Economic problem sets 2

ECON 456 San Diego State University Abman Fall 2020

Econ 456 - Problem Set 2

Instructions

Please answer the following practice questions. For full credit, you must show your work when asked. Partial credit may be given for incorrect answers with sensible work. You must upload your files to Canvas no later than Friday, October 23rd at noon. Late assignments will receive no credit.

Questions

1. Suppose you run a small oil well on the Western slope of Colorado. Your production is very small relative to that of the world and thus your production decisions do not impact the world price of oil. You have a stock of 1,200 barrels of crude underground which you can extract. Your annual marginal cost of extraction is equal to c∗q and for each barrel produced, you can sell it for $P (which is equal in both years unless explicitly stated otherwise). You must allocate production (extraction) across two years (0, 1). Assume r = 0.2 for all parts.

(a) If P = 100 and c = 0.25, will your resource constraint bind? Show your work.

(b) If P = 100 and c = 0.25, what are your optimal extraction quantities in both years?

(c) Find the present value of your two years of profits under these conditions.

War and Price Volatility

(d) If a war in the middle east doubles the price (such that P = 200) before you choose q0 and q1, what are your optimal extraction quantities in each year?

(e) Find the present value of your two years of profits under the price of $200.

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(f) Suppose the pre-war price is $125. If this war occurred after you had chosen q0 (such that P0 = 125 but P1 = 200) AND you anticipated the event (meaning you knew it would happen even before you chose q0), what are your optimal extraction quantities in each year?

(g) If this war occurred after you had chosen q0 (such that P0 = 125 but P1 = 200) and you had NOT anticipated the event (it is too late to change q0 and you had incorrectly assumed P1 would also be 125), what quantities would you have chosen for q0 and q1?

Technological Advancement

(h) Suppose a technology company develops a cheaper way to get extract oil such that c = .1 instead of 0.25. If this technology is available to you before you make your extraction decisions and the price is $100 per barrel. What are your optimal ex- traction quantities?

(i) How much more profit do you make in year 0 with this new technology compared to the profit made in year zero in part (b)?

(j) Suppose you heard that the company was working on the new technology. It is not available to you in period 0, but might be available in period 1. If you believe that the probability the new technology will be available to you in period 1 is 0.6 and the probability it is not available (and you use the old technology) is 0.4. If P = 150 for both years, what do you choose for q0?

Three years of extraction

(k) Now suppose you can extract for three years instead of two. If P = 100 and c = .25 for all periods, what are your optimal quantities, q0, q1, and q2?

(l) Now suppose the price increases to P = 150 for all three years. What are your optimal quantities, q0, q1 and q2?

Challenge Question - Refer to your intermediate micro notes [OPTIONAL]

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(m) Suppose you are a monopolist, you produce the only oil that can be consumed in Western Colorado. The annual demand for oil in this area is QD = 800 − P . If c = .25 what are your profit maximizing quantities q0 and q1 and how much total profit do you make?

2. Suppose Elon Musk is developing a new car that runs entirely on biofuels (a renewable energy source), yet it is so expensive that it currently costs approximately $2 per mile to drive. Under current prices, a conventional car costs uses roughly $0.60 per mile in gas. Assume the gas used in cars cannot be used anywhere else.

(a) If we consider the solar to be a ‘backstop’ technology for the gas in conventional cars, draw the long-run price path of $ per mile for gasoline. Indicate the time the solar technology becomes ‘relevant’ with t∗.

(b) Suppose the government introduces CAFE standards that are more strict than ex- isting ones, meaning the regulated miles per gallon drops and cars must be more efficient by law (thus using less fuel for every mile driven). Draw the new price path and label the time the solar technology becomes ‘relevant’ in this scenario with t∗∗. How does t∗∗ compare with t∗?

3. A new material used for cans has recently been discovered, campanilium. The metal can be extracted and sold at a price of $2 per ton and the demand for the metal is QD = 10 − P . Importantly, used campanilium can be recycled and the supply curve of recycled campanilium is QSR =

1 2 P + 1.

(a) Graph the demand for campanilium, the supply of recycled campanilium and the supply of newly extracted campanilium. Solve for the equilibrium quantity of all campanilium sold. What fraction of this is recycled campanilium?

(b) Suppose the government imposes a tax of $1 per ton on newly extracted campanil- ium. Find the new equilibrium total quantity. With the tax, what is the fraction of campanilium supplied from recycled sources?

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Short Answer:

4. Hotelling’s rule presents a very specific prediction for prices of a nonrenewable resource. What is this prediction? Give two reasons why we may not observe this pattern in the data and explain why these reasons would undermine the prediction.

5. What is meant by the ‘grade’ of a resource and what are the economic implications if grade decreases in quantity of mineral extracted?

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