Transcript Market structure and Competition

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 =
largest
Herfindahl index
the
Combined market share of the N
firms in the market.
= Sum of the squared market shares of all
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
Different forms of market structure
Perfect competition
-
There are many sellers and well informed buyers.
-
Profit is maximised when Price = Marginal cost.
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.
price, marginal revenue, marginal cost,
average total cost
The monopoly solution (Cont…)
Marginal cost
Average total
E
cost
G Marginal
Demand
revenue
Quantity per period
Monopolistic
competition
-
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.
-
Location can be a source of
preferences
idiosyncratic
-
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)
MC
ATC
P
Economic
profit
C
D
MR
Q
Oligopoly
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.
Game theory :Prisoners’ dilemma payoff matrix
3 years
10 years
Both admit
3 years
One denies,
other admits
1 year
1 year
One denies
other admits
2 years
Both deny
10 year
2 years
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
Do not expand $18, $18
Expand
$ 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
Do Not Expand 18, 18
Alpha
Small
Large
15, 20
9, 18
Beta
Small
20, 15
16, 16
8, 12
Large
18, 9
12, 8
0, 0
Equilibrium point is Small, Small
Alpha
Game Tree for Sequential Capacity Expansion Game
Do not
expand
Beta
($18,$18)
Do Not Expand
Small
Large
Do not
expand
Alpha
Beta
Small
Small
($15,$20)
($9,$18)
($20,$15)
($16,$16)
Large
($8,$12)
Do not
expand
Beta
Large
Small
($18,$9)
($12,$8)
Large
($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)
Cournot Model
-
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 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*
(Q
1*
, 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
Bertrand Model
-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
through business stealing.
come
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.
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.
x
=y
(Px – 20) (100 – 2 Px + Pyg)
= (Py – 20) (100 – 2 Py + Pxg)
d x
 0  with respect to P we get,
Differentiating
dx
d y
dy
0
100 – 4Px + Pyg + 40 = 0
100 – 4Py + Pxg + 40 = 0
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