Question 1 [rate of return + natural monopoly]:

Price taking consumers of electricity have a demand function given by:

2000 2 .

A single vertically integrated utility (VIU) has a cost function given by:

0.2 25 306250.

The VIU has convinced the public utility commission (PUC) that it is a natural monopoly and thus it has been granted an exclusive franchise to produce electricity.

At the most recent rate-hearing, the PUC established a target price based on rate of return regulation. During the hearing, the VIU claimed that its rate-base was $4,875,000 and that the market rate of return it should be allowed should be 10%. It provided receipts to the PUC showing expenses of $262,500. Suppose the PUC has complete knowledge of market demand.

What is the competitive equilibrium in the absence of rate of return regulation?

What is the monopoly equilibrium in the absence of rate of return regulation?

What is the target price set as a result of the regulatory hearing? Use the quantity from part a to calculate.

What is the monopoly equilibrium under the rate of return regulation?

What is the change in consumer surplus from the rate of return regulation relative to the competitive equilibrium? Relative to the no regulation monopoly equilibrium?

What is the change in producer surplus from the rate of return regulation relative to the competitive equilibrium? Relative to the no regulation monopoly equilibrium?

What is the change in total welfare from the rate of return regulation relative to the competitive equilibrium? Relative to the no regulation monopoly equilibrium?

The government provided the monopoly franchise under the assumption that the VIU was a natural monopoly. Was their assessment correct? Did society gain or lose because of the government?s decision? How much did they gain or lose? Please provide detailed reasoning for all three answers.

[monopoly vs. competitive equilibrium + energy efficiency]:

An investor-owned VIU serves a mid-sized market in a part of the U.S. that did not undergo restructuring. They can supply electricity given the following marginal cost function:

0.5 0.1 .

Demand for electricity in the market reflects price-taking behavior and is given by:

1000 0.5 ,

Where 1 is the amount of demand-side energy efficiency (DSEE).^[1] 1 reflects the amount of DSEE selected by consumers which need not be optimal.

Suppose the cost of investing in demand side energy efficiency programs is given by:

100 1 1000 1 .

Suppose the VIU behaves as an unconstrained monopolist who can make investments in DSEE if they so desire. For values of from 0.1 to 10 in increments of 0.1, calculate the VIU?s profits as a function of different levels of . In the same figure, 1. plot the VIU?s profits on the y-axis and on the x-axis, and 2: plot the Lerner index for the VIU on a second y-axis and on the x-axis. Explain the curious result that the VIU?s profits go down when the VIU?s Lerner index goes up.

Given the result from a, suppose that the VIU could fully expropriate consumer surplus gains from a change in (relative to 1 as additional profits. In a new figure, 1. plot the VIU?s profits with the change in consumer surplus on the y-axis and on the xaxis, and 2: plot the change in consumer surplus on a second y-axis and on the x-axis. What is the optimal amount of DSEE that the VIU selects in this case? Is this the one that maximizes the change in consumer surplus? Explain why or why not.

Now suppose instead that the VIU behaves as a price-taking producer. For values of from 0.1 to 10 in increments of 0.1, calculate the VIU?s profits as a function of different levels of , where profits include the change in consumer surplus as in b. In a new figure, 1. plot the VIU?s profits with the change in consumer surplus on the y-axis and on the x-axis, and 2: plot the change in consumer surplus on a second y-axis and on the x-axis. What is the optimal amount of DSEE that the VIU selects in this case? Is this the one that maximizes the change in consumer surplus? Explain why or why not.

Compare and contrast the results from b and c.

Question 3 [natural monopoly and subadditivity]:

In class, we discussed how firms that have decreasing average total costs can be classified as natural monopolies. The more precise definition of a natural monopoly is any industry that exhibits subadditive average total costs. Subadditivity refers to whether it is cheaper to have one firm produce total industry output or whether additional firms would yield lower total cost. Subadditivity is a weaker requirement than decreasing average total costs. Any firm that has decreasing average total costs also has subadditive average total costs (thus decreasing average total costs is a sufficient condition for subadditive average total costs), but some firms that have subadditive average total costs need not have decreasing average total costs (thus decreasing average total costs is not a necessary condition for subadditive average total costs).

Suppose output can only be added to an industry in lumpy amounts. That is, a single factory can produce according to the following average total cost function:

0.02 2 60,

And two factories can produce according to the following average total cost function:

0.02 4 210.

Suppose demand is given by: 300 7 . Should one factory supply the market or two? Explain your reasoning.

Suppose demand is given by: 250 3.5 . Should one factory supply the market or two? Explain your reasoning.

Suppose demand is given by: 200 1.75 . Should one factory supply the market or two? Explain your reasoning.

Up to what quantity does the first factory exhibit increasing returns to scale? Constant returns to scale? Decreasing returns to scale?

Up to what quantity does the second factory exhibit increasing returns to scale? Constant returns to scale? Decreasing returns to scale?

For the decreasing average total cost industry, the firm exhibited increasing returns to scale for all output levels. This is not the case here, in which production follows the standard three stages of production, although new production can only be added in a lumpy way. Up to what quantity should one factory produce? Two factories produce? Explain your reasoning.

[1] Following the lecture notes, it is the case that the demand of energy services is given by: 1000 0.5 ; this is the curve that should be used for calculating consumer surplus.

EBF 484ENERGY ECONOMICS FALL 2016 PROBLEM SET #5 Due at the beginning of class on December 6th, 2016. Recitation to be held on November 29th at 6:00-8:00PM in Walker 12. Please answer all questions clearly and completely. The goal is not just to show that you can identify the correct answer, but also to demonstrate that you understand the answer in light of the material and concepts discussed in lectures and in the assigned readings. If a question requires you to make calculations, you must show your work, including all steps. You may use graphs and tables in your answers as you find necessary or as requested below. I strongly recommend drawing yourself a picture before commencing with mathematics, although you need not incorporate your fine artwork into your submitted answers. If steps are omitted, full reasoning is not provided, and/or graphs and tables that you decide to include in your answers are not clear, points will be deducted. As stated in the syllabus, answers should be typed or neatly written and stapled in the upper left corner to receive full credit. When performing calculations, you should describe the major steps (e.g. \"we set supply equal to demand to identify the equilibrium\") used to obtain your answer, but you need not report minor intermediate steps. Basically the grader needs to be able to follow your work in order to provide partial credit; the more details you provide, the more likely you will receive partial credit when your answer is wrong. Please report final answers to two decimal places. Full Names of ALL Group Members (no more than five): Full Names of ALL Other Students Your Group Members Worked With: 1 Question 1 [rate of return + natural monopoly]: Price taking consumers of electricity have a demand function given by: 2000 2. A single vertically integrated utility (VIU) has a cost function given by: 0.2 25 306250. The VIU has convinced the public utility commission (PUC) that it is a natural monopoly and thus it has been granted an exclusive franchise to produce electricity. At the most recent rate-hearing, the PUC established a target price based on rate of return regulation. During the hearing, the VIU claimed that its rate-base was $4,875,000 and that the market rate of return it should be allowed should be 10%. It provided receipts to the PUC showing expenses of $262,500. Suppose the PUC has complete knowledge of market demand. a. What is the competitive equilibrium in the absence of rate of return regulation? b. What is the monopoly equilibrium in the absence of rate of return regulation? c. What is the target price set as a result of the regulatory hearing? Use the quantity from part a to calculate. d. What is the monopoly equilibrium under the rate of return regulation? e. What is the change in consumer surplus from the rate of return regulation relative to the competitive equilibrium? Relative to the no regulation monopoly equilibrium? f. What is the change in producer surplus from the rate of return regulation relative to the competitive equilibrium? Relative to the no regulation monopoly equilibrium? g. What is the change in total welfare from the rate of return regulation relative to the competitive equilibrium? Relative to the no regulation monopoly equilibrium? h. The government provided the monopoly franchise under the assumption that the VIU was a natural monopoly. Was their assessment correct? Did society gain or lose because of the government's decision? How much did they gain or lose? Please provide detailed reasoning for all three answers. Question 2 [monopoly vs. competitive equilibrium + energy efficiency]: An investor-owned VIU serves a mid-sized market in a part of the U.S. that did not undergo restructuring. They can supply electricity given the following marginal cost function: 0.5 0.1 . 2 Demand for electricity in the market reflects price-taking behavior and is given by: 1000 0.5 , Where 1 is the amount of demand-side energy efficiency (DSEE). 1 1 reflects the amount of DSEE selected by consumers which need not be optimal. Suppose the cost of investing in demand side energy efficiency programs is given by: 100 1 1000 1. a. Suppose the VIU behaves as an unconstrained monopolist who can make investments in DSEE if they so desire. For values of from 0.1 to 10 in increments of 0.1, calculate the VIU's profits as a function of different levels of . In the same figure, 1. plot the VIU's profits on the y-axis and on the x-axis, and 2: plot the Lerner index for the VIU on a second y-axis and on the x-axis. Explain the curious result that the VIU's profits go down when the VIU's Lerner index goes up. b. Given the result from a, suppose that the VIU could fully expropriate consumer surplus gains from a change in (relative to 1 as additional profits. In a new figure, 1. plot the VIU's profits with the change in consumer surplus on the yaxis and on the xaxis, and 2: plot the change in consumer surplus on a second y-axis and on the x-axis. What is the optimal amount of DSEE that the VIU selects in this case? Is this the one that maximizes the change in consumer surplus? Explain why or why not. c. Now suppose instead that the VIU behaves as a price-taking producer. For values of from 0.1 to 10 in increments of 0.1, calculate the VIU's profits as a function of different levels of , where profits include the change in consumer surplus as in b. In a new figure, 1. plot the VIU's profits with the change in consumer surplus on the y-axis and on the x-axis, and 2: plot the change in consumer surplus on a second y-axis and on the x-axis. What is the optimal amount of DSEE that the VIU selects in this case? Is this the one that maximizes the change in consumer surplus? Explain why or why not. d. Compare and contrast the results from b and c. Question 3 [natural monopoly and subadditivity]: 1 Following the lecture notes, it is the case that the demand of energy services is given by: 1000 0.5 ; this is the curve that should be used for calculating consumer surplus. 3 In class, we discussed how firms that have decreasing average total costs can be classified as natural monopolies. The more precise definition of a natural monopoly is any industry that exhibits subadditive average total costs. Subadditivity refers to whether it is cheaper to have one firm produce total industry output or whether additional firms would yield lower total cost. Subadditivity is a weaker requirement than decreasing average total costs. Any firm that has decreasing average total costs also has subadditive average total costs (thus decreasing average total costs is a sufficient condition for subadditive average total costs), but some firms that have subadditive average total costs need not have decreasing average total costs (thus decreasing average total costs is not a necessary condition for subadditive average total costs). Suppose output can only be added to an industry in lumpy amounts. That is, a single factory can produce according to the following average total cost function: 0.02 2 60, And two factories can produce according to the following average total cost function: 0.02 4 210. a. Suppose demand is given by: 300 7 . Should one factory supply the market or two? Explain your reasoning. b. Suppose demand is given by: 250 3.5 . Should one factory supply the market or two? Explain your reasoning. c. Suppose demand is given by: 200 1.75 . Should one factory supply the market or two? Explain your reasoning. d. Up to what quantity does the first factory exhibit increasing returns to scale? Constant returns to scale? Decreasing returns to scale? e. Up to what quantity does the second factory exhibit increasing returns to scale? Constant returns to scale? Decreasing returns to scale? f. For the decreasing average total cost industry, the firm exhibited increasing returns to scale for all output levels. This is not the case here, in which production follows the standard three stages of production, although new production can only be added in a lumpy way. Up to what quantity should one factory produce? Two factories produce? Explain your reasoning. 4