Question 1: Hotellings Rule in a rapidly changing market

Lets assume that oil was not discovered until the year 1999. The New York Times writes that a source of energy with potential disruptive effects on the world economy is now ready for production, and other countries are watching the developments closely. Along with many other producers, you own a small oil well. The market is very competitive. The marginal extraction cost is $10 per barrel. The interest rate is 5%. The annual demand for oil is Q = 90,000 2,000P where Q is in barrels per year and P is in dollars per barrel. Use your knowledge about Hotellings Rule to answer the following questions:

a. Oil is trading for $25/bbl on Jan 1st, 1999. What do you expect the path of oil prices and extraction quantities to be from 1999-2010 (assuming no shocks to the market)? A day later, on Jan 2nd, 1999, the Wall Street Journal opens with a story that there is now a more reliable reserves estimate. Total reserves are estimated at 760,000 barrels.

b. What is the oil price directly after this news becomes public? When will the world run out of oil, assuming no more oil is discovered? [Hint: use a spreadsheet.] You have a couple million dollars to spend on Dec 31st, 1999. You decide to quickly buy out all small oil producers. By Jan 1st, 2000, you are the owner of all remaining reserves.

c. [Note: this is the hardest part, and more challenging than what I would ask on an exam.] As a monopolist, how much oil would you extract in each of the following years, what is the oil price path, and when would you run out of oil? [Hint 1: you need to compute marginal revenues for the monopolist. Hint 2: you will run out of oil before 2040. Hint 3: dont forget that remaining reserves in 2000 are below 760,000 barrels.] On Jan 1st, 2001, the dotcom bubble bursts and leads the economy into recession. Total demand for oil decreases to Q = 80,000 2,000P for this and all future years. Whats worse, the competition authorities have discovered your monopoly and force you to divest your assets in many small pieces. As a result, the oil industry has become competitive again. [Note: if you did not solve part c, you can assume that reserves are 700,000 barrels at the start of 2001.]

d. What is the new oil price and extraction path from 2001 onward? Two years later, at the start of 2003, demand is still sluggish, but the International Energy Agency has released a report in which they predict a large surge in oil demand from China, starting in early 2010. World demand for oil is expected to be Q = 140,000 2,000P from 2010 onwards, but remains at Q = 80,000 2,000P until then.

ANSWER ONLY PARTS c and d