The Use of Oligopoly Equilibrium
for Economic and Policy Applications
Jim Bushnell, UC Energy Institute and Haas School of Business
A Dual Mission
• “Research Methods” - how oligopoly models can be used to tell us something useful about how markets work– Potentially very boring
• What makes electricity markets work (or not)?– Blackouts, Enron, “manipulation,” etc.– A new twist on how we think about vertical
relationships– Potentially very exciting
Oligopoly Models
– Large focus on theoretical results– Simple oligopoly models provide the
“structure” for structural estimation in IO
– Seldom applied to large data sets of complex markets• Some markets feature a wealth of detailed
data• Optimization packages make calculation of
even complex equilibria feasible
A Simple Oligopoly Model
• Concentration measures
where m is Cournot equilibrium margin.
HHI s i2
i
qi
Q
2
i
m p MC
p
1
n
HHI
Surprising Fact: Oligopoly models can tell us
something about reality• Requires careful consideration about the
institutional details of the market environment – Incentives of firms (Fringe vs. Oligopoly)– Physical aspects of production (transmission)– Vertical & contractual arrangements
• Recent research shows actual prices in several electricity markets reasonably consistent with Cournot prices
• Cournot models don’t have to be much more complicated than HHI calculations
b
nqap
bcn
bkaq i
i
,1
Empirical Applications
• Analysis of policy proposals– Prospective analysis of future market– Merger review, market liberalization, etc.
• Market-level empirical analysis– Retrospective analysis of historic market– Diagnose sources of competition problems– Simulate potential solutions
• Firm-level empirical analysis– Estimate costs or other parameters (contracts)– Evaluate optimality of firm’s “best” response– Potentially diagnose collusive outcomes
Oligopoly equilibrium models
• Cournot – firms set quantities– many variations
• Supply-function – firms bid p-q pairs– infinite number of functional forms– Range of potential outcomes is bounded by
Cournot and competitive– Capacity constraints, functional form
restrictions reduce the number of potential equilibria
• Differentiated products models (Bertrand)
Green and Newbery (1992)
Simple Example
• 2 firms, c(q) = 1/2 qi 2, c = mc(q) = qi
• Market supply = Q = q1 + q2
• Linear demand Q = a-b*p = 10 – p• NO CAPACITY CONSTRAINTS
3
10
2)(
0)2(
5.)( 2
jjiji
iji
i
i
iiji
i
q
b
qaqqBR
qb
qqa
q
qqb
qqa
2 Cournot FirmsBest Reply Functions
0
1
2
3
4
5
6
7
8
9
10
0 1 2 3 4 5 6 7 8 9 10
Firm 2
Fir
m 1
BR2(q1) BR1(q2)
Three Studies of Electricity
• Non-incremental regulatory and structural changes– Historic data not useful for predicting future behavior
• Large amounts of cost and market data available– High frequency data - legacy of regulation
• Borenstein and Bushnell (1999)– Simulation of prospective market structures
• Focus on import capacity constraints
• Bushnell (2005)– Simulation using actual market conditions
• Focus on import elasticities
• Bushnell, Saravia, and Mansur (2006)– Simulation of several markets
12
Western Regional Markets
• Path from NW to northern California rated at 4880 MW
• Path from NW to southern California rated at 2990 MW
• Path from SW to southern California rated at 9406 MW (W-O-R constraint)
• 408 MW path from northern Mexico and 1920 MW path from Utah
13
Cournot Equilibrium andCompetitive Market Price for Base Case - Elasticity = -.1
March
0
10
20
30
40
50
60
Pe
ak
15
0th
30
0th
45
0th
60
0th
74
4th
Demand Level
Pri
ce
($
/Mw
h)
June
0
10
20
30
40
50
60
Pe
ak
15
0th
30
0th
45
0th
60
0th
72
0th
Demand Level
Pri
ce
($
/Mw
h)
September
0100200300400500600700800900
1000
Pe
ak
15
0th
30
0th
45
0th
60
0th
72
0th
Demand Level
Pri
ce
($
/Mw
h)
December
050
100150200250300350400450500
Pe
ak
15
0th
30
0th
45
0th
60
0th
74
4th
Demand Level
Pri
ce
($
/Mw
h)
Table 1: Panel A, California Firm Characteristics
HHI of 620
Output Output Load Load Firm Fossil Water Nuclear Other Max Share Max Share PG&E 570 3,878 2,160 793 7,400 17% 17,676 39% AES/Williams 3,921 - - - 3,921 9% - - Reliant 3,698 - - - 3,698 8% - - Duke 3,343 - - - 3,343 8% - - SCE - 1,164 2,150 - 3,314 8% 19,122 42% Mirant 3,130 - - - 3,130 7% - - Dynegy/NRG 2,871 - - - 2,871 6% - - Other 6,617 5,620 - 4,267 16,504 37% 9,059 20% Total 24,150 10,662 4,310 5,060 44,181 45,857
Methodology for Utilizing Historic Market Data
• Data on spot price, quantity demanded, vertical commitments, and unit-specific marginal costs.
• Estimate supply of fringe firms.– Calculate residual demand.
• Simulate market outcomes under:– 1. Price taking behavior: P =
C’– 2. Cournot behavior: P + P’ * q = C’– 3. Cournot behavior with vertical
arraignments: P + P’ * (q-qc) = C’
Modeling Imports and Fringe
• Source of elasticity in model• We observe import quantities, market price, and weather
conditions in neighboring states• Estimate the following regression using 2SLS (load as
instrument)
9
6 1
7 24
2 2
ln( )S
fringet i it t s st
i s
j jt h ht tj h
q Month p Temp
Day Hour
• Estimates of price responsiveness are greatest in California (>5000) relative to New England (1250) and PJM (850)
Residual Demand function
ttt
actualt
actualtt
Qp
pQ
exp
)ln(
• The demand curve is fit through the observed price and quantity outcomes.
mean mean meanobservations Cournot PX Competitive
price ($/MWh) price ($/MWh) price ($/MWh)June 699 127.93 122.29 52.67July 704 131.84 108.60 60.27August 724 185.02 169.16 79.14September 696 116.26 116.64 75.12
Table 1: Cournot Simulation and Actual PX Prices - Summer 2000
Simulation ResultsCalifornia 2000
01
00
20
03
00
40
0co
urn
ot/
PX
_p
rice
/co
mp
etit
ive
0 5000 10000 15000dem_cal
cournot PX_price
competitive
Actual Counter-factualMW HHI MW HHI
AES 3921 550 1873 126Dynegy 2871 295 1165 49Duke 3343 400 1585 90
Mirant 2886 298 2886 298Reliant 3698 489 2306 190
SDG&E units NA NA 1407 71Alamitos NA NA 2048 150Ormond NA NA 1271 58
Moss NA NA 1474 78South Bay NA NA 704 18
16718 2032 16718 1126
Table 1: Actual and Hypothetical Thermal Ownership
Total Cost Total Cost Total CostCournot Divest Savings$ Million $ Million $ Million
June 1870 1410 466July 1830 1420 415August 2800 2190 605September 1570 1230 341
Total 8070 6250 1827Table 1: Market Savings from Further Divestiture
Impact of Further Divestiture
(summer 2000)
September 2000 Cournot Prices
0.00
50.00
100.00
150.00
200.00
250.00
300.00
0 2000 4000 6000 8000 10000 12000 14000 16000 18000
Residual Demand
Pri
ce (
$/M
Wh
)
Simple Cournot actual non-linear cournot
The Effect of Forward Contracts
• Contract revenue is sunk by the time the spot market is run– no point in withholding output to drive up a price
that is not relevant to you• More contracts by 1 firm lead to more spot
production from that firm, less from others• More contracts increase total production
– lower prices• Firms would like to be the only one signing
contracts, are in trouble if they are the only ones not signing contracts– prisoner’s dilemma
Simple Example
– 2 firms, c(q) = 1/2 qi 2, c = mc(q) = qi
– Market supply = Q = q1 + q2
– Linear demand Q = a-b*p = 10 – p– NO CAPACITY CONSTRAINTS
– Firm 2 has contracts for quantity qc2
3
10
2)(
0)2(
5.)(
2121212
2212
2
2
2222
122
cc
c
c
b
qqaqqBR
qb
qqqa
q
qqqb
qqa
2 Cournot FirmsBest Reply Functions
0
1
2
3
4
5
6
7
8
9
10
0 1 2 3 4 5 6 7 8 9 10
Firm 2
Fir
m 1
BR2(q1) BR1(q2)
2 Cournot FirmsBest Reply Functions
0
1
2
3
4
5
6
7
8
9
10
0 1 2 3 4 5 6 7 8 9 10
Firm 2
Fir
m 1
BR2(q1) BR1(q2)
Green and Newbery (1992)
0
$Dmax
DminBound on NCEquilibriumoutcomes
Cournot
competitive
Bounds on Non-Cooperative Outcomes
Qsupplied
0
$
Qsupplied
Dmax
DminBound on NCEquilibriumoutcomes
Cournot
competitive
Contracts Reduce Bounds
Contract Q
0
Dmax
Dmin Bound on NCEquilibriumoutcomes
Cournot
competitive
Contract QQsupplied
$
“Over-Contracting’ can drive prices below competitive
levels
Vertical structure and forward commitments
• Vertical integration makes a firm a player in two serially related markets
• Usually we think of wholesale (upstream) price determining the (downstream) retail price– Gilbert and Hastings– Hendricks and McAfee (simultaneous)
• In some markets, retailers make forward commitments to customers– utilities – telecom services – construction
• In these markets a vertical arrangement plays the same role as a forward contract– a pro-competitive effect
Retail and Generation in PJM, 1999
GPU Inc.GPU Inc.
Public Service Electric & Gas
Public Service Electric & Gas
PECO Energy
PECO EnergyPP&L Inc.
PP&L Inc.
Potomac Electric Power
Potomac Electric Power
Baltimore Gas & Electric
Baltimore Gas & ElectricOther
Other
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Retail Generation
Retail and Generation in New England 1999
Northeast Util.Northeast Util.
PG&E N.E.G.
PG&E N.E.G.
Mirant
Sithe
FP&L Energy
Wisvest
Other
Other
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Retail Generation
Retail and Generation in California 1999
PG&E
PG&E
SCE
SCE
AES/Williams
Reliant
Mirant
Duke
Dynegy/NRG
Other
Other
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Retail Generation
Methodology
• Simulate prices under:– Price taking behavior– Cournot behavior– Cournot with vertical arraignments (integration or
contracts)
, c tt i,t -i,t i,t i,t i,t i,t
, i,t
p=p (q ,q )+[q -q ]· -C (q ) 0
qi t
i tq
ci,tq
• Use market data on spot price, market demand and production costs.
• The first order condition is:
Methodology
• Data on spot price, quantity demanded, vertical commitments, and unit-specific marginal costs.
• Estimate supply of fringe firms.– Calculate residual demand.
• Simulate market outcomes under:– 1. Price taking behavior: P = C’– 2. Cournot behavior: P + P’ * q = C’– 3. Cournot behavior with vertical arraignments:
P + P’ * (q-qc) = C’
Summary
• Oligopoly models married with careful empirical methods are a useful tool for both prospective and retrospective analysis of markets
• Careful consideration of the institutional details of the market is necessary
• In electricity, vertical arrangements (or contracts) appear to be a key driver of market performance– The form and extent of these arrangements going
forward will determine whether the “success” of the markets that are working well can be sustained
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