Question

6. Assume there are ten countries of equal size in OPEC that face a demand for oil of P = 100 – 0.5Q. Marginal cost (MC) is constant and equal to $20. What will be the cartel price and quantity? How much will each country receive as a quota? What will be the deadweight loss as compared to a competitive oil industry?

Referring back to question 6, what factor makes it difficult for the cartel to stick to its agreement in the short run? What about the long run?

Answer 1

OPEC is a cartel so this will use MR = MC to determine the quantity and demand function to determine the price

MR is 100 - Q so that MR = MC gives 100 - Q = 20 or Q = 80 units. Price is P = 100 - 80*0.5 = $60 per unit

Each nation receives a quota of 80/10 = 8 units

Competition has P = MC or 100 - 0.5Q = 20 which gives Q = 80/0.5 = 160 units. Price = MC = $20

Hence, deadweight loss = 0.5*(60 - 20)*(160 - 80) = $1600

Members in the cartel can earn greater profits by producing more at the same price. This will increase its profits and since each member has the same incentive, cartel is not likely to sustain in the short run. In the long run however other cartel members can use different punitive measures for defecting members to control their behaviour.

Answer 2

To find the cartel price and quantity, as well as the quota for each country and the deadweight loss, we can use the concept of a cartel in an oligopoly market.

1. Cartel Price and Quantity: In a cartel, the countries act together as a monopoly, maximizing their joint profits. The total quantity supplied by the cartel is the sum of individual quotas allocated to each country.

Given demand: P = 100 - 0.5Q Given marginal cost (MC) = $20

In a monopoly or cartel, the profit-maximizing condition is MR = MC. Since the demand is given as P = 100 - 0.5Q, we can find the corresponding marginal revenue (MR) by differentiating the demand equation with respect to Q.

MR = d(100 - 0.5Q)/dQ = 100 - Q

Setting MR = MC: 100 - Q = 20 Q = 80

Now, we can find the cartel price (P) by substituting the quantity (Q) into the demand equation: P = 100 - 0.5(80) = 100 - 40 = $60

So, the cartel price is $60, and the cartel quantity is 80 units.

2. Quota for Each Country: Since there are ten countries of equal size, each country's quota will be the total cartel quantity divided by the number of countries: Quota per country = 80 units / 10 countries = 8 units

3. Deadweight Loss: Deadweight loss is the loss of economic efficiency that occurs when the market is not in perfect competition. In this case, the deadweight loss can be calculated by finding the difference between the total surplus in a competitive market and the total surplus in the cartel market.

In a competitive market, the quantity supplied will be at the equilibrium point where P = MC: 100 - 0.5Q = 20 Q = (100 - 20) / 0.5 Q = 160

The competitive price (P) can be found by substituting the competitive quantity (Q) into the demand equation: P = 100 - 0.5(160) = 100 - 80 = $20

Now, we can calculate the total surplus in the competitive market and the cartel market:

Total Surplus in Competitive Market: Consumer Surplus = (1/2) * (100 - 20) * 160 = $6400 Producer Surplus = (1/2) * (100 - 20) * 160 = $6400 Total Surplus = $6400 + $6400 = $12,800

Total Surplus in Cartel Market: Consumer Surplus = (1/2) * (100 - 60) * 80 = $1600 Producer Surplus = (1/2) * (100 - 60) * 80 = $1600 Total Surplus = $1600 + $1600 = $3200

Deadweight Loss = Total Surplus in Competitive Market - Total Surplus in Cartel Market Deadweight Loss = $12,800 - $3200 = $9600

4. Factors Affecting Cartel Stability: In the short run, it can be difficult for a cartel to stick to its agreement because individual countries may be tempted to cheat and produce more than their allocated quotas to earn higher profits. This can lead to price wars and undermine the cartel's ability to control the market.

In the long run, new countries or firms may enter the market, or existing countries may choose to leave the cartel to pursue individual profits. Additionally, technological advancements or changes in demand can impact the cartel's control over the market.

Overall, the stability of a cartel depends on the level of cooperation and trust among its members and the market conditions over time.