Extraction with increasing demand and a backstop

Consider the allocation of an exhaustible resource across three generations. The following information is
available:

• Demand in period 1: W2P1 = 1500 – (1/4)*Q1
• Demand in period 2: W2P2 = 2500 – (1/2)*Q2
• Demand in period 3: W2P3 = 4500 – Q3
• Resource available: 4400 units
• Marginal extraction cost: $500
• Interest rate: 200% (please note the 2)
  

Please answer the following questions:

1. Calculate the market equilibrium. Summarize your results in a table giving the values of the following variables in each of the three periods: royalty, price and quantity.
2. Now suppose that a backstop resource is available at a marginal cost of $3200. Please calculate the new equilibrium (royalty, price and quantity in each period). Also calculate the total amount of the backstop that will be produced.

 

When you're done, you can check your work via the link below: