Homework 4 Chapter 4

Geologists predict that non-renewable fuel sources like oil will be depleted in the near future due to overuse. Economists tend to disagree with this viewpoint. Explain the logic behind the economist’s viewpoint. Geologists base their view on absolute physical scarcity, while economists base theirs on relative scarcity, as measured by price or opportunity cost. The physical view, as typified by Hubbert, does not take price into account. Higher prices stimulate conservation, substitution, and new technologies, all of which help to alleviate relative scarcity.

QUIZ QUESTION 2 In a competitive industry with MC > 0, according to the Hotelling model of dynamic efficiency: a. Price (P) will increase over time at the rate of interest b. P-MC will increase over time at the rate of interest c. MC will increase at the rate of interest d. PV (P) will increase at the rate of interest e. PV (P-MC) will increase at the rate of interest b. P-MC will increase over time at the rate of interest

The Governor of Maryland is considering using her veto authority on a bill allotting $5 million in subsidies to Do Ray Me, a company that manufactures solar panels. According to the bill’s supporters, the $5 million in subsidies today will generate a lump sum of $30 million in benefits in 20 years. The governor believes the bill to be risky and decides to use a discount rate of 9%.Should the Governor veto this bill based on a cost/benefit analysis? The PV of $30 million in benefits 20 years from now is: 𝑃𝑉= $30𝑚 ( 1.09) 20 𝑃𝑉=$5,352,926.69 Net PV = PV (Benefits – Costs) = $352,926.69 Since NPV > 0, the project is worthwhile. (It’s a close call. At 9.5%, the project fails the CBA test.) No. The present value of the project’s benefits exceed its costs.

In what way is wood a renewable fuel In what way is wood a renewable fuel? In what way can it be a non-renewable fuel? Under what conditions would you allow it to be used to meet the requirements of a renewable portfolio standard? Wood is renewable if it grows faster than the rate at which it is harvested. Companies may operate tree plantation where they plant trees to replace the ones they have cut down. Some trees grow slowly. Trees in old-growth forests may be 500 years old, and so cannot be replaced within one or two generations. In that case, it is best to model them as non-renewable resources. I would allow wood to qualify for a RPS as long as it is a species that can be grown and replaced rapidly.

Duke Energy operates several nuclear plants in the Carolinas Duke Energy operates several nuclear plants in the Carolinas. Suppose it decides to own uranium mines, a competitive industry, and faces demand   P = 300 – 10 Q, where Q is tons of uranium and P is $/ton. Marginal extraction cost is $30. The discount rate is 20%. Assuming there are only 40 tons of uranium remaining in the mine, how much should Duke extract today, and how much a year from now? What will be the price of uranium today and one year from now? Using the equimarginal rule: 𝑀𝑁𝐵 0 = 𝑃 0 - 𝑀𝐶 0 = 𝑃𝑉(𝑀𝑁𝐵 1 ) = PV ( 𝑃 1 - 𝑀𝐶 1 ) 300 -10 𝑄 0 - 30 = (300−10 𝑄 1 −30) 1.2 270 –10 𝑄 0 = (270−10 𝑄 1 ) 1.2 324-12 𝑄 0 = 270 – 10 (40 - 𝑄 0 ) 454 = 22 𝑄 0 𝑄 0 = 20.64 tons. 𝑄 1 = 19.36 tons. 𝑃 0 = 300 -10 𝑄 0 . 𝑃 1 = 300 -10 𝑄 1 𝑃 0 = $93.60/ton 𝑃 1 = $106.40/ton.

Referring to question 4, Duke Energy is actually a monopoly Referring to question 4, Duke Energy is actually a monopoly. Given the information in question 4, how much will Duke Energy produce in each period, and what price will they charge? Using the equimarginal rule: 𝑀𝑅 0 - 𝑀𝐶 0 = PV ( 𝑀𝑅 1 − 𝑀𝐶 1 ) 300 -20 𝑄 0 - 30 = (300−20 𝑄 1 −30) 1.2 324 - 24 𝑄 0 = 270 – 20 (40 - 𝑄 0 ) 854 = 44 𝑄 0 𝑄 0 = 19.41 tons. 𝑄 1 = 20.59 tons. 𝑃 0 = 300 -20 𝑄 0 = $90.90/ton. 𝑃 1 = 300 -20 𝑄 0 = 109.10/ton.

In a monopoly with MC > 0: a. Price (P) will increase over time at the rate of interest b. P-MC will increase over time at the rate of interest c. PV (P) will increase at the rate of interest d. PV (P-MC) will increase at the rate of interest e. Hotelling’s Rule will not hold for a monopoly e. Hotelling’s Rule will not hold for a monopoly

Explain and provide an example of a backstop technology for natural gas, and how it would affect the firm’s decision about how much to produce today as compared to when there is no backstop technology. Solar power. The availability of a backstop technology limits the future price of the original fuel, shifting more production to today and leaving less for the future.

Explain the difference between a private and a social discount rate, and which one is likely to lead to producing more today and leaving less for the future. The private discount rate is the cost to borrow funds in the private market. The social discount rate is society’s time preference between consuming now rather than in the future. The private discount rate discounts the future more heavily and leads to producing more today and leaving less for the future.

Referring to the numbers in question 4, suppose demand increases next year compared to this year.  Will this year’s output increase or decrease compared to question 4? If next year’s demand increases, next year’s price will be higher. So produce less today and leave more for the future.