introductory microeconomics (es10001) topic 6: imperfect competition 1

Introductory Microeconomics (ES10001)

Topic 6: Imperfect Competition

1. Introduction

PC & Monopoly are useful benchmarks.

But, in more than half of the 800 major UK manufacturing product categories, 70% of market is shared by 5 largest firms in the market.

Real world markets are imperfectly competitive

Imperfectly competitive (IC) firms cannot sell as much as want at going market price; they face a downward sloping demand curve.

1. Introduction

Two models of imperfect competition Monopolistic Competition

Oligopoly

And in terms of Oligopoly

Non-Collusive

Collusive

2. Monopolistic Competition

Theory originally developed by Chamberlain (USA) and Robinson (UK) in early 1930s

Many sellers producing similar, but not identical, products that are close substitutes for each other

Each firm has only a limited ability to affect the

market price

Assumptions:

Large number of small firms; firms assume own behaviour has no influence on rivals actions;

Similar, but not identical, products;

Free entry and exit into industry

Implication

Each firm can, to some extent, influence its market share by changing its price relative to its competitors

Demand curve is downward sloping because different firms’ products are only limited substitutes for each other

Advertising; product differentiation

Short-run equilibrium of typical monopolistically competitive firm

Profit-maximising monopolist in its own brand

Thus MR = MC and (we assume) profit > 0

LAC0D = AR

Profit

Figure 1: Monopolosit Competition (SR)

π > 0

Existence of supernormal profit induces other firms to enter industry with their own brands

This shifts down/left demand curve facing existing monopolistically competitive firms

Moreover, demand curve becomes more elastic since consumers now have a greater variety of choice

Process continues until no more firms enter industry (i.e. all firms are earning normal profit)

Figure 2: Impact on AR of entry of rival brands

p0 = LAC0

D = ARMR

Figure 3: Monopolist LR Equilibrium

π = 0

Long-run tangency equilibrium where p = LAC

Monopolistically competitive firms are neither electively nor productively efficient

‘... too many firms each producing too little output.’ (Chamberlain)

But …

‘... excess capacity is the cost of differentness.’12

3. Oligopoly

‘Competition among the few’

Few producers, each of whom recognises that its own price depends on both its own output and the output of its rivals

Thus, firms are of a size and number that each must consider how its own actions affect the decisions of its relatively few competitors.

For example, firm must consider likely response of rivals before embarking on a price cutting strategy

3. Oligopoly

Collusion or competition?

Key element of all oligopolistic situations

Collusion; agreement between existing firms to avoid competition with one another

Can be explicit or implicit

3. Oligopoly

For example, existing firms might collude to maximise joint profits by behaving as if they were a multi-plant monopolist

i.e. restricting q to monopolist level, say q0, and then negotiating over the division of q and monopoly profits

Note, might not agree to divide up q equally; sensible for more efficient members of the cartel to produce q

D = ARMR

Figure 4: Collusion or Competition

3. Oligopoly

But, since cartel p > MC, each firm has an incentive to renege on the collusive agreement

... temptation to reach the ‘first best’ renders the ‘second best’ unsustainable and drives firms to ‘third best’

First-Best: I renege, you colludeSecond-Best: Neither renege; we both colludeThird-Best: We both renege

Cartels are inherently fragile!

D = ARMR

Figure 4: Collusion or Competition

Cartel price is above cartel member’s marginal cost, thus incentive to renege (i.e. increase q)

Normal profit equilibrium

3. Oligopoly

Collusion is easiest when formal agreements between firms are legally permitted (e.g. OPEC).

More common in 19th century, but increasingly outlawed

Collusion is more difficult the more firms there are in the market, the less the product is standardised, and the more demand and cost conditions are changing in the absence of collusion

3. Oligopoly

In absence of collusion, each firm’s demand curve depends upon how competitors react, and firms have to make assumptions about this

A simple model of this was developed by Sweezy (1945) to explain that apparent fact that prices once set as a mark-up on average costs, tend not too change

‘Kinked Demand Curve’ model

3. Oligopoly

Assume firm is at E0 selling q0 output at a unit price of p0

Firm believes that if it raises price, its rivals will not raise their price (i.e. DA), but that if it lowers price, then its rivals will follow him (i.e. DB)

Thus demand curve is kinked at E0 being flatter for p > p0 and steeper for p < p0

Figure 5a: Kinked Demand Curve Model

3. Oligopoly

Both the ‘no-follow’ demand curve (DA) and the ‘follow’ demand curve (DB) will have an associated MR curve (MRA, MRB)

Thus MR is discontinuous (i.e. vertical) at q0 since an increase in q beyond q0 will lead to a discontinuous fall in total revenue

Figure 5b: Kinked Demand Curve Model

MRBMRA

Figure 5c: Kinked Demand Curve Model

3. Oligopoly

Thus, fluctuations in marginal cost within the discontinuous part of the MR curve (i.e. within A-B) do not lead to a change in the firms profit-maximising level of output

Sweezy used the model to model the inflexibility of US agricultural prices in the face of cost changes

Figure 5a: Kinked Demand Curve Model

3. Oligopoly

But two key weaknesses:

EmpiricalFurther evidence suggested that agriculture prices did not behave asymmetrically

TheoreticalModel does not explain how we got to the initial equilibrium, or where we go if LMC moves outside of the discontinuity

3. Oligopoly

Cournot (1833)

Firms compete over quantities with ‘conjectural variation’ that other firm(s) will hold their output constant

Cournot originally envisaged two firms producing identical spring water at zero cost

3. Oligopoly

Two firms (a, b) costlessly produce identical spring water

Assume normal (inverse) demand curve for spring water is:

qd = 100 – 5p <=> pd= 20 – 0.2q

Assume that firm a believes that firm b will produce zero output (i.e. Ea{qb}= 0); firm a’s optimal q is that which maximises firm a’s total revenue vis.

D = AR

50 100

Figure 6a: Cournot Competition

Firm a’s optimal output if Ea{qb}= 0

3. Oligopoly

However, if firm a were to produce 50 units, then firm b would presume that it (i.e. firm b) faces a (residual) demand curve of:

i.e. a residual demand given by the market demand for the good less firm a’s output

And firm b would make its optimal choice of output accordingly

D´ = AR´

50 100

Figure 6b: Cournot Competition

Firm a’s supply Firm b’s (residual) demand

D = AR

Figure 6c: Cournot Competition

Firm b’s residual demand

3. Oligopoly

Thus, if qa = 50, then firm b would maximise its profit (i.e. revenue) by setting qb = 25

But this would imply that firm a would want to change its initial level of output; i.e. qa1 = 50 was optimal under the assumption that qb = 0

But now that qb = 25, firm a will want to revise its choice of q accordingly

3. Oligopoly

Thus, firm a will choose the level of output that maximises total revenue given qb = 25

Firm a’s residual demand curve is thus:

Such that

D´ = AR´

25 100

Figure 6d: Cournot Competition

Firm a’s supply Firm a’s (residual) demand

D = AR

37.5 75

Figure 6e: Cournot Competition

Firm a’s residual demand

3. Oligopoly

This process will continue until neither firm ‘regrets’ its optimal choice of output

i.e. until its ‘conjectural variation’ regarding the other firm’s response is validated

The Cournot equilibrium is thus where:

D = AR

MR MR´

33.3 33.3 100

Figure 6d: Cournot Competition

Cournot Equilibrium

3. Oligopoly

Cournot market shares

Round 1 2 3 4 n

Firm a

50 50 37.5 37.5 33.33

Firm b

0 25 25 31.25

3. Oligopoly

It can be shown that total (i.e. market) equilibrium output under Cournot competition is given by:

where qc is the perfectly competitive level of output (i.e. where p = MC)

N.B. Usually termed ‘Nash-Cournot’ equilibrium, hence superscript ‘n’

3. Oligopoly

Solution method without calculus:

Firm a’s residual demand curve:

3. Oligopoly

Setting MR = 0 implies:

3. Oligopoly

And similarly for Firm b, thus, two equations and two unknowns:

Solving …46

3. Oligopoly

Generally, assume:

And assume

3. Oligopoly

Generally:

3. Oligopoly

Recall:

3. Oligopoly

Monopoly

n = 1 qn = (1/2)qc

Duopoly

n = 2 qn = (2/3)qc

Perfect Competition

n = qn = qc

3. Oligopoly

Cournot originally envisaged his model in term of sequential decision making on the part of firms

But it would irrational for each firm to persist with the conjectural variation that its rival will hold output constant when they only do so in equilibrium

Moreover, the model implies the existence of a future, in which case it can be shown that profitable collusion is sustainable

3. Oligopoly

Economists have re-interpreted Cournot’s model in terms of a one-shot game

i.e. only one amount of output actually put onto market vis. Cournot equilibrium level of output qn

But, it is assumed that each firm goes through a rational sequential decision making process before implementing its output choice

3. Oligopoly

The Cournot equilibrium may be re-interpreted in this sense as a Nash Equilibrium

That is, an equilibrium in which each party is maximising his utility given the behaviour of all the other parties

I am doing the best I can do, given what you are doing; and vice versa

3. Oligopoly

Stackelberg competition

Variation of Cournot in which firm a announces its output and, once that announcement is made, the output cannot be changed.

i.e. one-shot game or repeated game in which firm a produces the same level of output in each period.

3. Oligopoly

Assume:

Firm 1 - market ‘leader’

Firm 2 - market ‘follower’

N.B. firm 1 has to be able to make a credible, binding commitment to a particular output level

D´ = AR´

50 25 75 100

Figure 7: Stackelberg Competition

3. Oligopoly

Bertrand Competition

Both Cournot and Stackelberg assume that firms chose outputs with prices determined by the inverse demand functions.

But in many oligopolistic markets firms appear to set prices and then sell whatever the market demands at those prices

3. Oligopoly

In perfect competition and monopoly, it makes no difference whether we carry out analysis in terms of prices or quantities

That is, price determines quantity and quantity determines price

But in oligopoly the distinction is crucial

3. Oligopoly

Bertrand presented an alternative to the Cournot model in his review of Cournot’s book.

He asked the question, what would be the outcome if the two firms chose prices:

(a) simultaneously(b) independently

And then sold all the output that was demanded at these prices via the inverse demand functions

3. Oligopoly

Conclusion

Completely different result emerges

Equilibrium which replicates perfectly competitive (i.e. allocatively efficient) equilibrium in which p = MC

3. Oligopoly

Firms compete with each other by marginally undercutting the other’s price (assuming homogenous good, costs etc.) and thus taking the whole market

Process continues until the only equilibrium is one where each firm sets price equal to marginal cost

3. Oligopoly

Nash equilibrium in Bertrand is p1 = MC = p2

Rationalisation for the equilibrium is on the same lines as in Cournot model vis. no other pair of prices has the property of mutual consistency.

Bertrand intended this to be a reductio ad absurdum and to demonstrate the weakness of Cournot’s approach

D = AR

MC = AC

Figure 8: Bertrand Competition

Bertrand Equilibrium

Monopoly Equilibrium

3. Oligopoly

Bertrand model yields a striking prediction from a quite reasonable model

If outputs are homogenous, an increase in the number of firms in the market from one to two leads from the monopoly equilibrium directly to the perfectly competitive equilibrium!

4. Game Theory

Game; situation in which intelligent decisions are necessarily interdependent

The players in the game attempt to maximise their own payoffs via a strategy

Strategy; game plan describing how the player will act (or move) in every conceivable situation.

Equilibrium Concept - Nash

4. Game Theory

Nash equilibrium occurs when each player chooses his best strategy, given the strategies of the other players.

Consider …

Prisoners’ Dilemma

4. Game Theory

Prisoner’s Dilemma

Player 2 Confess Deny

Player 1

Confess

-8, -8 0, -10

Deny -10, 0 -1, -1

4. Game Theory

Player 1

Confess

-8, -8 0, -10

Deny -10, 0 -1, -1

4. Game Theory

Player 1

Confess

-8, -8 0, -10

Deny -10, 0 -1, -1

4. Game Theory

Player 1

Confess

-8, -8 0, -10

Deny -10, 0 -1, -1

4. Game Theory

Player 1

Confess

-8, -8 0, -10

Deny -10, 0 -1, -1

4. Game Theory

Player 1

Confess

-8, -8 0, -10

Deny -10, 0 -1, -1

4. Game Theory

Player 1

Confess

-8, -8 0, -10

Deny -10, 0 -1, -1

4. Game Theory

Player 1

Confess

-8, -8 0, -10

Deny -10, 0 -1, -1

4. Game Theory

Player 1

Confess

-8, -8 0, -10

Deny -10, 0 -1, -1

4. Game Theory

Player 1

Confess

-8, -8 0, -10

Deny -10, 0 -1, -1

4. Game Theory

Player 1

Confess

-8, -8 0, -10

Deny -10, 0 -1, -1

4. Game Theory

Player 1

Confess

-8, -8 0, -10

Deny -10, 0 -1, -1

4. Game Theory

Player 1

Confess

-8, -8 0, -10

Deny -10, 0 -1, -1

4. Game Theory

Player 1

Confess

-8, -8 0, -10

Deny -10, 0 -1, -1

4. Game Theory

Player 1

Confess

-8, -8 0, -10

Deny -10, 0 -1, -1

4. Game Theory

Player 1

Confess

-8, -8 0, -10

Deny -10, 0 -1, -1

4. Game Theory

Player 1

Confess

-8, -8 0, -10

Deny -10, 0 -1, -1

4. Game Theory

Player 1

Confess

-8, -8 0, -10

Deny -10, 0 -1, -1

4. Game Theory

Player 1

Confess

-8, -8 0, -10

Deny -10, 0 -1, -1

4. Game Theory

Nash Equilibrium ; Confess, Confess

Indeed, to confess is each player’s ‘dominant strategy vis. optimal strategy that is independent of the strategy of the other player(s)

Recall, ‘collusion versus competition’

4. Game Theory

Collusion versus Competition

Firm 2 Renege Collude

Firm 1

Renege -8, -8 0, -10

Collude

-10, 0 -1, -1

4. Game Theory

Firm 1

Renege -8, -8 0, -10

Collude

-10, 0 -1, -1

4. Game Theory

Firm 1

Renege -8, -8 0, -10

Collude

-10, 0 -1, -1

4. Game Theory

Firm 1

Renege -8, -8 0, -10

Collude

-10, 0 -1, -1

4. Game Theory

Firm 1

Renege -8, -8 0, -10

Collude

-10, 0 -1, -1

3. Oligopoly

First-best (i.e. dominant strategy) would be to renege given that the other firm colludes

Second-best would to both collude (i.e. a voluntary agreement to maintain the cartel output – but restrictive practices are usually illegal and so agreements are usually tacit)

Third-best is to both renege and compete

3. Oligopoly

Again …

Temptation to reach the first-best renders the second-best unsustainable and so forces players to the third-best

introductory microeconomics (es10001) topic 6: imperfect competition 1

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