The Miss Manners Refinery in Dry Rock, Oklahoma, converts crude oil into gasoline. It takes 1 barrel of crude oil to produce 1 barrel of gasoline. In addition to the cost of oil there are some other costs involved in refining gasoline. Total costs of producing y barrels of gasoline are described by the cost function c(y) = y2/2+poy, where po is the price of a barrel of crude oil.
(a) Express the marginal cost of producing gasoline as a function of po and y. ______.
(b) Suppose that the refinery can buy 50 barrels of crude oil for $5 a barrel but must pay $15 a barrel for any more that it buys beyond 50 barrels. The marginal cost curve for gasoline will be ______ up to 50 barrels of gasoline and _____ thereafter.
(c) Plot Miss Manners’ supply curve in the diagram below using blue ink.
(d) Suppose that Miss Manners faces a horizontal demand curve for gasoline at a price of $30 per barrel. Plot this demand curve on the graph above using red ink. How much gasoline will she supply? _____.
(e) If Miss Manners could no longer get the first 50 barrels of crude for $5, but had to pay $15 a barrel for all crude oil, how would her output change?
(f) Now suppose that an entitlement program is introduced that permits refineries to buy one barrel of oil at $5 for each barrel of oil that they buy for $15. What will Miss Manners’ supply curve be now? __________. Assume that it can buy fractions of a barrel in the same manner. Plot this supply curve on the graph above using black ink. If the demand curve is horizontal at $30 a barrel, how much gasoline will Miss Manners supply now? ________.