Posted by joel on Friday, September 22, 2006 at 10:44pm.
Question 4. (50 points)
In an auction in the market for wholesale electricity, producers of electricity submit bids
for each generator that they operate. The bid is the minimum price the operator of the
generator is willing to accept for before it will turn it on to supply power to the electricity
grid. To keep the numbers simple, assume that each generator produces one unit of
electricity. In the table below, we see that the operator of generator G1 has put in a bid
for $3. This means that if the price is $3 or more, generator G1 will be switched on. At a
price of $2.99 or below, it will be switched off.
In a double auction, buyers also submit bids. Again, to keep the numbers simple,
assume that each buyer puts in a bid for one unit of power. In the table below, we see
that buyer B1 has submitted a bid to purchase one unit at $14. This means if the price is
$14 or less it will buy one unit. At a price of $14.01 or more, the buyer won’t take any
(a) You are the Independent System Operator (ISO) in an electricity market. You
have received the bid information in the table below. Clear the market, i.e. pick P, Q,
and Who. (The “Who” answers which generators produce and which buyers get
electricity.) Obtain your answer two ways. First, make a table. Second, plot the
information on a graph. Either use graph paper to make your graph by hand or use Excel.
(Offer to sell in $ )
(Offer to purchase in $)
G1 3 B1 14
G2 10 B2 4
G3 1 B3 10
G4 5 B4 2
G5 12 B5 15
G6 3 B6 2
G7 1 B7 1
G8 12 B8 15
G9 3 B9 1
G10 4 B10 12
(b) Suppose Acme Power owns generators G1 through G5. Suppose Giant Electric owns
generators G6 through G10. Calculate the revenues each receives as a result of the
auction. (This is the quantity each firm sells times the market price). Suppose that the
bids that are submitted equal the true cost to these firms of operating the individual
generators. Calculate the profit (revenue minus costs) that each firm receives as a result
of the auction.
Background for Part (c)
Auctions work very well when there are a large number of different bidders. However, if
there are only a small number of firms making bids, they can be subject to manipulation.
To illustrate this point, we look at how Acme and Giant might try to manipulate things in
the auction above. (There is evidence that something like this actually happened in
Regulators have some idea of the fuel costs for producing electricity out of a
given generator. If Acme were to offer a bid of $1000 for operating G1 when the cost is
known to be around $3, this might attract unwanted attention from regulators. Suppose
instead Acme were to say a generator was down for maintenance, even if there was
nothing wrong with it. Acme might be able to get away with this without attracting
(c) Specifically, suppose Acme and Giant work out the following deal before submitting
bids. Acme says generator G1 is broken, so doesn’t submit a bid for G1. Giant says
generators G6 and G9 are broken. So scratch out G1, G6, G9 in the table above. All
other bids remain the same. Clear the market with both a table and a graph. Calculate
the new price and quantity. Calculate the profit each firm receives as a result of the
manipulation. Do your calculations suggest this manipulation by Acme and Giant is a
good move if they can get away with it?
5. (20 points) Elasticity
(a) Use the information below to calculate an estimate of the short-run price elasticity of
demand for gasoline. Four months of data are reported, but you only need to use two of
them. Think carefully about which ones you should use.
(b) To calculate a price elasticity of demand, we look at the effect of changing price
while holding everything else affecting demand fixed. List two things that you are
holding fixed in your calculation. List two other things that are not being held fixed in
your calculation that could potentially be a problem for your estimate.
Table 5a Gasoline Shipments in the United States, Various Months
Apr-2004 375.7 183.9
Sep-2004 374.5 191.2
Dec-2004 393.7 188.7
Sep-2005 369.8 295.1
Source: U.S. Energy Information Administration
Table 5b Population of the United States
Source: U.S. Census Bureau
What exactly is your question?
In part a, sort, separately, the generators and buyers by their bid price, except generators go lowest to highest, for buyers go highest to lowest. Plot the points. Where the two curves cross is your equilibrium price and quantity.
In part b, the each generator's profit is the equilibrium price less his reservation (bid) price. Sum the profits for each firms set of generators.
in part c, repeat the steps in a and b.
in part 5, elasticity is (%change in Q)/(%change in P). Be very careful about drawing conclusions about the demand price elasticity. Your data shows equilibrium levels of price and quantity at different points in time. What must you assume about supply and demand to derive an elasticity?
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