AAE/Econ 371: Fall 2020

University of Wisconsin - Madison

Midterm Exam 2

Instructions: This is an 75 minute, 74 point exam. Submit your exam by uploading

it to Canvas just as you upload your homework assignments.

Suggestions: For the computational problems, show all your work for full credit, and, if

you only know part of an answer, write down that part since partial credit will be awarded.

If you are stuck on a problem, move on and go back to it later if you have time. You do not

need to answer the questions in order. Do not assume you cannot answer later subparts of

a question if you do not know the answer to an earlier subpart. I recommend that you do

not refer to your notes just to check an answer until you have completed the entire exam.

Otherwise you will likely run out of time.

For the Record: This examination is open internet and notes, but you must take

the exam individually. You may use a calculator.

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Multiple Choice (24 points)

Simply indicate your answer for each question. Only one choice per question is correct, so

choose the one, best answer for each question. Explanations are not required and will

not be read or graded. Each question is worth 4 points.

1. Which of the following is NOT a characteristic of electricity?

(a) Demand must equal supply at all times

(b) Storage is expensive

(c) Real-time demand is inelastic

(d) Demand is highest in the Spring

2. Why did California have rolling blackouts in the summer of 2020?

(a) A hurricane destroyed many of its electricity transmission lines

(b) The state did not have enough electricity generation capacity to meet demand

(c) The blackouts were scheduled to raise awareness about climate change

(d) The Independent System Operator incorrectly forecasted demand, so it did not

tell enough generators to supply electricity

3. What is the main advantage of having a restructured electricity market rather than a

traditional, non-restructured market?

(a) Firms in the generation segment have an incentive to reduce costs

(b) There is less likely to be over-investment in electricity transmission

(c) It is easier to ensure electricity supply always equals electricity demand

(d) Competition prevents firms from exercising market power

4. Suppose the price of natural gas falls. What happens to the LCOE for natural gas

generation?

(a) the natural gas LCOE rises

(b) the natural gas LCOE falls

(c) the natural gas LCOE does not change

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5. Suppose you are playing the OPEC game, and your country’s marginal cost is $15/barrel. Like in the game, the real interest rate is 10%. If the world price of oil in period 2 is

$80/barrel, what is the future value of profits (at the end of the game) from producing

one barrel of oil in period 2?

(a) $86.52

(b) $106.48

(c) $78.65

(d) $96.80

6. Suppose that the public utility regulator is choosing between two different rate structures. Both will ensure the utility recovers its costs and earns a fair rate of return on

capital. One combination of fixed and volumetric charges is F = $25/month and v =

$0.10/kWh. Which of the following could be the other combination?

(a) F = $20/month, v = $0.20/kWh

(b) F = $15/month, v = $0.15/kWh

(c) F = $10/month, v = $0.10/kWh

(d) Both A and B

(e) A, B, and C

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Computational Questions (50 points)

7. The following table shows the characteristics of electricity generating capacity and

emissions rates for a small electricity market.

Technology Capacity Marginal cost Emissions rates

(MW) ($/MWh) (ton CO2/MWh)

Solar 400 0 0

Natural gas 300 30 0.6615

Coal 500 40 1.2128

Electricity demand in this market is constant (and perfectly inelastic) at 900 MW.

(a) (5 points) Assume the existing market is competitive (so that generation is dispatched in order of increasing marginal cost). Carefully draw the supply curve

and find the price of electricity in this market.

Now suppose you are working as an analyst for the firm Genergy, which is considering

building a 600 MW natural gas plant. The plant would have a constant marginal

cost of $25/MWh and an initial construction cost of $350 million.

(b) (6 points) Find the inverse residual demand facing Genergy if it builds the natural

gas plant. Calculate the optimal generation quantity for Genergy. What will be

the market price?

(c) (4 points) What will be Genergy’s hourly profit? Assuming there are 24 hours

per day, 30 days per month, and 12 months per year, what is Genergy’s annual

profit?

[If you could not solve part (b), you can use p = $35/MWh, q= 400 MWh/hour]

(d) (5 points) Suppose the gas plant will last for 40 years and the annual interest

rate is 6 percent. What is the present value of profits from building the natural

gas plant? Should Genergy build it?

(e) (6 points) Now suppose the government is considering imposing a carbon tax

that is a fixed amount per ton of CO2. In the context of this problem,1 how

would the tax affect Genergy’s incentive to build the gas plant? How might your

1I.e., demand for electricity is perfectly inelastic, and Genergy is the only firm that may construct a new

plant.

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answer change if other firms were allowed to build electricity generation? No math

required for either answer.

8. DG&E is the only firm supplying electricity in Dallas, TX. Monthly demand for electricity in GWh is given by:

Q = 190 - P

Total costs for DG&E in 104 dollars (you can essentially ignore these units when solving

the problem) are given by:

TC = 875 + 10Q

DG&E’s marginal cost is

MC = 10

Note that $10x104/GWh is equal to $0.10/kWh.

(a) (4 points) Suppose DG&E, a monopolist, can set whatever price it likes. What

would be the DG&E’s profit-maximizing price and quantity?

(b) (4 points) Now suppose, more realistically, that DG&E is a regulated public utility,

and the regulator decides to set DG&E’s price at marginal cost. What would be

DG&E’s price and quantity?

(c) (6 points) Alternatively, suppose the public utility regulator decides to set DG&E’s

price so that it equals its average cost. What would be DG&E’s price and quantity? If you find multiple solutions, choose the solution that gives the lowest

price.

[Hint: The quadratic formula is on the last page of the exam. You could also use

an online calculator like this one: https://www.calculatorsoup.com/calculators/

algebra/quadratic-formula-calculator.php]

(d) (5 points) What is the main problem with (i) marginal cost pricing? What is the

main problem with (ii) average cost pricing?

(e) (5 points) Suppose half of DG&E’s electricity generation comes from natural

gas and half of its electricity generation comes from coal, though the marginal

generator that reduces or increases output when demand changes is always a

natural gas generator. Accounting for both carbon emissions and local pollutants,

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the marginal external cost of an additional kWh of coal generation is $0.05/kWh

and the marginal external cost of an additional kWh of natural gas generation

is $0.02/kWh. If Dallas has 400,000 households that pay electricity bills each

month, what is the socially optimal two-part tariff?

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Potentially useful formulas/conversions:

• Consider a stream of future payments of size x over the next T years. The present

value of these future payments is given by the following formula:

PV = x × AF

where AF = 1

r �1 - (1 +1r)T �

• The quadratic formula:

ax2 + bx + c = 0

x =

-b ± pb2 - 4ac

2a

•

LCOE =

F + PT t=1 (1+ ctqrt)t

PT t=1 (1+qtr)t

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