Consider a market in which today’s crude oil price is $100/bbl, and the marginal cost of extracting another barrel of oil is $50. The interest rate is 10% per year. Assume that the market is competitive.

a. What is the best prediction for the oil price 1, 2, 3, 4 and 5 years from now, based on the Hotelling model? Calculate the oil prices at the end of years 1, 2, 3, 4, and 5. The market suddenly learns that the marginal cost of extraction in years 2 and 3 will be only $40, after which the marginal cost is expected to fall to $20 for years 4 and 5.

b. What is your prediction for future oil prices based on this new information? Calculate the oil prices at the end of years 1, 2, 3, 4, and 5.

Now another piece of news hits the market. The International Energy Agency predicts that demand for oil from China, India and Brazil will increase dramatically from year 3 onwards, but demand in years 1 and 2 is unlikely to change.

c. Qualitatively, what will happen to prices and quantities, today and tomorrow? Draw a sketch of the price path in a figure in which you also graph the exact prices that you calculated in part b (i.e., a sketch of the new price path relative to the old price path).

d. Explain why, even though the Hotelling model gives clear predictions about long-term oil prices given today’s prices and marginal costs, most oil price predictions are quite far off, even in the short or medium term.