The current price of oil is about $80 per barrel, and global production is about 100 million barrels of oil per day. The elasticity of demand for oil has been estimated to be approximately 0.2.

(a) OPEC is responsible for roughly 40% of the world's oil production. Assuming no changes by any other oil producers, by how much would OPEC have to change its production in order to raise the market price to $90? There are a significant number of producers in the United States that can increase their supply when it is profitable by increasing capacity of shale oil. A typical location of shale oil production in the U.S. has a daily cost function of C(Q) = 12,960 + 13Q + .1Q ^2, where Q is daily production in thousands of barrels of oil. Assume that all shale oil producers are price takers.

(b) Based on the cost function above, identify the fixed costs and the variable costs of a typical shale oil producer.

(c) A typical shale producer with the cost function above has marginal costs given by MC (Q) = 13 + .2Q. At the current price of $80, how many barrels per day would a shale oil location in the U.S. produce to maximize profits in the short run? What about at OPEC's target price of $90? (Feel free to assume that any fixed costs are sunk in the short run.)

(d) How do these price-taking shale oil producers in the United States affect OPEC's plan to increase the price of oil to $90 through cuts to its production?

(e) If there are no major barriers to entry and exit from shale oil production in the United States, what is the highest price that OPEC can expect to sustain in the long run?