Question

Suppose you run a small oil well on the Western slope of Colorado. Your production is very small relative to that of the world and thus your production decisions do not impact the world price of oil. You have a stock of 1,200 barrels of crude underground which you can extract. Your annual marginal cost of extraction is equal to c*q and for each barrel produced, you can sell it for $P (which is equal in both years unless explicitly stated otherwise). You must allocate production (extraction) across two years (0; 1). Assume r = 0:2 for all parts.

(a) If P = 100 and c = 0:25, will your resource constraint bind? Show your work.

(b) If P = 100 and c = 0:25, what are your optimal extraction quantities in both years?

(c) Find the present value of your two years of profits under these conditions.

Answer 1

a) The Marginal Cost (MC) = 1200*0.25 = $300. This does not satisfy the solution. All the conditions need to be satisfied in a bindind constraint. Here MC is not equal to the equlibrium P
Here price is 100, but marginal cost (MC) is 300. So in order to make the resource constraint binding, the amount of barrels should be decreased.

b) The optima extraction in both years is equal to the price that is equal to

P = C*Q or

100 = 0.25*Q or

Q = 400

So the optimat quantity in both years is equal to 400.