Problem Set:

1. You have been hired to analyze the electricity market on the newly inhabited island of Paradisum. There are m identical households on the island that have a demand for electricity during the day but not during the evenings (they prefer the natural light of the stars). The daytime preferences from consuming electricity for household i is represented by 𝑈(𝑞𝑖) = 𝑎𝑞𝑖 − 𝑚𝑞𝑖 2 2 .

There are n identical producers of electricity in Paradisum. The cost function of producer j is 𝐶(𝑞𝑖) = 𝑤𝑞𝑗 2 + 𝑆𝐶, where SC is a one-time fixed start-up cost, incurred only when the producer decides to generate electricity.

Both households and suppliers are price takers (i.e., in Paradisum, we have perfect competition in the electricity market).

As the analyst of this electricity market, you are asked to answer the following questions.

Demand Side:

a. What is the daytime electricity demand curve for household i for a given price of electricity P?

b. What is the daytime demand curve of the entire market for a given price of electricity P?

Supply Side:

c. What is the supply curve for producer j for a given price of electricity P?

d. What is the market supply curve for a given price of electricity P?

Competitive Equilibrium:

e. Provide expressions for the competitive equilibrium daytime price and quantity of electricity as a function of the parameters a, n, m, w and SC.

f. What is the equation for how much each producer j generates as a function of the parameters a, n, m, w and SC?

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g. What is the equation for the profit for each producer j as a function of the parameters a, n, m, w and SC?

h. You have learned that a=100, w=$4, SC=$100, n=2 and m=10. Using the equations you derived above, what is the equilibrium market price and quantity? What is the quantity of electricity consumed by household i? What is the amount of electricity generated by producer j? What are the profits of producer j? What is the aggregate consumers’ surplus, producers’ surplus and total surplus?

i. Is this market equilibrium that you have found in h, a short-run or long-run equilibrium? Why? If the firm is not in long-run equilibrium, explain the adjustment process that will occur and derive the long-run equilibrium?

Monopolization:

j. A new company, Avarum, purchases the island and appropriates all the generation assets from the individual producers. Avarum will operate industry as a legal monopolist (with one plant as there are no capacity constraints to a plant). What is the new equilibrium price and quantity of electricity? What is Avarum’s producer surplus? What is the consumers’ surplus? Is this equilibrium more or less efficient than the previous competitive equilibrium? If yes, provide a measure of the inefficiency.

Data Set:

2. A load duration curve measures the number of hours per year the total load is at or above any given level of demand. It can be constructed for a given region by measuring the total load at hourly intervals for each of the hours in a year (typically 8760), sorting them, and graphing them starting from the highest load. The result is a curve that slopes downward from the maximum load in the peak hour, hour 1, to the minimum load, baseload, in the most off-peak hour (See Figure 1-4.1, page 42 of Stoft).

Hourly Ontario demand can be found at the IESO website http://reports.ieso.ca/public/Demand/ and hourly Alberta demand can be found at the AESO website http://ets.aeso.ca/ (hint Select Report called Pool Price).

a. Using the data found on the above websites, create load duration curves for each province for the years 2007 and 2017 (each province may be represented on a separate graph).

b. Describe some of the key trends in demand for each province (i.e., what has happen to demand over the ten years in terms of peak demand growth, peak demand vs baseload demand variation, other)?

c. A jurisdiction’s annual load factor is equal to the ratio of the annual average hourly demand to annual hourly peak demand. Calculate the annual load factor
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for each province. What might the differences between the load factors for each province suggest about the nature of electricity consumption in each market?

d. For each province, in what season did the peak demands occur? What might this suggest about the relative weather in each province and the nature of energy consumption?