microeconomics book solution 15

3 the market for olive oil in new york city is

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3. The market for olive oil in New York City is controlled by two families, the Sopranos and the Contraltos. Both families will ruthlessly eliminate any other family that attempts to enter the New York City olive oil market. The marginal cost of producing olive oil is constant and equal to $40 per gallon. There is no fixed cost. The accom- panying table gives the market demand schedule for olive oil. a. Suppose the Sopranos and the Contraltos form a cartel. For each of the quantities given in the table, calculate the total revenue for their cartel and the marginal rev- enue for each additional gallon. How many gallons of olive oil would the cartel sell in total and at what price? The two families share the market equally (each produces half of the total output of the cartel). How much profit does each family make? Price of olive oil Quantity of olive oil (per gallon) demanded (gallons) $100 1,000 90 1,500 80 2,000 70 2,500 60 3,000 50 3,500 40 4,000 30 4,500 20 5,000 10 5,500 S-210 C H A P T E R 1 5 O L I G O P O LY S209-S220_Krugman2e_PS_Ch15.qxp 9/16/08 9:23 PM Page S-210
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Solution b. Uncle Junior, the head of the Soprano family, breaks the agreement and sells 500 more gallons of olive oil than under the cartel agreement. Assuming the Contraltos maintain the agreement, how does this affect the price for olive oil and the profits earned by each family? c. Anthony Contralto, the head of the Contralto family, decides to punish Uncle Junior by increasing his sales by 500 gallons as well. How much profit does each family earn now? 3. a. The accompanying table shows the total revenue and the marginal revenue for the cartel. Since a cartel acts like a monopolist, it will maximize profits by producing up to the point where marginal cost equals marginal revenue. For all gallons up to 2,000 gallons, marginal revenue is greater than marginal cost. Producing any more would mean that marginal revenue is less than marginal cost. So the cartel will produce 2,000 gallons and sell them at $80 each. Since the two families share the market equally, each family has revenue of 1,000 × $80 = $80,000. The mar- ginal cost per gallon is constant at $40, so the total cost (remember there is no fixed cost!) of producing 1,000 gallons is $40,000. So each family makes a profit of $80,000 $40,000 = $40,000. b. Now the Sopranos sell 1,500 gallons and the Contraltos sell 1,000 gallons, for a total output of 2,500 gallons. So the price falls to $70 per gallon. The Sopranos have revenue of 1,500 × $70 = $105,000 and cost of 1,500 × $40 = $60,000. So their profit is $105,000 $60,000 = $45,000. The Contraltos have revenue of 1,000 × $70 = $70,000 and cost of 1,000 × $40 = $40,000. So their profit is $70,000 $40,000 = $30,000. Price of olive oil Quantity of olive oil (per gallon) demanded (gallons) Total revenue Marginal revenue $100 1,000 $100,000 $70 90 1,500 135,000 50 80 2,000 160,000 30 70 2,500 175,000 10 60 3,000 180,000 10 50 3,500 175,000 30 40 4,000 160,000 50 30 4,500 135,000 70 20 5,000 100,000 90 10 5,500 55,000 C H A P T E R 1 5 O L I G O P O LY S-211 S209-S220_Krugman2e_PS_Ch15.qxp 9/16/08 9:23 PM Page S-211
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c. If both the Contraltos and the Sopranos sell 1,500 gallons each, the total output in this duopoly is 3,000 gallons, and the price falls to $60 per gallon. Each family has revenue of 1,500 × $60 = $90,000 and cost of 1,500 × $40 = $60,000. So each family’s profit is $30,000.
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