Transcript Lecture #10

ECON 4925 Autumn 2007
Electricity Economics
Lecture 10
Lecturer:
Finn R. Førsund
Market power
1
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
Hydro power plants aggregated to a single
plant
Market power
2
Monopoly problem with hydo and thermal
plants
T
max
Th
[(
p
(
x
)
x

c
(
e
 t t t
t )]
t 1
subject to
xt  etH  etTh
T
H
e
 t W
t 1
etTh  e Th
xt , etH , etTh  0, t  1,.., T
T ,W , e Th given
Market power
3
Solving the optimisation problem

The Lagrangian function (eliminating total
consumption)
T
L   [ pt (etH  etTh )(etH  etTh )  c(etTh )]
t 1
T
t (etTh  e Th )
t 1
T
 ( etH  W )
t 1
Market power
4
Solving the optimisation problem, cont.

The Kuhn – Tucker conditions
L
H
Th
H
Th
H
Th


p
(
e

e
)(
e

e
)

p
(
e

e
t
t
t
t
t
t
t
t ) 0
H
et
( 0 for etH  0)
L
H
Th
H
Th
H
Th
Th


p
(
e

e
)(
e

e
)

p
(
e

e
)

c
'(
e
t
t
t
t
t
t
t
t
t )  t  0
Th
et
( 0 for etTh  0)
  0 ( 0 for
T
H
e
 t W)
t 1
t  0 ( 0 for etTh  e Th )
Market power
5
Interpreting the optimality conditions

Assumption: both hydro and thermal capacity
is used
pt ( xt )(1  t )    c(etTh )  t


Flexibility-corrected price equal to water
value equal to marginal thermal costs (plus
shadow value on the capacity constraint)
Same amount of thermal capacity used in
each period
Market power
6
Monopoly and extended bath-tub
Period 1
Period 2
p2M
p1M
λM
c’
c’
a
A
B c
C
D
d
Hydro energy
Thermal extension
Market power
7
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
Market power
8
The optimisation problem of the
dominant hydro firm
T
max
H
p
(
x
)
e
 t t t
t 1
subject to
xt  etH  etTh
T
H
e
 t W
t 1
pt ( xt )  c(etTh )
xt , etH , etTh  0, t  1,.., T
T ,W given
Market power
9
The reaction of the competitive fringe

Finding the reaction of the fringe to the
quantity of the dominant firm
pt (etH  etTh )  c(etTh ), t  1,..,T

Solving for thermal output as a function of hydro
output
etTh  ft (etH ), ft  0 (t  1,..,T )
Market power
10
The reaction of the competitive fringe,
cont

Determining the sign of the reaction function

Differentiating the behavioural condition
pt (etH  etTh )(detH  detTh )  c(etTh )detTh 
detTh
 pt (etH  etTh )

 0 (t  1,.., T )
H
H
Th
Th
det
pt (et  et )  c(et )
Market power
11
Solving the optimisation problem of the
dominant hydro firm

The Lagrangian function
T
L   pt (etH  f t (etH ))etH
t 1
T
 ( etH  W )
t 1

The Kuhn – Tucker conditions
Th
de
L
H
Th
H
Th
H
t


p
(
e

e
)

p
(
e

e
)
e
(1

) 0
t
t
t
t
t
t
t
H
H
et
det
( 0 for etH  0)
T
  0 ( 0 for  etH  W ) , t  1,.., T
t 1
Market power
12
Interpretations

Signing of the expression (1 + detTh/detH)
detTh
 pt (etH  etTh )
1 H 1

H
Th
Th
det
pt (et  et )  c(et )
c(etTh )
0
H
Th
Th
pt (et  et )  c(et )
Market power
13
Interpretations, cont.

Decomposition of conditional marginal
revenue
MRt pt c

etH
detTh H
 pt (1  t H
)  pt H et , t  1,.., T
Th
et  et
det
Conditional marginal revenue curve closer to
demand curve due to


Market share less than 1
Fringe reaction of increasing output when price
increases
Market power
14
A constraint on fringe thermal capacity

Advantage for the dominant firm when fringe
capacity constraint is biting

Limit on the fringe quantity reaction
pt ( xt )  ct(etTh )  t
t  0 ( 0 for etTh  e Th )

Fringe response
etTh  e Th for pt ( xt )  p  c(e Th )
Market power
15
The leader – follower game
Period 1
Period 2
p2
θ2
c’
p1
c’
λ
λ
A
B
C
D
E
Hydro energy
Thermal fringe
Market power
16
Extentions

Hydro as competitive fringe


Oligopoly game between hydro producers



Hydro fringe can release all water just in one
period, may restrict market power further
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
Market power
17
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?
Market power
18