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Forward Contracts, Auctions and
Efficiency in Electricity Markets
Pablo Serra
Universidad de Chile
Introduction
 The purpose of this work is to derive an efficient market
organization for the electricity industry.
 Stylized facts of Chilean economy
 Even if almost all consumption were traded in
future/forward markets, a spot market would still be
required for balancing short-term contingencies.
 The spot market, unless unregulated, is likely to be
inefficient as generating companies would exert market
power.
 Capacity is fixed in the short-run and no inventories are at hand
 The generation industry is not atomistic
Results
 Free entry, “efficient” regulation of the spot market
and demand participation are concurrent conditions
for an efficient market.
 If entry barriers limit the number of generators:
 Generators exert market power via their investment
decisions.
 Long-term forward contracting reduces market power.
 Achieving the efficient equilibrium requires that demand
be auctioned
 Market reform has not worked.
The basic model
 Single-technology model with linear costs.
 The per-unit operating cost is c, the per unit capacity
cost is r, and k represents the industry’s installed
capacity.
 Power generation, however, has an upper bound equal to
θk, where  is a random variable representing, for
instance, hydrology with a distribution function dF().
 Demand is given by q = a-p, where p denotes the
price.
The basic model
 Efficient regulation: mandatory dispatch of units in merit
order as long as the spot price exceeds the variable cost.
 Capacity is always fully used (conditions are in the paper).
 Thus the spot price equals:
p ( k ,  )  a  k
 All parties are risk-neutral and have rational expectations
 The industry’s expected profits are given by:
 (k )  (a  c)kE( )  k 2 E ( 2 )  rk
Efficient solution
 Consumer surplus
 Social welfare we (k )  (a  c)kE( )  k 2 E ( 2 ) / 2  rk
 Efficient solution
(a  c) E ( )  r
k* 
E ( 2 )
 Notice that π(k*)= 0.
 Hence free entry and perfect regulation of the spot
market ensure efficiency.
Oligopolistic equilibrium
 Firm i’s payoff function is:
 ie (k i, ki )  (a  c)ki E ( )  ki kE( 2 )  rki
 Reaction curve
(a  c) E ( )  kE( 2 )  r
ki 
E ( 2 )
 Nash equilibrium with n symmetrical firms:
k*
nk *
n
n
ki 
k 
n 1
n 1
Long-term forward market
 Three-period static game (extends Allaz and Vila
1993 to consider stochastic supply)
 Period 1, firms offer forwards that atomistic speculators buy to
resell in the spot market.
 Period 2, generators simultaneously commit their investments
given existing forward contracts.
 Period 3, after uncertainty is solved, the dispatcher determines
the spot price that balances supply and demand.
 Supply contracts are enforceable and observable.
 The game is solved by backwards induction.
Period 2: Capacity choices
 For simplicity, the discount rate is assumed to be zero.
 Then firm i’s value function is:
 i (k i , k , xi )  a(ki E ( )  xi )  ki kE( 2 )  xi kE( )  cki E ( )  rk i
 The reaction function of firm i is:
(a  c  xi ) E ( )  kE( 2 )  r
ki 
E ( 2 )
 The Nash equilibrium quantities
kc
E ( )
k ( xi , xi )   nxi  xi 
n
(n  1) E ( 2 )
Period 1: Forward market trading
 In period 1, firms simultaneously choose the amount
of forwards they want to sell for delivery in period 3.
 Demand for forwards comes from competitive
speculators making zero profits,  forward trading
equals the producers’ offers.
 Denoting pf the forward price, the expected profits
of firm i are given by:
i ( xi , xi )   i (ki ( xi , xi ), k ( x), xi )  p f xi
The Nash equilibrium
 Rational expectations and risk neutrality by
speculators imply that the forward price equals the
expected spot market price, thus:
i ( xi , xi )  (a  c) E ( )  k ( x) E ( 2 )  r ki ( xi , xi )
 Hence
i 
E ( )  nE ( )
E ( )
 ki ( xi , xi )  xi
 ki ( xi , xi )
2 
xi 
E ( )  n  1
n 1
 Thus the game Nash equilibrium quantities are:
n  1 E ( )
xˆ  2
k*
n  1 E ( )
2
2
2
2
n

n
n
kˆ( xˆ )  2
kc  2
k*
n 1
n 1
Long-term auctions
 Mass of consumers coordinate themselves to auction a long



term supply contract before investments are committed.
The entire forward contract is awarded to the firm that bids
the lowest price.
In the spot market purchase consumers who do not contract
energy in advance, and generators and contracted consumers
trade energy.
In the first period a contract to supply a given quantity in the
spot market is auctioned, and in the second period, the
producers decide on their capacities.
The game is solved by backwards induction.
Period 2: Capacity choices
 Firms simultaneously choose their capacity depending on the
outcome of the auction.
 Let 1 be the firm that won the contract in period 1 and xa the
quantity auctioned. Then, its expected spot market profits are
given by  i (k 1, k , x a )
 The value function for other firms is simply  i (k i , k ,0)
 Thus the second-period equilibrium quantities are:
(a  c  nx a ) E ( )  r
k1 ( x ,0) 
(n  1) E ( 2 )
a
(a  c  x a ) E ( )  r
ki 1 (0, x ) 
(n  1) E ( 2 )
a
Period 1: Contract awarding
 A long-term contract to supply xa is awarded in a competitive bid.
Profits of the award-winning firm are:
1 ( x a ,0)   1 (k1 ( x a , x a ), k ( x a ))  p a x a
 Profits of other firms are given by:
i (0, x a )  (a  c) E ( )  k ( x a ) E ( ) 2  r ki (0, x a )
 All firms have equal profits in the Nash equilibrium of the game,
hence
(k ( x a )  k*)E ( )  ( p a  a  k ( x a ) E ( ))
 The auction price equals the expected efficient price. The auction
also reduces the spot price.
The optimal auction
 In order to achieve the welfare maximizing capacity k*, the supply
auctioned has to equal:
E ( 2 )
x* 
k*
E ( )
 The implementation of such contract raises practical questions.
Consumers contract a supply x*, but available supply equals θk*.
 If x* > θk*, then the firm will have to purchase in the spot market
an amount x* - θk*. Consumers will sell this amount if the price
offered equals p(θk*). (ignoring income effects)
 If x* < θk*, then firms will have to sell in the spot market the
amount θk*-x*. Consumers will purchase this quantity if the
price equals p(θk*).
Crucial efficiency condition
 Long-term contracts: generators determine their
investment after contracts are awarded.
 Implicit assumption: bidding is costless and
generation costs are known (price index is chosen
by the bidder).
 But obtaining environmental permits is time and
resource consuming and uncertain.
 Generation costs depend on environmental
requirements.
Future work
 Firms participating in contract markets take into
consideration theirs and their rivals project with
approved environmental studies.
 Moreover, permit applications could be used by
generators to tacitly collude in the contract
market.
 Future work should extend modeling in this
direction; otherwise, any policy recommendation
would be flawed.