Market structure and competition

By

A.V. Vedpuriswar

Competitors and Competition

A given firm may compete in several input and output markets simultaneously.

It is important to analyse each market separately.

Two firms directly compete if a price increase by one causes many of its customers to do business with the other.

When firms are direct competitors, the strategic choices of one directly affect the performance of the other.

Products tend to be close substitutes when three conditions hold:

- Same or similar product performance characteristics.

- Same or similar occasions for use.

- Sold in the same geographic market.

The degree to which products substitute each other is measured by the cross price elasticity of demand.

Cross price elasticity = percentage change in demand for good Y that results from 1% change in the price of X

Market Structure

Market structure refers to the number and distribution of firms in a market.

We can measure this in many ways.

N firm concentration ratio = Combined market share of the N largest firms in the market.

Herfindahl index = Sum of the squared market shares of all the firms in the market

Problem

The following are the approximate market shares:

Coke – 40%, Pepsi – 30%, 7 Up – 10%, Dr Pepper – 10%

All other brands – 10%

Calculate the Herfindahl index

Herfindahl index = (.4)**2 + (.3)**2 + (.10)**2 + (.10)**2 + (.10)**2

=.16 + .09 + .01 + .01 + .01

=0.28

What would happen if Pepsi took over 7 Up?

Herfindahl index =(.4)**2 + (.4)**2 + (.10)**2 + (.10)**2

= 0.34

Perfect competition

- There are many sellers and well informed buyers.

- Profit is maximised when Price = Marginal cost.

Different forms of market structure

Monopoly

- A firm is a monopolist if it faces little or no competition.

- A monopolist faces a downward sloping demand curve.

- A monopolist selects the price such that marginal revenue equals marginal cost.

- A monopolist can set the price without regard to how other firms will respond.

The monopoly solution (Cont…)

E

G Marginal revenue

Demand

Marginal cost

Quantity per period

pri

ce, m

arg

inal

rev

enu

e, m

arg

inal

co

st,

aver

age

tota

l co

st Average total

cost

- There are many sellers

- Each seller sells a differentiated product

- A product is vertically differentiated when it is unambiguously better or worse than competing products

- A product is horizontally differentiated when only some consumers prefer it to competing products.

- Horizontal differentiation results when consumers have idiosyncratic preferences.

Monopolistic competition

- Location can be a source of idiosyncratic preferences

- Tastes can be a source of idiosyncratic preferences

- The degree of horizontal differentiation depends on the magnitude of search costs, i.e., how easy or hard it is for customers to get information about alternatives.

Monopolistic competition (short run)

MR

D

ATC

MC

Economic profit

C

P

Q

A market in which the actions of individual firms materially affect the industry price level is called Oligopoly.

Each firm has to take into account the strategies of other firms even as it frames its strategy.

Game theory is useful here.

Oligopoly

Game theory :Prisoners’ dilemma payoff matrix

3 years

3 years

10 years

2 years

2 years

1 year

10 year

Both deny

One denies

other admits

Both admit

One denies, other admits

1 year

Game Theory

Consider two firms, Alpha and Beta.

Each firm must decide whether to increase production capacity in the coming year.

The consequences of the firm’s actions are summarised below.

Beta

Do Not expand Expand

Do not expand $18, $18 $ 15, $ 20

Alpha

Expand $ 20, $15 $ 16, $ 16

Game Theory (Cont..)

Consider pay off for Alpha

If Beta expands

and Alpha expands, profit = $16

and Alpha does not expand, profit= $ 15

If Beta does not expand

and Alpha expands, profit = $20

and Alpha does not expand, profit = $18

So it makes sense for Alpha to expand in both cases.

See previous slide

Game Theory (Cont..)

Consider pay off for Beta

Say Alpha expands

Beta does not expand profit = $15

Beta expands profit = $16

Say Alpha does not expand

Beta does not expand profit = $18

Beta expands profit = $20

So it makes sense for Beta to expand in both cases

See earlier slide

So the Nash equilibrium is that each firm expands its capacity.

At the Nash equilibrium, each player is doing the best it can, given the strategies of other players.

If each party expects the other to choose its Nash equilibrium strategy, then in fact both parties will choose their Nash equilibrium strategies

The Nash equilibrium does not necessarily correspond to the outcome that maximises the aggregate profit of the players.

Beta

Do Not Expand Small Large

Do Not Expand 18, 18 15, 20 9, 18

Small 20, 15 16, 16 8, 12

Large 18, 9 12, 8 0, 0

Beta

Alpha

Equilibrium point is Small, Small

Alpha

Game Tree for Sequential Capacity Expansion Game

Do Not Expand

Alpha

Small

Large

Beta

Small

Do not expand

Large

Beta

Small

Do not expand

Large

Beta

Small

Do not expand

Large

($18,$18)

($15,$20)

($9,$18)

($20,$15)

($16,$16)

($8,$12)

($18,$9)

($12,$8)

($0,$0)

If both firms decide simultaneously, the equilibrium is (Small, Small)

What happens if Alpha first decides?

In a sequential move game, Alpha’s capacity choice has commitment value. It forces Beta into a corner.

By committing to a large capacity expansion, Alpha forces Beta into a position where Beta’s response yields the outcome that is most favourable to alpha.

So Alpha makes a large expansion while Beta does not expand.

The payoff is (18,9)

- Consider only two firms in the market.

- They produce identical goods and charge the same prices.

- The sole strategic choice is the total amount they produce, Q1 + Q2

- The market price is that which enables both firms to sell all their output.

- Each firm’s optimal level of production is the best response to the level it expects its rivals to choose.

-This model applies to situations where firms must make production decisions in advance and are committed to selling all their output.

-This may be so if bulk of the production costs are sunk or it is costly to hold inventory.

Cournot Model

Cournot Equilibrium

Suppose there are two players in the market.

For A, TC1 = 10 Q1

For B, TC2 = 10 Q2

Marginal cost = ?

Market demand is given by Q1+Q2 = 100 – P or P = 100 – (Q1+Q2)

At Cournot equilibrium,

P1* = 100 – Q1

* - Q2* (Q1* , Q2* are market clearing output)

Q1* is A’s profit maximising output given that it guesses B will produce Q2

*

Q2* is B’s profit maximising output given that it guesses A will produce Q1

*

Assume that A guesses B will produce Q2g

Then A’s profit = Revenues - Total cost

= P1 Q1 - 10 Q1

= (100 – Q1-Q2g) Q1 – 10 Q1

= 100 Q1 – Q12 – Q2g Q1 – 10 Q1

Profit = 90 Q1 – Q12 – Q2g Q1

We differentiate and equate to zero to find out maxima/minima.

d (profit) / d Q1 = 90 – 2Q1 – Q2g

d 2(profit) / dQ12 = -2Q1 = always - ve

So it is a maxima point

90 – 2Q1 – Q2g = 0

2Q1 = 90 - Q2g

Q1 = 45 - .5 Q2g

So if A expects B to increase its output, it will reduce the output and vice versa.

Similarly profit maximising value of Q2 = 45 - .5 Q1g

So Q1 = 45 - .5Q2g

Q2 = 45 - .5 Q1g

At equilibrium,

Q2g = 45 - .5 (45 - .5Q2g )

Q2g = 45 – 22.5 + .25 Q2g

0.75 Q2g = 22.5

Q2g = 22.5 /.75 = 30

Q1g = 45 - .5 (30) = 30

So at equilibrium, Q1* = Q2

* = 30

Process of adjustment in Carnot equilibrium( Q2 = 45 -0.5*Q1)Q2 ,Q1 are both 40

Starting Q1 Starting Q2 Adjusting firm

Ending Q1 Ending Q2

40 40 1 25 40

25 40 2 25 32.5

25 32.5 1 28.75 32.5

28.75 32.5 2 28.75 30.63

28.75 30.63 1 29.69 30.63

-Each firm selects a price and stands ready to meet all the demand for its products at that price.

-Each firm selects a price to maximise its own profits, given the price that it believes the other firm will select.

-When the firm’s products are perfect substitutes, price competition will be severe.

-Rivalry between the two firms is enough to achieve the perfectly competitive outcome.

-The Bertrand model applies to markets in which capacity is sufficiently flexible so that firms can meet all the demand that arises at the prices they announce.

-Firms expect all increases in sales will come through business stealing.

Bertrand Model

P = 100 – (Q1 + Q2)

Cournot equilibrium is P = 100 – 30 – 30 = 40

But this is not the Bertrand equilibrium.

If B charges 40, A may charge 39 and grab the entire market, i.e., Q1 = 100 – P = 61

Profits for A in Cournot equilibrium = (40) (30) – (10) (30) = 900

Profits for B now = (39) (61) – (10) (61)

= (29) (61)

= 1769

As long as both firms set prices that exceed marginal costs, one firm will have an incentive to undercut the other and grab the entire market. The only possibly equilibrium is P1 = P2 = marginal cost = 10.

In Bertrand model, rivalry between the two firms is enough to achieve the perfectly competitive outcome.

Price competition will be fierce if the products are perfect substitutes.

When products are differentiated, competition will be less intense.

Differences between Cournot and Bertrand model

Cournot competitors can be thought of as choosing capacities and then competing as price setters given the capacities chosen earlier.

The Cournot model applies most naturally to markets when firms must make production decisions in advance and are committed to selling all of their output.

This might occur because the bulk of the production costs are sunk or because it is costly to hold inventory.

So prices will adjust more quickly than quantities. Each firm will try to keep sales equal to planned production volumes.

Business stealing is not an option.

Bertrand model applies to markets in which capacity is sufficiently flexible.

Firms can meet all of the demand that arises at the prices they announce.

When products are substitutes, each firm believes it can steal business from its competitors through a small cut in price.

Firms expect all the increase in sales to come from business stealing.

In equilibrium, margins are driven to zero.

Horizontally differentiated markets

Undercutting will not lead to loss of entire business.

Say Q1 = 63.42 - 3.08 P1 + 2.25 P2

Q2 = 49.52 – 5.48 P2 + 1.40 P1

A’s Marginal cost = 4.96

B’s Marginal cost = 3.94

A’s profit = (P1 – 4.96) (63.42 – 3.98 P1 + 2.25 P2g)

P1 = 10.44 + .2826 P2g

B’s profit = (P2g - 3.94) (49.52 – 5.48 P2 + 1.40 P1g)

P2 = 6.40 + .1277 P1g

Solving P1 = 12.72, P2 = 8.11

(4)

Consider a market with two horizontally differentiated firms, X and Y. Each has constant marginal cost of $20. Demand functions are:

Qx = 100 – 2 Px + 1 Py

Qy = 100 – 2 Py + 1 Px

Calculate the Bertrand equilibrium.

= (Px – 20) (100 – 2 Px + Pyg)

= (Py – 20) (100 – 2 Py + Pxg)Differentiating with respect to P we get,

100 – 4Px + Pyg + 40 = 0

100 – 4Py + Pxg + 40 = 0

x

y

0x

x

d

d

0y

y

d

d

At equilibrium, Px = Pxg , Py = Pyg

100 – 4Pxg+ Pyg + 40 = 0

100 – 4Pyg+ Pxg + 40 = 0

Or 400 – 16 Pyg+ 4Pxg + 160 = 0

Adding, we get

500 – 15 Pyg + 200 = 0

Pyg = 700/15, Pxg = 140 + 700/15 =700/15