Chapter 14, Problem 3P

To determine

Concept Introduction:

Cartel: In order to eliminate competition; manufacturers or suppliers, or an association creates a formal agreement to earn profits, by manipulating prices.

Total Revenue: It refers to the total receipts received by selling a given quantity of goods or services; it is also known as the total income of a business or a firm. The formula to calculate the total revenue is:

Here,

• P is the price of a commodity.
• Q is the quantity of the commodity.

Marginal Revenue: It refers to the additional revenue gained by producing one additional unit of a product or service. The formula to calculate the marginal revenue is:

Here,

• is the change in Total Revenue
  
• is the change in Quantity of that commodity.
  

Explanation of Solution

a. Calculation of total revenue and marginal revenue.

Price of Olive oil (per gallon)($)(A)	Quantity of olive oil demanded (gallon)(B)	Change in Quantity(C)	Total Revenue($)	Change in Total Revenue(D)	Marginal Revenue
100	1,000	-	100,000	-	-
90	1,500	500	135,000	35,000	70
80	2,000	500	160,000	25,000	50
70	2,500	500	175,000	15,000	30
60	3,000	500	180,000	5,000	10
50	3,500	500	175,000	-5,000	-10
40	4,000	500	160,000	-15,000	-30
30	4,500	500	135,000	-25,000	-50
20	5,000	500	100,000	-35,000	-70
10	5,500	500	55,000	-45,000	-90

• As the cartel acts like a monopolist, it will maximize profits at a point where the marginal revenue is equal to or more than the marginal cost, which is $40 per gallon.

• For all gallons up to 2,000 gallons, the marginal revenue is greater than the marginal cost.

• Therefore, the cartel will produce 2,000 gallons at a per gallon price.

• As there are two families sharing the market equally, therefore each family will have a revenue of

• The cost of producing 1000 gallons is

Conclusion:

Thus, each family makes a profit of $40,000

b. Effect on the price of olive oil and the profit of each family.

• If the Sopranos family sells 500 more gallons of oil after breaking the cartel agreement, then the total quantity of oil will increase to 2,500 from 2,000. As a result, the price of olive oil will fall to $70 from $80 per gallon.

• The Sopranos family has earned a revenue of $105,000 and cost of $60,000

• Similarly, Contraltos have earned a revenue of $70,000 and cost of $40,000

• Profit for Sopranos family will be calculated by subtracting the total cost from the total revenue, which is $45,000 and profit for Contraltos family will be $30,000

Conclusion:

Thus, the profit for Sopranos family is $45,000 and profit for Contraltos family is $30,000.

c. Profit earned by each family.

• If the Contraltos also break the cartel agreement and sell 500 more gallons of oil then this will increase to 3,000 from 2,000 gallons.

• Therefore, the price of an olive oil falls to $60 from $80 per gallon.

Conclusion:

Thus, each family has earned a revenue of $90,000 and cost of $60,000 and hence, the profit is $30,000.