Market power 1

ECON 4925 Autumn 2007 Electricity Economics Lecture 10

Lecturer:

Finn R. Førsund

Market power 2

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 3

Monopoly problem with hydo and thermal plants

1

1

max [( ( ) ( )]

subject to

, , 0, 1,..,

, , given

TTh

t t t tt

H Tht t t

THt

t

Th Tht

H Tht t t

Th

p x x c e

x e e

e W

e e

x e e t T

T W e

Market power 4

Solving the optimisation problem The Lagrangian function (eliminating total

consumption)

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

Market power 5

Solving the optimisation problem, cont. The Kuhn – Tucker 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

Market power 6

Interpreting the optimality conditions Assumption: both hydro and thermal capacity

is used

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

( )(1 ) ( )Tht t t t tp x c e

Market power 7

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

Market power 8

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 9

The optimisation problem of the dominant hydro firm

1

1

max ( )

subject to

( ) ( )

, , 0, 1,..,

, given

TH

t t tt

H Tht t t

THt

t

Tht t t

H Tht t t

p x e

x e e

e W

p x c e

x e e t T

T W

Market power 10

The reaction of the competitive fringe Finding the reaction of the fringe to the

quantity of the dominant firm

Solving for thermal output as a function of hydro output

( ) ( ), 1,..,H Th Tht t t tp e e c e t T

( ), 0 ( 1,.., )Th Ht t t te f e f t T

Market power 11

The reaction of the competitive fringe, cont Determining the sign of the reaction function

Differentiating the behavioural condition

( )( ) ( )

( )0 ( 1,.., )

( ) ( )

H Th H Th Th Tht t t t t t 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 et T

de p e e c e

Market power 12

Solving the optimisation problem of the dominant hydro firm The Lagrangian function

The Kuhn – Tucker conditions

1

1

( ( ))

( )

TH H H

t t t t tt

THt

t

L p e f e e

e W

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

Market power 13

Interpretations

Signing of the expression (1 + detTh/detH)

( )1 1

( ) ( )

( )0

( ) ( )

Th H Tht t t tH H Th Tht t t t t

Tht

H Th Tht t t t

de p e e

de p e e c e

c e

p e e c e

Market power 14

Interpretations, cont.

Decomposition of conditional marginal revenue

Conditional marginal revenue curve closer to demand curve due to Market share less than 1 Fringe reaction of increasing output when price

increases

(1 ) , 1,..,t

H ThHt t

t t t t tp c H Th Ht t t

e deMR p p e t T

e e de

Market power 15

A constraint on fringe thermal capacity Advantage for the dominant firm when fringe

capacity constraint is biting Limit on the fringe quantity reaction

Fringe response

( ) ( )

0 ( 0 for )

Tht t t t t

Th Tht t

p x c e

e e

for ( ) ( )Th Th Tht t te e p x p c e

Market power 16

The leader – follower game

θ2

p2

c’p1

Thermal fringe

λλ

A B C D E

Hydro energy

c’

Period 1 Period 2

Market power 17

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

Market power 18

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?