Suppose that, over the short run (next five years), demand for OPEC oil is given

Question

Suppose that, over the short run (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 5 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? (All values are present value.)

Explanation / Answer

For part a.: A monopolist determines quantity where MR=MC. Total revenue is P*Q = (115-2Q)*Q = 115Q - 2Q^2. This means that marginal revenue is 115 - 4Q (by taking the derivative of the equation for TR). So for Q: MR = MC, 115-4Q = 15, 100-4Q=0, 100=4Q, 25=Q. The price they would charge is P = 115-2Q = 115-2*25 = 65.

For part b., the monopolist has two choices: stick with high prices for the first five years, and then reduced demand for the next five years; or keep prices at $50 for the whole time.

First scenario: With Q = 25 and P = 65, profits are 1625-375=1250 in the first five years. You have to work out their Q and P again when demand changes. TR = P*Q = (105-2.5Q)*Q = 105Q-2.5Q^2. MR = 105 - 5Q. MR = MC means 105-5Q = 15, 90-5Q = 0, 90=5Q, 18=Q. Price is P = 105-2.5Q = 105-2.5*18 = 105-45 = 60. Profits are P*Q - C*Q = 60*18 - 15*18 = 1080-270= 810. for the second half of the decade. Total decade profits are 1250 + 810 = 2060.

Second scenario: Keeping prices at 50 means that they can produce up to Q = 57.5 - .5P = 57.5 - .5*50 = 57.5 - 25 = 32.5. With this P and Q, their profits are P*Q  - C*Q = 50 * 32.5 - 15*32.5 = 1625 - 487.5 = 1137.5 in each half of the decade. Overall profits are 1137.5+1137.5=2275. This is the more profitable scenario.

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