Exploration

Suppose an exhaustible resource is to be used over three identical periods. In each period, the following equations hold:

• W2Pi = 500 - (1/3)*Qi
• MECi = 50

In addition, the interest rate is 50% and 2340 units of the resource are available.

1. Find the efficient allocation. What will the values of the following variables be in each year: royalty, price and quantity?

Now suppose that it's possible to find more of the resource via exploration. Drilling costs $450 per well but the amount of the resource found is uncertain: 60% of the time nothing is found, 20% of the time 1 unit is found, and 20% of the time 9 units are found. Any units found would still be subject to the $50 MEC.

2. What is the expected number of units found per well drilled? Solve for the minimum price of the resource at which firms will be willing to explore.
3. Calculate the new equilibrium taking exploration into account. What will be the new values of the royalties, prices and quantities in each period?
   
4. How much does exploration change the price in period 1? How many new units will be found via exploration? How many wells will need to be drilled to bring that about?

 

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