Problem
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.
1. If P = 100 and c = 0.25, will your resource constraint bind? Show your work.
2. If P = 100 and c = 0.25, what are your optimal extraction quantities in both years?
3. Find the present value of your two years of profits under these conditions. War and Price Volatility
4. 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?
5. Find the present value of your two years of profits under the price of $200.
6. 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?
7. 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?