Assume That You Own an Exhaustible Resource That Is Sold

Essay

Assume that you own an exhaustible resource that is sold competitively. The price of the resource is:
P_{t + 1} - C = 1.08(P_t -
C),
where t = 0 at the beginning of 2005,
and
It is also known that the demand for the resource is:
Q = 1,000,000 - 25,000 P,
where Q represents output in tons per year. If the beginning of 2005 price is $30 per ton and the marginal cost of extraction is $10 per ton, what will the price be at the end of 2009? What is the user cost of production in 2009? Is it different from the user cost for 2005? Explain. How much of the resource will be extracted in 2009? What is the market rate of interest on money? Explain.