GG/EE 550

Lab 8

As the operator of a mine with known initial endowment of 80,000 units of a nonrenewable resource you are asked to determine the extraction quantities Q in each year so that the cumulative present value of profits are maximized over the entire lifetime of the mine.  You are operating in a perfectly competitive market with a known demand curve:

P = 10 - .00338*Q

Your costs are given by the following cost function.

C = 0.1*Q^1.2

The discount rate is 5% per year.

There is no change in the discount rate over the lifetime of the mine, no refilling of the mine, no recycling, no substitute for the mineral from your mine until you hit the choke price, and no discovery of new minerals.

a)      Calculate the optimal extraction path for the mine, the corresponding cumulative present value of profits, and the price path over the lifetime of the mine.

b)      How do the results change if the discount rate is 10%?

c)      Return to a 5% discount rate and extend the model such that costs increase now not only as a function of how much you extract but are also a function of resource depletion. Here you need to extend the cost function such that the remaining size of the mine becomes a factor influencing costs. Make sure you state/explain  all assumptions you make to do this extension.

Given this new condition, estimate the optimal extraction path for the mine, the corresponding cumulative present value of profits, and the price path over the lifetime of the mine. Does the extraction/price path look different from what you saw in question a? Why?