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Express the marginal cost of producing gasoline

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Problem: A refinery in Edmonton converts crude oil into gasoline. It takes 1 barrel of crude oil to produce 1 of gasoline. In addition to the cost of oil there are some other costs involved in refining gasoline. Total costs of producing ybarrels of gasoline are given by 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 andy.

b) Suppose 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. What will be the marginal cost curve for gasoline up to 50 barrels, and what will it be thereafter?

c) Plot the refinery supply curve in a diagram.

d) Suppose the refinery faces a horizontal demand curve for gasoline at a price of $30 per barrel. Plot this is on the graph. How much gasoline will the refinery supply?

e) If the refinery 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 the refinery's 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 (that is, for each barrel of oil they buy at $15, they get a $10 discount). What will the Edmonton refinery's supply curve be now? If the demand curve is still horizontal at $30 a barrel, how much gasoline will the refinery supply?

Reference no: EM132422667

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