Please, try to explain the answer Please, try to explain the answer Please, try
ID: 1126774 • Letter: P
Question
Please, try to explain the answer
Please, try to explain the answer
Please, try to explain the answer 25. Assume there are barrels of oil available for purchase that can go to two refineries. The production functions for the two refineries are: Refinery A: Q-35Ma-.5MA2 Refinery B: Q = 20MB-MB2 There are 78 barrels of oil available to purchase. The cost of a barrel of oil is $80 and you have a firm budget of $5,800 to purchase barrels of oil, and can only buy whole barrels of oil (not portions). Assuming the company is maximizing profit, how many barrels of oil will they end up sending to Refineny A? Enter as a value.
Explanation / Answer
Consider the given problem here we have given the production function of 2 “refinery.
So, for “Refinery A”, Q = 35*Ma – 0.5*Ma^2, Marginal Productivity of A, “35 – 0.25*Ma”.
Now, the production function of “Refinery B”, is “Q = 20*Mb – Mb^2,
=> Marginal Productivity of B, “20 – 2*Mb”. Now, if we compare both the MP we can see that MPa > MPb always.
=> it is profitable to send “barrels” of oil to “A”, until MPa is “0”.
Now, MPa =0, => 35 – 0.25*Ma = 0, => 0.25*Ma = 35, => Ma = 35/0.25 =140.
=> Maximum “A” can take “140” barrels of oils to refine.
Now, there is budget of “5800” and the price of “80”, => 5800/80=72.5, => the company can purchase maximum 72 barrels of oil.
Now, “A” is more efficient compared to “B” and the company can purchase “72” barrels of oil, => the company sends “72” barrels of oil to “A”.