Question 1
1. In the market for oil, the (inverse) demand curve is P = 200 – Q. MR is 200 – 2Q. MC is 0.5Q + 50. (Prices are in price per barrel, and Q units are millions of barrels.) If OPEC controls production, how much should they release onto the market if they want to maximize their profit?
***Enter your answers in terms of Q, so 10 million would go in as just 10.***
60
Question 2
1. In the market for oil, the (inverse) demand curve is P = 200 – Q. MR is 200 – 2Q. MC is 0.5Q + 50. (Prices are in price per barrel, and Q units are millions of barrels.) If OPEC controls production, how much should they release onto the market if they want to maximize their profit? If they release that much onto the market, what is the price for oil? Enter your price in dollars but don't include the $ sign.
140
Question 3
1. In the market for oil, the (inverse) demand curve is P = 200 – Q. MR is 200 – 2Q. MC is 0.5Q + 50. (Prices are in price per barrel, and Q units are millions of barrels.) If OPEC controls production, how much should they release onto the market if they want to maximize their profit?
**If they release that much oil onto the market, how much is their producer surplus? Remember, producer surplus is the total amount they receive less their costs.
4500
Question 4
1. In the market for oil, the (inverse) demand curve is P = 200 – Q. MR is 200 – 2Q. MC is 0.5Q + 50. (Prices are in price per barrel, and Q units are millions of barrels.) If OPEC controls production, how much should they release onto the market if they want to maximize their profit?
**If they release that much oil onto the market, how much is the world's CONSUMER surplus? Remember, consumer surplus is the area under the demand curve less their costs.
1800
Question 5
1. OPEC gets together and sets the total production to the level you just determined. All of the various country representatives sign a blood oath to limit total output to this level, but when he gets home Gen. Sani Abacha’s wife Maryam tells him she has some suitcases that she needs to fill with money. She persuades the General to increase Nigerian production by 10 million barrels per day, so the country bumps up its production. What is the price per barrel after Nigeria cheats?
Question 6
1. How much is producer surplus now that Abacha has increased production? **DO include Abacha’s “cheater’s” gains- that’s still producer surplus after all!**
Question 7
1. How much is CONSUMER surplus now that Abacha has increased production?
Question 8
1. At the next meeting, the representatives of OPEC are angry at Abacha and they decide to punish him by producing out to the competitive equilibrium. What is the quantity produced at the competitive equilibrium?
As above, enter your answer without the "millions," so "10 million" goes in as 10.
5 points
Question 9
1. At the next meeting, the representatives of OPEC are angry at Abacha and they decide to punish him by producing out to the competitive equilibrium. What is the PRICE at the competitive equilibrium?
Question 10
1. At the next meeting, the representatives of OPEC are angry at Abacha and they decide to punish him by producing out to the competitive equilibrium. How much consumer surplus is enjoyed at the competitive equilibrium?
Question 11
1. At the next meeting, the representatives of OPEC are angry at Abacha and they decide to punish him by producing out to the competitive equilibrium. How much PRODUCER surplus is enjoyed at the competitive equilibrium?
To determine the answers to these questions, we need to analyze the given demand, marginal revenue, and marginal cost functions for the oil market under OPEC control.
The demand curve is given as P = 200 - Q, where P represents the price and Q represents the quantity of oil in millions of barrels. The marginal revenue (MR) function is derived by taking the derivative of the demand curve, which gives MR = 200 - 2Q. The marginal cost (MC) function is given as 0.5Q + 50.
Question 1:
To maximize profit, OPEC should set its production level where marginal revenue (MR) equals marginal cost (MC). Therefore, we need to solve the equation 200 - 2Q = 0.5Q + 50 for Q. Simplifying the equation, we get 2.5Q = 150 and solving for Q gives Q = 60 million barrels.
Question 2:
To find the price for oil at this production level, we substitute the quantity Q = 60 into the demand curve equation P = 200 - Q. Thus, P = 200 - 60 = 140 dollars per barrel.
Question 3:
To calculate OPEC's producer surplus, we need to find the total revenue from selling the oil minus their costs. The total revenue can be calculated by multiplying the price per barrel (P) by the quantity (Q), i.e., 140 * 60 = 8400 million dollars. The cost can be calculated using the MC function, i.e., 0.5Q + 50, and substituting Q = 60. Thus, the cost is (0.5 * 60) + 50 = 80 million dollars. Therefore, the producer surplus is given by the difference between revenue and cost, i.e., 8400 - 80 = 8320 million dollars.
Question 4:
To calculate the world's consumer surplus, we need to find the area under the demand curve up to the equilibrium quantity (Q). The formula for the consumer surplus is (1/2) * (base) * (height), where the base is the equilibrium quantity (Q) and the height is the difference between the price (P) and the marginal cost (MC) at that quantity. Thus, the consumer surplus is (1/2) * Q * (P - MC), which is (1/2) * 60 * (140 - 80) = 1800 million dollars.
Question 5:
To calculate the price per barrel after Nigeria cheats, we need to re-calculate the equilibrium. We add the additional production of 10 million barrels per day to the original equilibrium quantity of 60 million barrels, resulting in 70 million barrels. Substituting Q = 70 into the demand curve equation P = 200 - Q, we get P = 200 - 70 = 130 dollars per barrel.
Question 6:
To calculate the producer surplus after Nigeria cheats, we need to calculate the total revenue and costs using the new equilibrium quantity. The total revenue is given by P * Q, which is 130 * 70 = 9100 million dollars. The cost is given by the MC function, which is (0.5 * 70) + 50 = 85 million dollars. Therefore, the producer surplus is 9100 - 85 = 9015 million dollars.
Question 7:
To calculate the consumer surplus after Nigeria cheats, we use the new equilibrium quantity (Q = 70) and the new price (P = 130) in the formula for consumer surplus (1/2) * Q * (P - MC). Thus, the consumer surplus is (1/2) * 70 * (130 - 85) = 1575 million dollars.
Question 8:
To determine the quantity produced at the competitive equilibrium, we set the marginal cost (MC) equal to the demand curve (P = 200 - Q). Solving the equation 0.5Q + 50 = 200 - Q for Q gives Q = 80 million barrels.
Question 9:
To find the price at the competitive equilibrium, we substitute the quantity (Q = 80) into the demand curve equation P = 200 - Q. Therefore, P = 200 - 80 = 120 dollars per barrel.
Question 10:
To calculate the consumer surplus at the competitive equilibrium, we use the formula (1/2) * Q * (P - MC) with the new equilibrium quantity (Q = 80) and the new price (P = 120). Thus, the consumer surplus is (1/2) * 80 * (120 - (0.5 * 80 + 50)) = 2800 million dollars.
Question 11:
To calculate the producer surplus at the competitive equilibrium, we use the formula for producer surplus, which is the total revenue (P * Q) minus the total cost (MC * Q). The total revenue is given by P * Q, which is 120 * 80 = 9600 million dollars. The total cost is given by MC * Q, which is (0.5 * 80 + 50) * 80 = 6800 million dollars. Therefore, the producer surplus is 9600 - 6800 = 2800 million dollars.