Suppose that, over the short run (say, the next five years), demand for OPEC oil is given by Q = 57.5 - .5P or, equivalently, P = 115 - 2Q.

(Here Q is measured in millions of barrels per day.) OPEC’s marginal cost per barrel is $15.

a. What is OPEC’s optimal level of production? What is the prevailing price of oil at this level?

b. Many experts contend that maximizing short-run profit is counterproductive for OPEC in the long run because high prices induce buyers to conserve energy and seek supplies elsewhere. Suppose the demand curve just described will remain unchanged only if oil prices stabilize at $50 per barrel or below. If oil price exceeds this threshold, long-run demand (over a second five-year period) will be curtailed to Q = 42 - .4P (or P = 105 -2.5Q). OPEC seeks to maximize its total profit over the next decade. What is its optimal output and price policy? (Assume all values are present values.)