Regulate or Deregulate

1
Regulate or Deregulate?

• Markets for Electricity

2
The Competitive Benchmark

• Electricity is non-storable and dated
• For simplicity, we assume power is consumed over
  only two time periods, which we can think of as
  peak and off-peak periods
• Non-storability means that power must be
  generated on the fly by producers once
  capacity is reached, no further power generation
  to accommodate demand can occur, so demand must
  either be rationed or prices must rise
  sufficiently to equate demand with supply
• We assume there is also a consumption good other
  than electricity available, and we take this good
  as the numeraire (i.e. we set its price to 1)

3
Competitive Benchmark

• Producers must burn ? units of the numeraire
  good to produce one kilowatt hour of electricity.
  Each producer faces a capacity constraint in the
  short-run of K kilowatt hours of possible
  electricity production. In the long-run,
  producers can add capacity at a cost of ? units
  per kilowatt hour of capacity
• An individual producers profit in a competitive
  market environment if he produces (x1,x2)
  kilowatt hours in each of the two periods and the
  prices of power are (p1,p2) is given by

4
Competitive Benchmark

• Profit maximization
• If ptlt? then optimal output is zero
• If ptgt ? then optimal short-run output is K
• If 0ltxtltK, then pt ?
• Hence, under perfect competition, the short-run
  off-peak price will simply be the marginal cost
  of producing an additional kilowatt hour of
  electricity
• Consumers
• Two types Electricity consumers and numeraire
  consumers
• Electricty consumers own the numeraire good and
  exchange it for electricity
• Numeraire consumers own power plants and purchase
  the numeraire good both for consumption and for
  production of power

5
Competitive Benchmark

• We assume that electricity consumers care only
  about electricity and have log-linear preferences
• Electricity consumers maximize utility subject to
  the budget constraint
• where ? is the consumers endowment of the
  numeraire good

6
Competitive Benchmark

• Electricity producers also have log preferences
  but care only about consumption of the numeraire
  good
• A producers budget constraint is given by
• where ?producer is the producers endowment of
  the numeraire good

7
Competitive Benchmark

• Equilibrium Analysis (on blackboard)
• Demand functions
• Short-run off-peak and peak equilibrium
  prices/allocations
• Long-run equilibrium prices/allocations

8
Imperfect Competition

• Market game formulation
• Markets for electricity in different periods, and
  for the numeraire good are organized as trading
  posts where buyers and sellers can bid to buy
  commodities, and offer to sell commodities
• We assume there are M electricity consumers and
  denote them by h1,,M. As before electricity
  consumers have log-linear preferences and care
  only about consuming electricity. They are
  endowed, as in the competitive model, with ?
  units of the numeraire good.
• Each electricity consumer makes a bid to purchase
  electricity on the trading post for period 1 and
  for period 2

9
Imperfect Competition

• Buyer hs bid on trading post t is denoted bht
  for t1,2.
• The aggregate bid on trading post t is
• It will be useful for the analysis of the model
  to define
• Electricity consumers finance their purchases of
  electricity by offering the numeraire good for
  sale on the numeraire trading post.

10
Imperfect Competition

• To keep the model simple, we assume that
  electricity consumers offer their full endowment.
• Let
• Electricity consumers face a budget constraint on
  what they may bid for the purchase of electricity
  given by
• where B0 is the aggregate bid (from producers)
  for the numeraire good.

11
Imperfect Competition

• Producers again have log utility and care only
  about consumption of the numeraire. Their costs
  of production are the same as in the competitive
  framework.
• We assume there are Pgt1 producers in the model.
• Producers are indexed by j1,,P, and producer j
  offers quantities of electricity qjt and qjt in
  each period. In the short-run, quantities must
  be such that qjt is less than or equal to
  capacity K for each period t1,2.
• For this analysis, it will also simplify the
  model to assume that producers have zero
  endowment of the numeraire.
• Producers then bid only on the trading post for
  the numeraire good, with each producer receiving
  a pro rata share of the total bids for
  electricity in each period.

12
Imperfect Competition

• Let
• be the aggregate amount of power offered by
  all producers in period t. As with the
  electricity consumers, it will be useful to
  define
• Producer js budget constraint is given by

13
Imperfect Competition

• Consumption allocations are given as follows

14
Imperfect Competition

• Electricity consumers optimization problem is
• First-order conditions On board

15
Imperfect Competition

• Electricity producers optimization problem is
• First-order conditions On board

16
Imperfect Competition

• We thus find that the off-peak Nash equilibrium
  bids and offers for electricity are

17
Imperfect Competition

• From the equilibrium bids and offers, we can
  calculate the off-peak prices of electricity as
• Note that this is the off-peak price in terms of
  money to compare with our results from the
  competitive model, we need to express this price
  in terms of the numeraire good.

18
Imperfect Competition

• To convert to a numeraire price, we divide the
  money price by the money price of the numeraire
  the numeraire price is
• Doing the indicated price renormalization, we get

19
Imperfect Competition

• Peak-load prices
• When the optimal offer of a producer exceeds
  capacity, the producer is constrained to offer K
  rather than the best-response quantity. In this
  case, the price of electricity will be
• To compare this with the results from the
  competitive model, we again renormalize prices to
  express the peak price in terms of the numeraire
  good.

20
Imperfect Competition

• The renormalization yields
• Long-run analysis
• In the long-run, producers can increase capacity
  to accommodate peak load demand.
• They will do so if the additional utility benefit
  from doing so exceed the additional cost of
  installing capacity

21
Imperfect Competition

• To calculate the long-run benefit, let us assume
  that period 1 is off-peak and period 2 is peak.
  Then a producers consumption is given by

22
Imperfect Competition

• If the producer expands capacity to cover the
  peak period demand, her consumption is
• We can use these expressions to calculate the
  gain to expanding capacity
• ON BOARD

23
Imperfect Competition

• The condition for expansion
• will never be satisfied in fact, we can show
  that producers will always have an incentive to
  reduce capacity, unless there is either
  sufficient capacity that all prices are off-peak,
  or there are sufficiently many producers that the
  capacity constraints of an individual producer
  never bind.

24
Policy Implications

• Actual markets are never perfectly competitive
• U.S. Department of Justice uses a benchmark of 5
  mark-up over marginal cost as signifying an
  acceptable level of competition
• Small numbers of producers in markets for
  electricity will lead to prices above marginal
  cost
• Model predicts, for example, that in the
  California market (with 7 producers), the mark-up
  will be around 36. In the New England market
  (which has 29 producers), the implied mark-up is
  only around 7, while in the Missouri-Kansas
  market (with 22 producers), it is around 10.
• Model hits DOJs competitive benchmark with 50
  producers.

25
Policy Implications

• Small numbers of producers lead to problems with
  peak-period price spikes and incentives to reduce
  capacity
• Important to note, however, that the equilibria
  in the model is non-cooperative
• Agents are reacting in their own best interests
  given the actions of others and the structure of
  the market
• Limited scope for anti-trust actions
• Importance of fostering competition
• During divestiture phases
• Reducing costs of entry