a large extent these firms furnish your television programs, movies, videos, radio shows, music, and books

In general, an oligopolistic market is characterized by existence of a relatively small number of sellers with interdependence among sellers

Firms produce either a homogeneous product (called perfect oligopoly) or heterogeneous products (imperfect oligopoly) An example of a homogeneous oligopoly market is steel industry Automobile, cigarette, gasoline, and cola industries are heterogeneous

markets If there are only two sellers, it is called a duopoly

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Oligopoly Relatively small number of sellers in an oligopoly is result of

barriers to entry which may result from Product differentiation

• May result in brand identification Difficult for new firms to break through this attachment

Economies of scale • May result where total market size permits only a few optimally-sized plants

Control over indispensable resources • Prevents entry on technological grounds

Exclusive franchises • Present legal barriers to entry

Oligopoly markets are also characterized by mutual dependence Necessary for each firm to consider reactions of its competitors

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Price and Output Determination Oligopolistic firms must determine an associated price and

output policy based on some objective Firm may have a pricing policy that results in less-than-

maximum profit to discourage potential entrants An example of contestable markets

• Even threat of entry will prevent firms from maximizing profit

Thus, instead of maximizing profit, a firm might attempt to maximize sales in an effort to maintain control over a share of market

To determine price and output of an oligopolistic firm, consider a duopolist market selling an undifferentiated product (perfect duopolist) In terms of politics, this may be Democrats and Republicans selling

alternative solutions for providing public goods

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Price and Output Determination Let p denote a common selling price

q1 and q2 are output of first and second firm, respectively

Determine common selling price, p, by total market output of the two firms, Q, where q1 + q2 = Q Then, p = p(Q)

• An increase in either output will result in a decrease in price p ÷ q1 < 0, p ÷ q2 < 0

Total revenue for jth firm is then

• TRj = p(Q)qj, j = 1, 2,

Total cost for jth firm is

• j(qj)

Assuming firms’ objectives are maximizing their own profit, profit for each firm is

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Price and Output Determination Firm j must predict the other firm’s output decision as

its profit depends on amount of output chosen by other firm

If one firm changes its output, other firm may react to this change by adjusting its output Each player (firm) must predict strategies of other players

• A one-shot game where profit of firm j is its payoff and strategy set of firm j is the possible outputs it can produce

• An equilibrium is a set of outputs (q1*, q2*) in which each firm is choosing its profit-maximizing output level, given

Its beliefs about other firm’s choice And each firm’s belief about other firm’s choice is actually correct

Called a Nash equilibrium

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Price and Output Determination Assuming an interior optimum for each firm, F.O.C. for firm

1, using product rule for differentiation, is ∂1/∂q1 = p(Q*) + (∂p(q)/∂q1)q*1 – MC(q*1) = 0

Employing chain rule for second term on right-hand side, where Q is a function of q1 and q2 and q2 is a function of q1, yields

This results in

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Price and Output Determination

To solve F.O.C.s for optimal level of outputs, q1* and q2*, we require the functional forms of

• dq2/dq1 and dq1/dq2

Called conjectural variations Represent one firm’s conjecture or expectation of how other firm’s output will alter

as a result of its own change in output

A variety of different duopoly models result• Depending on what economic assumptions are made regarding conjectural

variations

The F.O.C. for firm 2 is

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Cournot Model Developed by French mathematician Augustin Cournot in 1838 Assumes conjectural variations are zero

dq2 ÷ dq1 = dq1 ÷ dq2 = 0

A firm, setting its own output, assumes other firm’s output will not change Firms make their independent output decisions simultaneously

• Simultaneous output decision by firms is directly related to Nash equilibrium associated with simultaneous-moves games

For example, a firm may determine its output capacity without regard to capacity of other firms

Firms do not realize interdependence of their output decisions in their attempts at maximizing profit Cournot duopoly solution implies that each firm equates its own MR to MC without regard to

any possible reaction by other firm• p(Q*) + [p(Q) ÷ Q]q*j = MC(q*j), j = 1, 2

Even with zero conjectural variations, solution for (q1, q2) still involves simultaneous solution of each firm’s F.O.C.

Firms may not realize their decisions affect their competitor But since output price is determined by each firm’s output level

• Their decisions do affect other firm’s output determination

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Cournot Model An example of Cournot firms is commercial real estate market

in large metropolitan cities When market for commercial real estate is very tight (limited

supply of commercial buildings), price per square foot for office space increases Increase in price stimulates speculative building of office buildings by a

number of firms• However, each individual firm does not consider effect on its total revenue of

other firms’ building office space When additional office space becomes available, market is flooded and price

drops

Result is magnified when high price for office space is during an economic boom period in city’s cyclical economy

• If city’s economy is in a slump when office space becomes available, price drop can be substantial

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Cournot Model, Perfect Competition, and Monopoly

Factoring out p(Q*) from F.O.C. for profit maximization and multiplying second term by 1 = Q*/Q*, yields

Since elasticity of demand is D = (Q/p)Q*/p* < 0, then

• P(Q*)(1 + j/D) = MC(q*j)

• P(Q*)(1 + 1/(D/j)) = MC(q*j) Where j = qj/Q is share of total output by firm j

If there is only one firm in this industry, then j = 1

• F.O.C.s reduce to monopoly solution

As number of firms increases, each firm’s share of total output declines

• Results in D/j declining toward -

• Firms are facing a more elastic demand curve as number of firms increase

In the limit, as number of firms approaches infinity, perfectly competitive solution of p = MC results

• At this perfectly competitive solution, Cournot assumption of zero conjectural variations is correct

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Cournot Model, Perfect Competition, and Monopoly

As an example of price and output determination by Cournot firms, consider inverse linear market demand function for a duopoly market p = a – b(Q), a > 0, b > 0

• Where Q = q1 + q2 is combined output of the two firms

Cost functions for these firms are

• STC1 = cq1 + TFC and STC2 = cq2 + TFC Where c > 0 and a > c

• With a greater than firms’ SAVC, they will each supply a positive level of output

Assuming each firm maximizes profit

F.O.C. for firm 1 is

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Cournot Model, Perfect Competition, and Monopoly

F.O.C. for firm 2 is

Since Cournot firms’ conjectural variations are both zero, Firm 1’s F.O.C. reduces to a = b(q1 + q2) – bq1 – c = 0

Solving for q1 gives

• q1 = (a – c – bq2)/2b This is firm 1’s reaction function

States how firm 1’s output changes (reacts) when firm 2’s output changes

Similarly, firm 2’s reaction function is q2 = (a – c – bq1)/2b

• Reaction functions are illustrated in Figure 15.2 Cournot equilibrium level of outputs for firms 1 and 2 result at their intersection

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Figure 15.2 Cournot equilibrium

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Cournot Model, Perfect Competition, and Monopoly

Nash equilibrium can be found by substituting firm 2’s reaction function into firm 1’s and solving for q1

Substituting this equilibrium level of output, q1C into firm 2’s reaction

function yields Nash equilibrium output for firm 2

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Cournot Model, Perfect Competition, and Monopoly

Market output, QC, and price, pC, are

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Isoprofit Curves Dynamics of Cournot approach can be analyzed using reaction curves

that show optimal profit-maximizing output for each firm, given output of competitor

Consider some profit level for firm 1 πº

1 = [a – b(q1 + q2)]q1 – cq1 – TFC = aq1 – bq21 – q1q2 – cq1 - TFC

• Equation for firm 1’s isoprofit curve for πº1 level of profit

Isoprofit curve represents an equal level of profit for alternative levels of a firm’s output

As illustrated in Figure 15.3, isoprofit curves radiate out from firm 1’s monopoly solution When firm 2’s output is zero, firm 1 is sole supplier

• As a monopoly will maximize profit at Q = q1 = (a – c)/2b

• Represents highest possible level of profit for firm 1 As firm 2 increases its output from zero, profit for firm 1 declines

Illustrated by isoprofit curves with lower levels of profit as q2 increases

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Figure 15.3 Dynamic adjustment to the Cournot equilibrium

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Isoprofit Curves Firm 1 will maximize its profit for a given level of q2

by shifting to isoprofit curve with highest profit As illustrated in Figure 15.3, isoprofit curve tangent

to constraint of firm 2’s output equaling q2° is firm

1’s profit-maximizing level given q2°

At tangency point, slope of lowest possible isoprofit curve is equal to zero slope of constraint

F.O.C. for maximizing profit, given firm 2’s level of output, yields firm 1’s reaction curve Passes through all tangency points of isoprofit curves

and firm 2’s output constraint

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Isoprofit Curves Similarly, firm 2 will maximize its profit for a given level of

firm 1’s output Firm 2’s isoprofit curves radiate out from its monopoly solution with

profit declining as q1 increases Maximum profit level for firm 2, given some output level for firm 1, is

where isoprofit curve is vertical and tangent to constraint of firm 1’s output

Firm 2’s reaction curve passes through this tangency• Given these isoprofit and reaction curves, firm 1 will react to firm 2’s

output level q2°

Results in a movement to point A Firm 2 will then react to this positive output level by firm 1 by decreasing

output, yielding point B These Cournot firms have no capacity for learning

Adjustment process continues until Cournot equilibrium is established

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Stackelberg Model Stackelberg model

Developed by German economist Heinrich von Stackelberg A duopoly quantity leadership model where one firm (leader) takes likely

response of competitor (follower) into consideration when maximizing profit Model allows for leader to have a nonzero conjectural variation on follower

Follower behaves exactly as Cournot firm, so its conjectural variation is still zero• Leader then takes advantage of assumption that other firm is behaving as a follower

A sequential game-theory problem where leader has advantage of moving first

Industries with one dominant large firm and a number of smaller firms are examples of markets with possible Stackelberg characteristics For example, in personal computer operating systems industry Microsoft is

dominant leader firm with a number of smaller follower firms

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Stackelberg Model As an example of Stackelberg model, reconsider Cournot linear

demand function example Firm 1 is leader and firm 2 is follower

Suppose firm 1 believes that firm 2 would react along Cournot reaction curve q2 = (a – c – bq1)/2b

Firm 1’s conjectural variation is q2 ÷ q1 = -b ÷ 2b = -1/2

Given F.O.C. associated with firm 1 1/ q1 = a – b(q1 +q2) – bq1 + ½bq1 – c = 0

• Reaction curve for firm 1 is a – bq1 – bq2 – bq1 + ½bq1 - c = 0

3/2bq1 = a – c – bq2

q1 = (a – c – bq2)/(3/2)b

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Stackelberg Model The way we calculated firm 1’s conjectural variation and substituted it

into firm 1’s F.O.C. is Same as maximizing firm 1’s profit subject to firm 2’s reaction function In a sequential game, this corresponds to firm 1 setting its output first

• Firm 1 will set its output level by considering how firm 2 will react to it Given firm 2’s reaction function, we can determine subgame perfect Nash equilibrium

for Firm 1

Specifically

Substituting the constraint into objective function results in the same F.O.C. for firm 11/q1 = a – b(q1 +q2) – bq1 + ½bq1 – c = 0

Outcome for both firms depends on behavior of firm 2• If firm 2 is using Cournot reaction curve, as firm 1 believes

Solution is Stackelberg equilibrium for firm 1 qS

1 = (a – c)/2b, qS2 = (a – c)/4b

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Stackelberg Model

Solution is derived from F.O.C.s of profit maximization (reaction functions) for the two firms Equating these F.O.C.s yields

• a – b(q1 + q2) – bq1 + ½bq1 – c = a – b(q1 + q2) – bq2 – c

-bq1 + ½bq1 = -bq2

½bq1 = bq2

½q1 = q2

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Stackelberg Model Substituting this solution into firm 1’s reaction function results in solution

for firm 1 a – b(q1 + ½q1) - ½bq1 – c = 0

• a – bq1 - ½bq1 - ½bq1 – c = 0

• a – 2bq1 – c = 0

• qS1 = (1 – c)/2b Results in firm 1 earning a higher profit and firm 2 earning a lower profit than at

Cournot equilibrium

As illustrated in Figure 15.4, firm 1 maximizes profit subject to firm 2’s reaction curve Results in a tangency of firm 1’s isoprofit curve with firm 2’s reaction function

• Firm 1 is able to increase its profit with knowledge of Firm 2’s reaction function Similarly, as illustrated in Figure 15.4, if firm 2 is the Stackelberg firm facing Cournot

firm 1 Equilibrium output and profit levels are reversed

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Figure 15.4 Stackelberg equilibria and disequilibrium

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Stackelberg Disequilibrium

Suppose firm 2 is using Stackelberg reaction curve instead of Cournot reaction curve Each firm incorrectly believes the other is a

follower using naive Cournot assumption Firms each set their output at (a - c)/2b

Expecting their competitor will be a follower and set its output at (a - c)/4b• Result is Stackelberg disequilibrium

Illustrated in Figure 15.4

• Both firms earn lower profit than Cournot equilibrium

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Collusion Rather than attempt to guess reactions of competing firms

Firms can increase their profit by colluding and maximizing joint profit

F.O.C.s are ∂/∂q1 = ∂/∂q2 = a – b(q1 + q2) – b(q1 + q2) – c = 0

Solving for Q = (q1 + q2) gives Q = (q1 + q2) = (a – c)/2b

Firms set total output equal to the monopoly solution Then determine how to divide this output among themselves

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Collusion Alternative divisions of this total output yield Pareto-optimal

surface in Figure 15.4 At any point off this optimal surface one firm can be made better off without

making other firm worse off On this optimal surface, one firm cannot be made better off without making

the other firm worse off For the firms to be on the optimal surface, their marginal profit must be

equal• If they are not equal, joint profit could be increased by shifting production toward

firm with higher marginal profit

• Equality of marginal profit is illustrated in Figure 15.4 By tangency of isoprofit curves along optimal surface

• Given that costs of two firms are the same, one possible division would be for total output to be divided evenly

Results in symmetric joint maximization position (also illustrated in Figure 15.4) q1 = q2 = (a – c)/4b

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Collusion How this maximum joint profit is distributed among members of the

collusion is not yet determined If producers have identical cost functions

• Seems plausible for profit to be evenly distributed

In contrast, if producers have different cost functions• May divide up output based on setting their marginal costs equal to overall

marginal revenue

Decision on how to allocate resulting profit is still required Ultimately allocation depends on bargaining power of the firms

• Leads to game theory discussed in Chapter 14

Although collusion offers highest joint profit for firms Firm can increase its individual profit if the other firm does not deviate from

agreed upon output limits• Called cheatingeach firm has a profit incentive to cheat

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Collusion

Suppose firms agree to evenly divide total monopoly output If firm 1 assumes firm 2 will abide by this agreement

• Firm 1 can increase its output and shift to lower isoprofit curves yielding higher profit

Firm 2 has an equal incentive to cheat by also increasing output

• Both firms now believe other firm’s output decision is independent of theirs

Underlying assumption of Cournot model

• Collusion collapses (when firms increase their output) in a failed attempt to further increase their individual profit

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Bertrand Model Cournot and Stackelberg models assume firms determine their

output Based on total output supplied, market determines the price

However, in many markets the reverse behavior is observed Firms determine their price and market then determines quantity sold

• Examples include commercial airlines in pricing tickets, hotels in setting room rates, and automobile firms in setting sticker prices for their vehicles

A model incorporating this pricing behavior is Bertrand model Named after French mathematician Joseph Bertrand

• Proposed model as an alternative to Cournot model

Bertrand model assumes simultaneous instead of sequential decision making

• Results in a Nash equilibrium set of prices for the firms

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Perfect Oligopoly In Bertrand model, assuming homogeneous products (perfect oligopoly)

Each firm has an incentive to undercut price of its competitors • Thus would capture all the sales

A firm will undercut its competitors’ prices as long as its price remains above marginal cost• If all firms have identical marginal costs

Any firm setting a price higher than marginal costs will be undercut by another firm offering a slightly lower price

Thus, perfectly competitive solution that yields a Pareto-efficient allocation will exist with each firm setting price equal to marginal cost With as few as two firms, result is a consequence of the firms setting their bid price equal to

marginal cost• Firms are in effect auctioning off their output in a first-bid common-value auction

Yields a Pareto-efficient allocation

Note that this Bertrand model Pareto-efficient solution for as few as two firms contrasts with Cournot solution Only when number of firms approach infinity will Cournot model yield a Pareto-efficient solution

• Efficiency depends on how firms strategically interact

Bertrand, Cournot, and Stackelberg models illustrate how equilibrium outcomes and efficiency in an oligopoly industry depend on type of strategic interaction engaged in by firms

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Imperfect Oligopoly Bertrand solution only holds for a perfect oligopoly If consumers perceive differences among products offered by

firms Product differentiation exists

Thus, an imperfect oligopoly market exists with each firm having some monopoly power With this monopoly power, a profit-maximizing firm will set price in excess

of marginal cost and thus operate inefficiently

Specifically, consider two firms each with constant marginal cost c Demand for firm j’s output is

• qj = qj(p1p2), j = 1, 2, An increase in p1 lowers quantity demanded q1 and raises q2

∂q1/∂p1 < 0 and ∂q2/∂p1 > 0

An increase in p2 has the reverse effect

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Imperfect Oligopoly

Each product is a gross substitute of the other In Bertrand model, each firm takes its competitor’s price

as given for maximizing profit

• Where c is constant marginal cost

In an imperfect-oligopoly market characterized by product differentiation Equilibrium prices will be set above marginal cost

• Results in an inefficient allocation

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Imperfect Oligopoly As an example, consider again firms 1 and 2 and assume

each firm faces the following linear demand functions q1 = a – bp1 + dp2, q2 = a – bp2 + dp1

• Where q1 and q2 are substitutes (but not perfect substitutes) Some degree of product differentiation exists

In this Bertrand model, each firm attempts to maximize profit by choosing its own price

• Given that the price of its competitor does not change

For simplicity, assume firms have zero cost Firm 1’s profit-maximization problem reduces to maximizing total

revenue

• The F.O.C. is ∂1/∂p1 = a – 2bp1 + dp2 = 0

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Imperfect Oligopoly Solving for p1 results in firm 1’s reaction function to a change in firm 2’s price

p1 = a/2b + d/2bp2

Similarly, maximizing profit for firm 2, holding firm 1’s price constant, yields Firm 2’s reaction function p2 = a/2b + d/2bp1

• These reaction functions are illustrated in Figure 15.5 with Bertrand equilibrium corresponding to where they intersect

Thus, equilibrium prices are determined by solving simultaneously the two reaction functions Setting reaction functions in implicit form and equating yields

• 1 = 2bp*1 + dp*2 = a – 2bp*2 + dp*1 = 0

• p*1 = p*2

Substituting equality of prices into either of the firms’ reaction functions and solving for price results in equilibrium prices

• p*1 = p*2 = a/(2b – d) > AC = MC = c = 0

• Firms will maximize profits by setting price above marginal cost At p1* = p2* an equilibrium is obtained

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Figure 15.5 Bertrand equilibrium

59

Collusion As with Cournot model, firms could improve their Bertrand profits by

colluding Instead of setting their prices independently

They collude and jointly determine the same price Maximizing joint profit yields

• F.O.C. is d/dp = 2a – 4bpJ + 4dpJ = 0 so

pJ = a/(2(b – d))

Results in the firms jointly increasing their prices and associated profit

As discussed in Chapter 14, repeatedly-played games can be directly applied to firm behavior involving strategic interactions For example, Bertrand model in game theory yields the same results as

Prisoners’ Dilemma when it also is played repeatedly

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Collusion

Assumptions of Bertrand model result in the impossibility of collusion over a finite time period In contrast, over a horizon of infinitely repeated

games, no final period exists• Prevents punishment in ensuing rounds

• Thus, as in Prisoners’ Dilemma, cooperation can be the optimal strategy

This type of cooperation is termed tacit collusion Firms behave as a cartel without ever developing a joint

marketing strategy

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Generalized Oligopoly Models Other combinations of assumptions exist concerning firms’ actions, reactions, and

conjectures about other firms’ behavior There are other decision variables besides output and price

Including advertising expenditures, market shares, and new market penetration In each case, an alternative model of firms’ interaction would be required

• Major difficulty with these models is determining conjectural variations

No general agreement among economists that any existing oligopoly model is appropriate for analyzing firm behavior in a specific industry Difficult to predict equilibrium solution for a particular oligopolistic market

Economic models are generally weak in predicting expected reactions of individual agents to market prices, output and input levels, shifts in demand and supply, technological change, and variations in tax rates Thus, economists have developed models that don’t focus on these reactions and then measure

the conjectural variation terms One approach is to consider these interactions by employing game-theory models A summary of characteristics associated with these oligopoly models, along with other

market structures, is provided in Table 15.1

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Table 15.1 Market Structures

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Generalized Oligopoly Models In all these market structures we assume transaction costs to be small or zero Distinguishing feature between perfect competition and monopolistic

competition Assumption of heterogeneous products under monopolistic competition

• Results in advertising and product promotion

Oligopoly markets are distinguished from monopolistic competition by Relatively large size and small number as a consequence of barriers to entry Results in interdependence among firms within oligopoly markets

• Oligopoly models vary according to their assumptions concerning how firms respond to this interdependence

In the polar case, the monopoly is the industry In reality, markets for differentiated products represent a continuum across these market

structures

For applied research, an economist will investigate characteristics of a particular market Select appropriate market model with modifications to use for analysis

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Collusion in Oligopoly Markets The idea of oligopoly firms engaged in collusive production or

pricing agreements has always existed in economics Generally, there is an incentive for members of a collusive

arrangement (called a cartel) to cheat Can apply game theory to investigate behavior of firms

involved with collusive arrangements For example, consider the payoff matrix in Table 15.2

• The establishment of a cartel by these two firms will yield a payoff of 10 for each firm

However, this is not a pure Nash equilibrium outcome

• Each member can cheat by defecting from cartel and increase its payoff

• Thus, there is an incentive for both firms to cheat and defect For this reason, it is generally thought that cartels are inherently unstable in the

absence of some binding constraints on participants

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Collusion in Oligopoly Markets Economists have suggested that purpose of many

government regulatory agencies and minimum-price laws Is to institutionalize cartels to prevent cheating

Even without binding constraints, long-run viability of a cartel may be supported By establishment of a firm’s reputation for cooperation Encouraging other firms to also cooperate

With repeated opportunities for showing this cooperation through regular cartel meetings on price and output determination Cooperative equilibrium may result

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Table 15.2 Cartel

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Legal Provisions Antitrust restrictions attempt to make cartels illegal

However, some cartels are actively supported by governments

• For example, within U.S. for certain industries, Section 1 of Sherman Antitrust Act (1890) prohibits contracts, combinations, or conspiracies in restraint of trade

Section 2 declares it is unlawful for any person to monopolize, attempt to monopolize, or conspire to monopolize trade

• Clayton Act (1914) prohibits price discrimination where it substantially lessens competition or creates a monopoly in any line of commerce

• Federal Trade Commission (FTC) Act (1914) supplements Sherman and Clayton acts

Prohibits unfair and anticompetitive practices such as deceptive advertising and labeling

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Legal Provisions

Either government or private agencies, including firms and households, can bring suit against a cartel However, a number of U. S. industries are not covered by

these acts• For example, by the Capper-Volstead Act (1922), agriculture is

not included under antitrust acts

• Section 7 of Taft-Hartley Act (1935) allows labor unions, which are a type of collusive activity, to form

In terms of export markets, Webb-Pomerence Act (1918) allows price fixing and other forms of collusion for exporting commodities