market power1 econ 4925 autumn 2006 resource economics market power lecturer: finn r. førsund
TRANSCRIPT
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Market power 1
ECON 4925 Autumn 2006 Resource Economics Market power
Lecturer:
Finn R. Førsund
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Market power 2
Background
The use of market power is a potential problem of the deregulated electricity sector
20 % of the world’s electricity is produced by hydropower and 1/3 of the countries have more than 50%
Hydro power is a special case due to zero variable cost, water storage, high effect capacity and maximal flexible adjustment
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Market power 3
Plan of the talk
The basic hydropower model Hydropower model with limited reservoir Hydropower and thermal power Hydropower with thermal competitive fringe
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Market power 4
The basic hydropower model
Discrete time periods (weeks) over a natural inflow cycle (one year) Deterministic demand and total water
All inflow occur in the first period, e.g. after snow melting, spring rain, autumn rain
The reservoir limit of the system will not be reached
Zero variable costs in the hydro system Only variable cost alternative value of water
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Market power 5
Social utilisation of water
Social planning: maximising sum of consumer plus producer surplus = area under the demand curves
No discounting Free terminal value of reservoir Optimal solution: arbitrage price of stock of
water (Hotelling); marginal willingness to pay (price) equal for all time periods
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Market power 6
The monopoly model
Problem formulation The Lagrangian
First-order condition1
1
( )
. .
, given
TH H
t t tt
THt
t
Max p e e
s t
e W
W T
1 1
( ) ( )T T
H H Ht t t t
t t
p e e e W
1
( ) ( ) 0
( 0 for 0) , 1,..,
0 ( 0 for )
H H Ht t t t tH
t
Ht
THt
t
Lp e e p e
e
e t T
e W
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Market power 7
The monopoly model, Interpretation of the conditions Maximising profit introduces marginal revenue
functions
Marginal revenue can be expressed as demand-flexibility corrected prices
Optimality condition: flexibility - corrected prices equal for all time periods
Market prices will vary with relative elastic periods having lower prices than relative inelastic periods
' ' '( )(1 ) ( )(1 ) , , ' 1,..,H Ht t t t t tp e p e t t T
( ) ( )H H Ht t t t tp e e p e
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Market power 8
Social optimum, and monopoly
p1(e1H)
p2M
Period 1 Period 2
p2S = λSp1
S= λS
p1M
λM
p2(e2H)
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Market power 9
Spilling and monopoly
Depending on the characteristics of the demand functions it may be optimal for the monopoly to spill water
Spilling can be regulated by prohibition Zero-spilling regulation will reduce the
monopoly profit
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Market power 10
Spilling and zero-spilling regulation
p1M
Period 2
λ<0
Period 1
p2M
λ<0
Total available energy
p2p1
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Market power 11
Limited reservoir and the social solution Reservoir dynamics: water at the end of a
period = water at the end of previous period plus inflow minus release of water during the period
Shadow prices on water and reservoir limit recursively related, solving using backward induction (Bellmann)
Overflow is waste Social price may vary if reservoir constraint is
binding
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Market power 12
Limited reservoir and monopoly Problem formulation The Lagrangian
1
1
( )
. .
, , 0 , 1,..,
, , given, free
TH H
t t tt
Ht t t t
t
Ht t t
o T
Max p e e
s t
R R w e
R
R w e t T
T R R R
1
11
1
( )
( )
( )
TH H
t t tt
TH
t t t t tt
T
t tt
L p e e
R R w e
R R
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Market power 13
Limited reservoir and monopoly, cont. First-order conditions
1
1
( ) ( ) 0 ( 0 for 0)
0 ( 0 for 0)
0 (0 for )
0 (0 for ) , 1,..,
H H H Ht t t t t t tH
t
t t t tt
Ht t t t t
t t
Lp e e p e e
e
LR
R
R R w e
R R t T
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Market power 14
Limited reservoir and monopoly, cont. The flexibility-corrected price substitute for
the social price Flexibility-corrected prices may differ if
reservoir constraint binding Social solution may be optimal if binding
constraint Differences with social solution depend on
the demand elasticities Spilling may be optimal
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Market power 15
Illustration of monopoly solutionwith reservoirPeriod 1
p1M
p2M
A B C D
Period 2
p1S
P2S
λM
p1M
Spill
λ2M
λ1M
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Market power 16
Hydro and thermal
Thermal plants aggregated by merit order to a convex group marginal cost function
Total capacity is limited Static problem: no start-up costs, no ramping
constraints or minimum time on – off Shadow price on water equal to flexibility-
corrected prices and equal to marginal cost of thermal capacity
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Market power 17
Hydro and thermal, the model Problem formulation The Lagrangian
1
1
[( ( ) ( )]
. .
, , 0, 1,..,
, , given
TTh
t t t tt
H Tht t t
THt
t
Th Tht
H Tht t t
Th
Max p x x c e
s t
x e e
e W
e e
x e e t T
T W e
1
1
1
[ ( )( ) ( )]
( )
( )
TH Th H Th Th
t t t t t tt
TTh Th
t tt
THt
t
L p e e e e c e
e e
e W
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Market power 18
Hydro and thermal model, cont First-order conditions
1
( )( ) ( ) 0
( 0 for 0)
( )( ) ( ) '( ) 0
( 0 for 0)
0 ( 0 for )
0 ( 0 for )
H Th H Th H Tht t t t t t t tH
t
Ht
H Th H Th H Th Tht t t t t t t t t tTh
t
Tht
THt
t
Th Tht t
Lp e e e e p e e
e
e
Lp e e e e p e e c e
e
e
e W
e e
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Market power 19
Monopoly and extended bath-tub
c’λM
c’
Hydro energy
p2M
Period 1 Period 2
p1M
Thermal extension
a A B c C D d
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Market power 20
Hydro with competitive fringe Thermal fringe modelled by a convex
marginal cost function with limited capacity The fringe is a price taker and sets market
price equal to marginal cost The dominant hydro firm must take fringe
reaction into consideration Market power is reduced due to the fringe Conditional marginal revenue curve closer to
demand curve due to market share less than 1 and fringe quantity adjustment
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Market power 21
Hydro with competitive fringe; the model Problem formulation
Fringe response
Total differentiation1
1
( )
. .
( ) ( )
, , 0, 1,..,
, given
TH
t t tt
H Tht t t
THt
t
Tht t t
H Tht t t
Max p x e
s t
x e e
e W
p x c e
x e e t T
T W
( ) ( )
( ), 0
H Th Tht t t t
Th Ht t t t
p e e c e
e f e f
( )( )
( )
( )0
( ) ( )
1,..,
H Th H Tht t t t t
Th Tht t
Th H Tht t t tH H Th Tht t t t t
p e e de de
c e de
de p e e
de p e e c e
t T
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Market power 22
Hydro with competitive fringe First-order conditions
1
( ) ( ) (1 ) 0
( 0 for 0)
0 ( 0 for ) , 1,..,
ThH Th H Th H t
t t t t t t tH Ht t
Ht
THt
t
deLp e e p e e e
e de
e
e W t T
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Market power 23
Hydro with competitive fringe, cont. Conditional marginal revenue
Closer to the demand function due to Market share effect Fringe quantity reaction effect
(1 )t
H ThHt t
t t t t tp c H Th Ht t t
e deMR p p e
e e de
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Market power 24
The leader – follower game
θ2
p2
c’p1
Thermal fringe
λλ
A B C D E
Hydro energy
c’
Period 1 Period 2
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Market power 25
Extentions Hydro as competitive fringe
Hydro fringe can release all water just in one period, may restrict market power further
Oligopoly game between hydro producers Essentially a dynamic game, reduces the
possibilities of strategic shifting of water Quite complex to find solutions to dynamic gaming
Uncertainty Future water values become stochastic variables,
system must avoid overflow or going dry, qualitatively the same problem for social planner and monopoly
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Market power 26
Conclusions Hydro monopoly shifts water from relatively
inelastic periods to elastic ones May be difficult to detect because variable
cost is zero, only alternative value of water is variable cost and not readily observable
Reservoir constraints, production constraints, etc. reduce the impact of market power
Competitive fringe may block use of market power
Fear of hydro market power exaggerated?