Oil, technology, and ANWR

The total amount of oil beneath the Arctic National Wildlife Refuge is very uncertain but some recent estimates put it at 10 billion barrels. Suppose the marginal cost of extracting the oil is $30 per barrel, and that we are interested in allocating the 10 billion barrels between two periods. Period 1’s demand for oil is given by P1 = 100 – 4*Q1. Period 2’s demand, however, is expected to be significantly higher and is given by P2 = 150 – 4*Q2. The interest rate is 100 percent (the periods are a generation apart).

1. Find the efficient allocation of oil. What will the price, quantity, marginal social surplus and royalty be in each period?
2. Now suppose that before any oil is actually extracted, a team of researchers announces a breakthrough in the technology for producing synthetic fuel from coal. It is possible to make as much fuel as needed at a cost of $90 per barrel, and the fuel is a perfect substitute for oil. Please calculate the new equilibrium and discuss how it compares to the one from part (1).