Comments on
Inflow Uncertainty in Hydropower
Markets
by
Petter Vegard Hansen
June 9, 2008
Mats Bergman
([email protected])
Saltsjöbaden,
June 9, 2008
Hydropower uncertainty
Mats Bergman
1
Main idea & findings
• Effect of (inflow) uncertainty on prices and
efficiency in a hydropower system
• With certainty and equal demand in both
periods, a social planner and firms with
market power would equalize prices (and
hence output) between periods
– Assuming no spilling, non-binding storage
constraints, no discounting
Saltsjöbaden,
June 9, 2008
Hydropower uncertainty
Mats Bergman
2
Market power with
identical demand
D2
D1
MR2
MR1
Q
Saltsjöbaden,
June 9, 2008
Hydropower uncertainty
Mats Bergman
3
Market power with
non-identical demand
Saltsjöbaden,
June 9, 2008
Hydropower uncertainty
Mats Bergman
4
• With uncertainty, the curvature of the
demand function (utility function) becomes
important
• With convex demand, expected price in
second period rises as inflow variation rises
• Socially and privately optimal to shift
production to period 2
Saltsjöbaden,
June 9, 2008
Hydropower uncertainty
Mats Bergman
5
• A social planner equalizes first-period price with
expected second-period price
• A monopoly equalizes first-period marginal
revenue with expected second-period marginal
revenue
• Compared to the social planner, the monopoly
– produces equally much with linear and constant-elastic
demand
– in general picks other quantities; more or less
depending on a condition that includes 1st, 2nd and 3rd
order derivatives of the demand function
Saltsjöbaden,
June 9, 2008
Hydropower uncertainty
Mats Bergman
6
Comments
• While it is true that a monopoly will
equalize marginal revenues in both periods,
• This does not necessarily imply that
production will be equalized over the two
periods under certainty, even for identical
demand functions
• Hence, market power can reduce welfare
even without uncertainty, as illustrated by
the following example
Saltsjöbaden,
June 9, 2008
Hydropower uncertainty
Mats Bergman
7
50
40
30
P1
20
D
MR
10
P2
0
1 2
3 4
5 6
7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
X2
-10
X1
-20
Saltsjöbaden,
June 9, 2008
Hydropower uncertainty
Mats Bergman
8
50  6 x  0.2 x 2
P
if
5
x  15
x  15
X  x1  x2  30
x1  5
p1  15
x2  25
p2  5
Total supply (in
both periods)
The firm’s optimal
solution
p( x) x  2 p( x)  0
Saltsjöbaden,
June 9, 2008
Demand
Hydropower uncertainty
Mats Bergman
Condition that guarantees a monotone
MR – and hence that the monopoly
under certainty equalizes period 1 and
2 quantities. A standard assumption –
but maybe not inocuous, as shown by
the example.
9
How to exert market power
with hydro
• Export hydro-generated power during the
summer to create a shortage during the
winter
• Generally, price is set lower in the more
elastic markets or periods
• In the long run, invest too little
- How important is the curvature of the
demand curve, compared to these effects?
Saltsjöbaden,
June 9, 2008
Hydropower uncertainty
Mats Bergman
10
Technical comment
• Why both  and /? Sufficient with one
variable to represent uncertainty?
Saltsjöbaden,
June 9, 2008
Hydropower uncertainty
Mats Bergman
11