The market for olive oil in New York City is controlled by...

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 accompanying 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 revenue 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? 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 profit 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?

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 accompanying 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 revenue 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?
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 profit 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?

Key Concepts

Cartel Formation

A cartel is a group of firms that collude to reduce competition by agreeing on production quantities or prices to maximize their joint profits. Members of a cartel restrict output to raise prices above competitive levels, and then share the monopoly-like profits. In the context of the oligopoly market, the families coordinate production to maximize overall revenues while strategically splitting the market output and profits.

Total Revenue and Marginal Revenue

Total revenue is the total income a firm (or cartel) earns from selling a given quantity of goods at a certain price. Marginal revenue is the change in total revenue produced by selling one additional unit. Understanding these concepts is crucial for determining the optimal output level where additional sales still contribute positively to revenue without significantly lowering the market price due to the downward sloping demand curve.

Marginal Cost and Profit Maximization

Marginal cost represents the cost of producing one more unit of output. Profit maximization occurs when marginal revenue equals marginal cost (MR = MC). With a constant marginal cost, the decision on how much to produce is guided by equating this cost with the marginal revenue derived from selling additional units. This condition is a cornerstone of microeconomic theory relating to production and profit decisions.

Deviation from Cartel Agreement

If one member of a cartel deviates from the agreed production level, it may be able to capture a larger market share and temporarily increase its profit by selling additional units. However, such unilateral deviation typically leads to lower prices due to the increase in total market supply, and may force retaliatory actions by other cartel members. This breakdown of collusion often results in reduced profits for all parties in the long run.

Reaction Strategies in Oligopoly

In oligopolistic markets, firms must consider how their rivals will react to changes in output or pricing. Reaction strategies, such as punishment for deviatory behavior, are employed to maintain the collusive agreement. When one firm deviates, other firms may retaliate by expanding output, thereby lowering market prices to reduce the deviator’s profit. This strategic interplay emphasizes the importance of credible threats and cooperation in sustaining collusive arrangements.

Transcript

00:02 The sopranos and the contraltoes are two families that produce olive oil.

00:08 And in the left -hand two columns, we have the demand curve, the total demand for olive oil in gallons.

00:15 And our first job is to find total revenue and marginal revenue.

00:19 And so to get total revenue, we multiply our price times quantity.

00:24 So my first total revenue would be $100 per gallon times 1 ,000 gallons is $100 ,000.

00:30 My next total revenue would be $90 a gallon, and at that lower price, they can sell 1 ,500 gallons, so my total revenue will be $135 ,000.

00:44 All of the other total revenues are calculated in the same way.

00:49 My marginal revenue is the change in total revenue when we sell one more gallon.

00:54 So my first change in total revenue is from $100 ,000 to $135 ,000, so that's.

01:01 That's a change of $35 ,000, and that's not for one more gallon, but my output changed by 500.

01:10 So 35 ,000 divided by the change and output of 500 gives me the marginal revenue of 70.

01:18 And all of the other marginal revenues are calculated the same way.

01:23 If the two families form a cartel and act like a monopoly, how much would they produce? and what price would be charged.

01:34 So our rule of monopoly is produced as long as marginal revenue is greater than or equal to marginal costs.

01:41 So that would take us up to an output of 2 ,000 that would sell for $80.

01:48 And so the quantity that the sopranos would sell would be 1 ,000 gallons because they'd split the market equally.

01:56 Their profit would be the $80 price less since the marginal cost is a constant $40.

02:06 It's also the average cost.

02:09 And so their profit would end up being $40 ,000.

02:18 And the same would be true for the contraltoes...

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