e. Each generator has a capacity of 1,000 MW. Marginal costs vary across generation types: $10 per MWh for coal and $20 per MWh for natural gas. During peak hours, demand is given by Q = 30,000 – 100P (measured in MWh). During semipeak hours, demand is given by Q = 22,000 – 100P. During off-peak hours, demand is given by Q = 20,000 – 100P. Assume that a day consists of one off-peak hour and either a semi-peak or a peak hour (so a day contains two hours only!). Probabilities of semi-peak vs. peak hours are 50%- 50%. For now, assume that the market is competitive. a. Calculate the peak, the semi-peak, and the off-peak prices of electricity. b. What are the expected daily profits for each plant? The Independent System Operator (ISO) is worried that the peak price is too high, and asks
Consider a wholesale electricity market with two types of generators: coal plants and natural gas
plants. There are 10 generators for each fuel type. Each generator has a capacity of 1,000 MW.
Marginal costs vary across generation types: $10 per MWh for coal and $20 per MWh for natural
gas. During peak hours, demand is given by Q = 30,000 – 100P (measured in MWh). During semipeak hours, demand is given by Q = 22,000 – 100P. During off-peak hours, demand is given by Q
= 20,000 – 100P. Assume that a day consists of one off-peak hour and either a semi-peak or a
peak hour (so a day contains two hours only!). Probabilities of semi-peak vs. peak hours are 50%-
50%. For now, assume that the market is competitive.
a. Calculate the peak, the semi-peak, and the off-peak prices of electricity.
b. What are the expected daily profits for each plant?
The Independent System Operator (ISO) is worried that the peak price is too high, and asks
investors to build an additional 1,000 MW natural gas fired plant.
c. If the investment cost (pro-rated per day) equals $40,000, will there be an incentive
to build an additional gas-fired generator?
2
After careful consideration, no one decides to build a new plant. Meanwhile, the Environmental
Protection Agency (EPA) has become very worried about methane leaks from hydraulic fracturing,
and has successfully lobbied Congress for a $10/MWh tax on gas-fired electricity.
d. How will daily profits for a gas plant change as a result? How about profits for a coal
plant? Will the industry overall gain or lose from this tax?
Technology advances have led to a breakthrough in batteries, which can be used to store
electricity during semi-peak hours and release the stored electricity during peak hours. The end
result is that demand for generation during semi-peak and peak hours is now equal. Now, a day
in the electricity market consists of one off-peak hour and semi-peak/peak hour (from now on,
“peak hour”). The new peak hour demand is Q = 25,000 – 100P. (The tax is still in place.)
e. Calculate the daily profits for each plant in the new market.
A sophisticated ratepayer lobby group calculates the Lerner index during peak hours and finds
that it is substantially larger than zero.
f. What value does the Lerner index have during peak hours for a marginal plant? Does
this mean that at least some degree of market power must be exercised in this market?
Now let’s assume that you have acquired all the power plants. The ISO asks you how much you
would like to generate in any given hour. The ISO chairman is a golf buddy of yours, so you can
schedule as much unexpected maintenance as you like – no questions asked.
g. Could you profitably exercise any market power during peak hours? If so, how much
capacity would you withhold, and by how much does it increase your peak hour profits?
The Department of Justice (DOJ) has become worried about your
order to split up your company. After the spin-off, you are left with five natural gas generators.
Assume that all other firms except yours cannot exercise any market power.
h. Would you now withhold any capacity during peak hours? Compare the new peak
price to the monopoly price in part h. Why has it changed so much?
Suppose you have successfully challenged the DOJ in court, the spin-off is reversed and your
monopoly is reinstated. Your state government quickly responds by implementing a “demand
response program” for industrial customers which makes these consumers more elastic to the
electricity price. The new peak demand is Q=25,000 – 200P.
i. How much capacity would you withhold as a monopolist? Compare to the monopoly
profit in part g, and explain the difference
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