Transcript ECONOMICS 3150B

ECONOMICS 3200M
Lecture 6
Ch. 6, 7
February 27, 2013
1
Oligopoly
Cournot competition
• Duopoly case
• Homogeneous products, single instrument – Qi (quantity produced by
each firm)
• Demand function: P(Q) = 1 – Q = 1- Q1 – Q2
• Ci (Qi) = Ci Qi (constant returns), where C1  C2
• Firm 1:
–
–
–
–
–
Max 1 (Q1, Q2) = Q1 (1- Q1 – Q2) – C1 Q1
d 1 /d Q1 = 1- 2 Q1 - Q2 - C1 = 0
Reaction function for firm 1: Q1 = [1- Q2 - C1]/2 = R1 (Q2)
Strategic substitutes since d Q1/d Q2 < 0
Reaction function for firm 2: Q2 = [1- Q1 – C2]/2 = R2 (Q1)
2
Oligopoly
Cournot competition
• Nash equilibrium: solve by equating reaction functions:
– R1 (Q2) = R2 (Q1)
– Q1* = [1 + C2 – 2C1 ]/3
– Q2* = [1 + C1 – 2C2 ]/3
•
P* = [1 + C1 + C2 ]/3
•
1* = [1 + C2 – 2C1 ]2/9
2* = [1 + C1 – 2C2 ]2/9
If C1 < C2  1 > 2
•
With symmetric costs and N firms [Ci = C]
•
•
– Qi* = [1 - C]/(N+1)
– P* = [1+ NC]/(N+1)
– As N increases, Qi* decreases, P decreases towards C and the profit for each firm
decreases towards 0
3
Q1
Q2 = R2 (Q1, C2)
1
Q1 = R1 (Q2, C1)
Q2
4
Oligopoly
• In monopoly (if no X-inefficiency), Bertrand competition
and perfect competition models, production occurs at
lowest cost
– Higher cost producer cannot survive
• With Cournot competition, higher cost producer can
survive
5
Oligopoly
Stackelberg competition
• Firm 1 is the leader and firm 2 is the follower – why?
• Firm 1 knows firm 2’s reaction function – assume same demand and
cost conditions as in Cournot example
• Firm 1:
– Max 1 (Q1, Q2) = Q1 (1- Q1 – Q2) – C1 Q1
– Q2 = [1- Q1 – C2]/2 = R2 (Q1)
– Max 1 (Q1) = Q1 (1- Q1 + C2)/2 – C1 Q1
– d 1 /d Q1 = 0.5- Q1 + 0.5C2 - C1 = 0
– Q1* = [1 + C2 – 2C1 ]/2 > Q1* (Cournot) = [1 + C2 – 2C1 ]/3
– Q1* (follower) < Q2* (Cournot)
– Leader has higher profits than in Cournot game – Firm 1 a leader
most likely because it ahs lower costs
6
Q1
Q2 = R2 (Q1, C2)
S
N
Q1 = R1 (Q2, C1)
Q2
7
Oligopoly
• Equilibrium prices (highest to lowest)
–
–
–
–
Monopoly/Infinite period repeated duopoly
Cournot duopoly
Stackelberg duopoly
Competition/Bertrand duopoly/Single game duopoly
• Extensions:
• (1) Bertrand with sunk costs, firm 1 incumbent, firm 2 potential entrant
– Unless potential entrant has a cost advantage, firm 2 anticipates that
incumbent will lower price to eliminate economic profits (firm 1 will
ignore its sunk costs in setting price in response to entry: P < AC where
AC includes sunk costs), so firm 2 will not invest ex ante in what will
become sunk costs ex post because it will not be able to earn competitive
return on investment
– First mover advantage with sunk costs
8
Oligopoly
• Extensions:
• (2) Stackelberg with capacity constrain for leader
– If leader (firm 1) does not have capacity to produce Q1* = [1 + C2 –
2C1]/2, firm 1 will produce up to its capacity
– Resulting equilibrium: pt. 2 in following
9
Q1
Q2 = R2 (Q1, C2)
Q1
S
2
Q1
NQ1
S
2
N
Q1 = R1 (Q2, C1)
Q2
10
Oligopoly
• Extensions:
• (3) Repeated game Bertrand
– Cooperation with P=PM , and monopoly profits shared
– Competition shifts away from prices to other strategies involving
instruments that cannot be easily detected or imitated
• Research
• Marketing, sales
11
Oligopoly
Examples of non-cooperation
• Overcapacity
• Price wars
• Advertising
– Fixed end-point – financially weak competitor
•
•
•
•
Lobbying to change bankruptcy laws to make it more difficult to exit
Aggressive pricing
Rumors
Banks unwilling to lend to weak financial institutions
12
Oligopoly
Factors facilitating cooperation
• Competition law
• No leader
• Low costs for detecting cheating
– Small numbers, homogeneous product, transparency in pricing
• Expected benefits
• MAD strategy
• Contracts
– Most favored nation clause
– Meet the competition
13
Oligopoly
Competition shifts to difficult to detect, time-consuming to
respond strategies
•
•
•
•
•
Product innovations/introductions
Marketing
Lobbying
Production technology innovations
Exclusive contracts – suppliers, distributors
14
Oligopoly
• Oligopoly markets generally consist of one to three
dominant firms and several smaller firms
• Dominant position may not survive over time
• How does a firm become dominant – see discussion
regarding how a monopoly develops
• Why doesn’t dominance survive?
– Consider case of Canadian steel companies (Dofasco, Stelco,
Ipsco, Algoma) and Arcelor Mittal
• Canadian steel companies have been acquired
– RIM, Blockbuster, Nokia, GM, PanAm, Sears, Groupon, Merrill
Lynch, Xerox, Kodak, Nortel, etc.
15
Hollowing Out
• Canadian companies acquired by foreign companies:
– Inco; Falconbridge; Dofasco; Ipsco; Stelco; Algoma; Masonite;
ATI; Moore; Four Seasons; Fairmont Hotels; The Bay; Domtar;
Alcan; Molson’s; Labatt’s; Vincor; Future Shop; Nexen
• Definition of hollowing out:
– As Canadian-owned, Canadian-headquartered companies are
bought up by foreigners, head-office jobs, capital markets listings,
corporate tax revenues, and charitable donations are disappearing
potentially resulting in the hollowing out of Canada’s economic
sovereignty
– Not a Canadian phenomenon alone
16
Hollowing Out
• Debate
– Causes – government policies or management?
• In a spiky world, firms either globalize or eventually get swallowed
up by a globalizing corporation, typically headquartered elsewhere
• Canadian managers that ignore this reality are fooling themselves and
selling Canada short (Roger Martin and Gordon Nixon)
– Good or bad for Canada – employment, productivity, standard of
living
– Policies: corporate taxation; screening foreign takeovers;
regulations; inter-provincial trade barriers; human capital;
infrastructure; subsidies
17
Hollowing Out
• Michael Porter: explained why entire global industries were often
headquartered in a single country if not a single region within a single
country
• Set of conditions in local market creates a cluster of competitive
companies that pressure each other to innovate and upgrade, teach
local customers to be ever-more demanding, draw in and develop
human resources, and attract co-location of helpful related and
supporting industries – external economies of scale
• Result: cluster that keeps getting better and better and, on the basis of
that beneficial local competition, helps its members succeed
internationally against competitors from elsewhere who don't have the
power of a strong local cluster behind them
• Porter's theory predicts a spiky world in which most of the successful
competitors in a global industry come from very few places and export
to the rest of the world
18
Hollowing Out
• Increasing favorable trade conditions and falling transportation and
communications costs combine to make globalizing more of a reality
as leading national firms find themselves pressured by capital markets
to expand globally rather than stay at home
• Research and development-intensive firms find that the only way they
can afford to invest in competitive technological solutions is to utilize
the scale economies of a global market
• Transformation proceeding in one direction only – to a spikier world in
which all the globally competitive firms in all industries are
headquartered in a limited number of locations
19
Monopolistic Competition
• Product differentiation
– Product consists of bundle of characteristics – quality, location, color,
time of availability, etc.
– Computers, laptops, clothing, air travel
• Firms have some degree of market power
• Standard model
– Free entry may drive profits to 0, at least for marginal firms in
market
– Definition of industry/market?
– Critical value for cross-price elasticity of demand?
20
Monopolistic Competition
• Vertical differentiation model – characteristic: quality
• Quality (S): S [0, 1]
– Consumers agree over most preferred mix of characteristics and over
preference ordering: S1 > S2 implies that quality S1 exceeds quality S2 and
higher quality preferred over lower quality
– Consumers have perfect information regarding quality
– Value (utility – U) to consumer: U = S – P
• Model:
– Consumer buys if U > 0  S > P
– Does not buy if U  0  S  P
– Distribution of tastes ( ) across all consumers: F(), where F(min) = 0
and F(max) = 1
– F(0): proportion of all consumers with taste parameter   [0, 0]
21
Monopolistic Competition
Case 1
• 2 products with qualities S1 > S2 and P1 > P2
• Assume:
– S1/P1 > S2/P2   S1/P1 >  S2/P2
• Consumers will prefer the higher quality product if:
–  S1 – P1 >  S2 – P2 and
–  S1 – P1 > 0
• Since  S1/P1 >  S2/P2 then:
–
–
–
–
[ S1/P1 – 1] > [ S2/P2 – 1]
P1[ S1 – P1] > P2[ S2 – P2]
Since P1 > P2 , consumers prefer higher quality product
Product differentiation, but only high quality variety of product is
produced and sold
22
Monopolistic Competition
Case 2
• 2 products with qualities S1 > S2 and P1 > P2
• Assume:
– S1/P1 < S2/P2   S1/P1 <  S2/P2
• Consumers will prefer the higher quality product if:
–  S1 – P1 >  S2 – P2 and
–  S1 – P1 > 0
• Since  S1/P1 <  S2/P2 then:
– [ S1/P1 – 1] < [ S2/P2 – 1]
– P1[ S1 – P1] < P2[ S2 – P2]
– Since P1 > P2 , consumer preference indeterminate
23
Monopolistic Competition
Case 2
• Critical value for  separates consumers into two groups: one group
prefers S1 { S1 – P1 >  S2 – P2} and the other prefers S2 { S1 – P1 < 
S2 – P2}
• Critical value (*):
– Consumers indifferent when:  S1 – P1 =  S2 – P2
– * = [P2 – P1]/[S1 – S2]
24
Monopolistic Competition
Case 2
• When  > *, consumer prefers higher quality variety (S1)
– Demand for high quality product: consumers with   [(P2 – P1)/(S1 – S2),
max]
– Aggregate demand: D(S1, S2, P1, P2) = N[1-F((P2 – P1)/(S1 – S2))]
– D(S1, S2, P1, P2) increases if S1 increases, S2 decreases, P1 decreases and/or
P2 increases
• When  < *, consumer prefers lower quality variety (S2)
– Demand for low quality product: consumers with   [P2/ S2, (P2 – P1)/(S1
– S2)]
– Aggregate demand: D(S2, S1, P1, P2) = N[F((P2 – P1)/(S1 – S2)) – F(P2/ S2)]
– D(S2, S1, P1, P2) increases if S1 decreases, S2 increases, P1 increases and/or
P2 decreases
25
Monopolistic Competition
• Location model – example of differentiation
• Different locations represent different varieties of a product
– Varieties differentiated by geographic location or other characteristics
• Consumers have preferred location/characteristics for a product
– For given price, utility maximized at preferred location
– Utility declines as actual product location differs (moves farther away)
from preferred location
• To make problem manageable, focus on one characteristic
26
Monopolistic Competition
Hotelling model
• Horizontal differentiation – location (nearness in terms of product
characteristics other than quality) matters
• Transportation cost – disutility of choice/location different from
preferred choice/location: T per unit of “distance”
• Competition drives two firms to locate at same place/location if
consumers uniformly distributed (tastes regarding preferred locations)
along product/geographic space
– No product differentiation
• Identical location result reinforced if consumers normally distributed
along product/geographic space
– Largest concentration of consumers around mean of distribution
• Identical location – homogeneous products, Bertrand price competition
27
Monopolistic Competition
Hotelling model
• Assume two firms locate at end-points (maximize product
differentiation) to minimize price competition/maximize market power
• Product differentiation establishes clienteles (market niches) and
allows firm to enjoy some market power over clientele
• 2-stage game: firms choose location (anticipating outcome of price
competition), then firms simultaneously chooses prices
– Optimal location at end-point of 2-dimensional geographic space (straight
line)
– Consumers located at X  [0, 1] – total cost to each consumer of two
products located at respective end-points
• Product at 0: P0 + TX
• Product at 1: P1 + T(1-X)
28