Market power 1

ECON 4925 Autumn 2006 Resource Economics Market power

Lecturer:

Finn R. Førsund

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

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

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

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

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

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

Market power 8

Social optimum, and monopoly

p1(e1H)

p2M

Period 1 Period 2

p2S = λSp1

S= λS

p1M

λM

p2(e2H)

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

Market power 10

Spilling and zero-spilling regulation

p1M

Period 2

λ<0

Period 1

p2M

λ<0

Total available energy

p2p1

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

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

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

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

Market power 15

Illustration of monopoly solutionwith reservoirPeriod 1

p1M

p2M

A B C D

Period 2

p1S

P2S

λM

p1M

Spill

λ2M

λ1M

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

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

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

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

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

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

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

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

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

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

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?