Supplementary Exercises > Exhaustible and Recyclable Resources

Rising demand with constant costs

Suppose an exhaustible resource is to be allocated across three periods, with demand is increasing over time. In particular, suppose that the following is true:

Throughout this problem you may assume the interest rate is 25%.

  1. Find the efficient allocation of the resource across the three periods. What will the price, quantity and royalty be in each period? Be sure to show all your work.
  2. Now suppose that a backstop resource is available at a marginal cost of $70. Calculate how the backstop would change the efficient use of the resource. Be sure to show what happens to prices, royalties and production in each period. Also, calculate how much of the good is produced via the backstop. You should assume that everyone knows about the backstop at the beginning of period 1.

When you're done, you can check your work via the link below:
Site Index | Zoom | Admin
URL: https://wilcoxen.maxwell.insightworks.com/pages/2259.html
Peter J Wilcoxen, The Maxwell School, Syracuse University
Revised 05/10/2006