Economics 359M

Peter J. Wilcoxen
Department of Economics
University of Texas at Austin

Exercise 12

Due Thursday 5/3

Suppose we're interested in the allocation of oil over 5 periods. In each period the demand curve for oil is given by Pi = 100 - Qi, where Pi and Qi are the price and quantity of oil in period i. The marginal cost of extracting oil is given by MEC = QT/10, where QT is the total amount extracted to date (QT = Q1 in period 1, QT = Q1+Q2 in period 2, etc.) To keep the algebra simple, let the interest rate be zero.

  1. Find the efficient allocation of oil among the periods. Calculate and graph the quantity, price, marginal extraction cost and royalty in each period.

  2. Now suppose there is a backstop technology available in unlimited supply at a marginal cost of $20. Draw a graph showing how this changes the oil market. In what year will the backstop begin to be used? Calculate and graph the new efficient quantity, price, marginal extraction cost and royalty for each period.

  3. How does the backstop affect the owners of oil reserves? Why? How much do oil owners gain or lose in part (2) relative to part (1)? How much do consumers gain or lose?

Key Concepts