An oil refinery converts crude oil to gasoline. It takes one barrel of crude oil
ID: 1253744 • Letter: A
Question
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?
Explanation / Answer
W is fixed, so there is only one variable here, q. To clear up any potential confusion I will substitute w with the hypothetical number 5. 1. In this case, the marginal cost would be 1/2q^2 + wq - (1/2(q-1)^2 + w(q-1)) [trust me, this took me a while to figure out, but with whatever value W you pick, plug both those equations into a graphing calculator and you will find that the table for this second equation gives you the marginal cost for whatever value W you used] 2. The MC for 50 barrels would simply be a substitution of w with the number 5 into the equation from question one; so MC for 0 - 50 barrels would be: 1/2q^2 + 5q - (1/2(q-1)^2 + 5(q-1)) The MC for >50 barrels would be 1/2q^2 + 15q - (1/2(q-1)^2 + 15(q-1)), since you don't have to consider anything less than 50 barrels, and the $15 per barrel is fixed. 3. For maximum profit, the firm will supply 25 barrels, based on function of Profit = 30q -(1/2q^2 + 5q); note that I neglected to plug in the whole "$15 per barrel for purchases of over 50 barrels of oil", because the maximum is at a number less than 50. Hope this helps!