Exploration in a one period model

Suppose an exhaustible resource is used for only one period and is subject to the demand and MEC equations below.

• WTP = 1000 - 2*Q
• MEC = 300

In addition, 200 units of the resource are available.

1. Find the market equilibrium. What will the values of the following variables be: royalty, price and quantity?

Now suppose that it's possible to find more of the resource via exploration. Drilling costs $400 per well but the amount of the resource found is uncertain: 80% of the time nothing is found but 20% of the time 10 units are found. Any units found would still be subject to the MEC above.

2. 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 royalty, price and total quantity consumed?
4. How many new units will be found via exploration? How many wells will need to be drilled to bring that about?
5. What are the equilibrium costs, revenues and profits associated with the units found by exploration?
6. What effect does exploration have on consumer surplus and the producer surplus of owners of the original 200 units?  What is the effect on overall social surplus?

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