Abman Spring 2023
Econ 456 – Problem Set 2
Instructions
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. 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.
(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 extraction 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?
(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. 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 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 campanilium. Find the new equilibrium total quantity. With the tax, what is the fraction of campanilium supplied from recycled sources
