Transcript Price competition

Chapter 11
Oligopoly
memory industry

DRAM: dynamic random access memory
 A key component in computers
 Flash memory is essential in mobile devices.
 Competition is intense, but the industry is highly
concentrated.
 little
product differentiation
 large fixed costs
 top 4 account for 90% of market shares
2
Memory industry
3
memory industry

A example of oligopoly:
 Market with a small number of sellers who behave
strategically

Samsung
 How to adjust pricing and capacity as Korean
Won appreciates against U.S. dollar?
 How to respond as smaller competitors merge or
exit?
4
Learning objectives





For sellers competing on price to sell differentiated
products, identify the price that maximizes profit.
Appreciate that prices can be strategic complements.
For sellers competing on capacity to sell a homogeneous
product, identify the capacity that maximizes profit.
Appreciate that capacities can be strategic substitutes.
Apply limit pricing to deter entry.
5
Outline

Price competition
 Limit pricing
 Capacity competition
 Capacity leadership
 Restraining competition
6
Benchmark: Monopoly
7
Price competition:
Homogeneous product



Bertrand model: Luna and Mercury
 Produce at constant marginal cost with unlimited
capacity
 Compete on price to sell a homogeneous product.
Extreme competition – selling undifferentiated
commodities
Game in strategic form – competing sellers set prices
simultaneously
8
Price competition:
Homogeneous product

Marginal cost = $30 per subscriber per month
 Suppose that Luna charges $32.
 Mercury has three choices:
 Price > $32: no customers
 Price = $32: split the market demand in half
 Price < $32: gain the whole market – the best
strategy.
 Nash equilibrium: Both sellers charge price = $30
(marginal cost).
 Bertrand paradox
9
Price competition:
Differentiated products



Hotelling model: Luna and Mercury
 Produce at constant marginal cost with unlimited
capacity
 Compete on price to sell a product differentiated by
distance from consumer.
Game in strategic form – competing sellers set prices
simultaneously
Competition is moderated by
 Differentiation
 Consumer preferences
10
Price competition:
Differentiated products

Examples:
 Retailing – literally distance from shops
 Taste – consumers distributed on spectrum
from sweet to savory
 Political competition – voters distributed on
spectrum from left to right
11
Price competition:
Differentiated products



Residual demand: Demand given the actions of
competing sellers.
Given Mercury's price and any price that Luna could set
 Consumers relatively closer to Luna would buy from
Luna
 Consumers relatively closer to Mercury would buy
from Mercury
Residual demand curve slopes downward
 If Luna raises price, some consumers (located
relatively far from Luna) would switch to Mercury
12
Price competition:
Differentiated products


Luna’s profit maximum
 Produce at scale where residual marginal revenue =
marginal cost
 Set price accordingly – as function of Mercury’s price
Best response function: Seller’s best action as a function
of the actions of competing sellers.
13
Price competition:
Differentiated products
14
Price competition:
Differentiated products
15
Hotelling Model…
p1 + txm = p2 + t(1 - xm) 2txm = p2 - p1 + t
xm(p1, p2) = (p2 - p1 + t)/2t
There are N consumers in total
So demand to firm 1 is D1 = N(p2 - p1 + t)/2t
Price
Price
p2
p1
xm
Shop 1
16
Shop 2
Hotelling Model…
Profit to firm 1 is p1 = (p1 - c)D1 = N(p1 - c)(p2 - p1 + t)/2t
p1 = N(p2p1 - p12 + tp1 + cp1 - cp2 -ct)/2t
Differentiate with respect to p1
N
(p2 - 2p1 + t + c) = 0
p1/ p1 =
2t
p*1 = (p2 + t + c)/2
What about firm 2? By symmetry, it has a
similar best response function.
p*2 = (p1 + t + c)/2
17
Solve this
for p1
Hotelling Model…
Finding the Bertrand-Nash Eq.:
p*1 = (p2 + t + c)/2
p2
R1
p*2 = (p1 + t + c)/2
2p*2 = p1 + t + c
R2
= p2/2 + 3(t + c)/2 c + t
 p*2 = t + c
(c + t)/2
 p*1 = t + c
Profit per unit to each
(c + t)/2 c + t
firm is t
Aggregate profit to each firm is Nt/2
18
p1
Hotelling Model…
Price
Price
p*2 = t+c
p*1 = t+c
xm = (p2 - p1 + t)/2t
xm =1/2
Shop 1
19
Shop 2
Price competition:
Differentiated products

V=100, t=4
 Marginal consumer
100  pL  4 x*  100  pM  4(1  x* )
1
 x ( pL , pM )  ( pM  pL  4)
2
*

Best response function
 Equilibrium prices
*
pL  pM*  c  4
20
Price competition:
Differentiated products



“Transport cost” = strength of consumer preference
Higher transport cost
 Residual demand more inelastic => higher price
 Best-response function shifts toward higher prices
 Equilibrium: Higher prices
Stronger consumer preference softens competition
21
Price competition:
Differentiated products

Higher demand
 Higher residual demand
 Best-response function shifts toward higher prices
 Equilibrium: Higher prices
 Higher marginal cost
 Best-response function shifts toward higher prices
 Equilibrium: Higher prices
22
Strategic complements



Strategic complements: The adjustment by one party
leads other parties to adjust in the same direction
Hotelling model: Prices are strategic complements
 Best-response functions slope upward
Military example – arms race
 If enemy buys more weapons, then we must also buy
more weapons
23
Outline

Price competition
 Limit pricing
 Capacity competition
 Capacity leadership
 Restraining competition
24
Limit pricing


What if one seller can act before others?
Game in extensive form – competing sellers set prices in
sequence
25
Limit pricing

Limit pricing
 Entrant must incur fixed cost of production
 Set such price so low that potential
competitor’s residual demand is so low that
potential competitor cannot break even.
26
Limit pricing
27
Limit pricing

Limit pricing – Necessary conditions
 Production requires substantial fixed cost
 Leader’s price must be credible
Potential competitors must believe that leader will not
change price if potential competitor enters
 For leader, must be more profitable to produce at entrydeterring price than to accommodate entry and produce
an equal share with competitors.

28
Outline

Price competition
 Limit pricing
 Capacity competition
 Capacity leadership
 Restraining competition
29
Capacity competition:
Homogeneous product


Cournot model: Luna and Mercury
 Produce at constant marginal cost
 Compete on capacity to sell a homogeneous product
Game in strategic form – competing sellers set
capacities simultaneously
30
Capacity competition:
Homogeneous product



Residual demand: Demand given the actions of
competing sellers.
Given Mercury’s capacity, Luna’s residual demand curve
slopes downward
 If Luna raises price, some consumers would switch to
Mercury
Luna’s profit maximum
 Produce at scale where residual marginal revenue =
marginal cost
 Set capacity accordingly – as function of Mercury’s
capacity
31
Capacity competition:
Homogeneous product
32
Capacity competition:
Homogeneous product
Best response function:
Seller’s best action as a
function of the actions
of competing sellers.
33
Capacity competition:
Homogeneous product



Higher demand
 Higher residual demand
 Best-response function shifts toward higher capacity
 Equilibrium: Higher capacities
Higher marginal cost
 Best-response function shifts toward lower capacity
 Equilibrium: Lower capacities
Seller with lower cost gains
 Directly, from lower cost
 (Strategic response) Forces competitor to reduce
capacity
34
Strategic substitutes



Strategic substitutes: The adjustment by one party leads
other parties to adjust in opposite direction
Cournot model: Capacities are strategic substitutes
 Best-response functions slope downward
Other business choices – strategic
complements/substitutes?
 Advertising
 R&D
35
Key takeaways

For sellers competing on price to sell differentiated
products, to maximize profit, set price so that residual
marginal revenue equals marginal cost.
 When demand or costs change, adjust price so that: (i)
residual marginal revenue equals marginal cost, and (ii)
the best-response price is a Nash equilibrium.
 If prices are strategic complements, then adjust price in
the same direction as competitors' prices.
 For sellers competing on capacity to sell a homogeneous
product, to maximize profit, set capacity so that residual
marginal revenue equals marginal cost.
 When demand or costs change, adjust capacity so that:
(i) residual marginal revenue equals marginal cost, and
(ii) the best-response capacity is a Nash equilibrium.
36
Key takeaways, cont’d




If capacities are strategic substitutes, then adjust
capacity in the opposite direction to competitors'
capacities.
To deter entry through limit pricing, set price so low that
potential competitors cannot break even.
To apply capacity leadership, choose capacity to
maximize profit given that competitors would choose
capacity according to their best-response functions.
Limit competition through agreements and horizontal
integration.
37