In an article appearing in the Dow Jones News Service on February 5^th, 2004, the agency cites Saudi Arabia’s concern about the production of oil by the OPEC cartel. Assume the current daily demand for OPEC’s oil is given by the following equation: 

P = 50 – 0.001Q 

where P is the price per barrel (ppb) and Q is the quantity of barrels sold daily (in   thousands). Moreover, suppose the marginal cost of producing a barrel is constant at zero. 

a. Would it surprise you to learn that OPEC’s declared objective is to sell 25 million barrels a day for an average price of $25 per barrel? Why or why not? Explain. You may use a graph to support your argument. 

b. Assume that after OPEC’s meeting this week, the new demand for OPEC oil will be given by: P = 40 - .001Q. Would OPEC’s stated objective (25 million barrels at an overall price of $25) be attainable after this change? Explain. Assume OPEC ignores the demand shift. What’s the maximum price per barrel they can charge if they decide to keep producing 25 million barrels per day? What is the profit in this case? 

c. Now suppose that OPEC recognizes that demand has changed (as in (b)) and wants to maximize profits. What is the daily quantity they should supply? At what price? What is the profit in this case? What is the price elasticity of demand at this price/quantity combination? Explain.