An oil refinery converts crude oil to gasoline. It takes one barrel of crude oil to produce one barrel of gasoline. Total cost of producing q barrels of gasoline at the refinery is
TC=1/2q2 + wq
where w is the price of a gallon of crude oil
1) Express the marginal cost of producing gasoline as a function of q and w.
2) Suppose the refinery can purchase 50 barrels of oil for $5 per barrel, but must pay $15 per barrel for any barrels it buys beyond 50 barrels. What is the marginal cost of producing a quantity of gasoline of less than or equal to 50 barrels? What is the MC of producing a quantity of gasoline of more than 50 barrels?
3) Suppose the demand for gasoline facing the refinerey is perfectly elastic at $30 per barrel. How much will the firm supply?