1. Let’s start off by working out a few examples to illustrate the lure of the cartel. To keep it simple on the supply side, we’ll assume that fixed costs are zero so marginal cost equals average cost. We’ll compare the competitive outcome (P = MC) to what you’d get if the firms all agreed to act “as if” they were a monopoly. In all cases, we’ll use terms from the following diagram:

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2. Take a look at the reasons why cartels collapse presented in this chapter. For each of the following pairs, choose the case where the cartel is more likely to stick together.

3. The prisoner’s dilemma game is one of the most important models in all of social science: Most games of trust can be thought of as some kind of prisoner’s dilemma. Here’s the classic game: Two men rob a bank and are quickly arrested. The police do not have an airtight case; they have just enough evidence to put each man in prison for one year, a slap on the wrist for a serious crime.

If the police had more evidence, they could put the men away for longer. To get more evidence, they put the men in separate interrogation rooms and offer each man the same deal: If you testify against your accomplice, we will drop all the charges against you (and convict the other guy of the full penalty of 10 years of prison time). Of course, if both prisoners take the deal, the police will have enough evidence to put both prisoners away and they will each get 6 years. And, as noted, if neither testifies, both will get just 1 year of prison time. What’s the best thing for each man to do?

In each cell in the following table, the first number is the number of years Butch will spend in prison, and the second is the number that Sundance will spend in prison given the strategies chosen by Butch and Sundance. If years in prison are minuses, then we can write up the problem like this:

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4. Your professor probably grades on a curve, implicitly if not explicitly. This means that you and your classmates could each agree to study half as much, and you would all earn the same grade you would have earned without the agreement. What do you think would happen if you tried to enact this agreement? Why? Which model in this chapter is most similar to this conspiracy?

5. In many college towns, rumors abound that the gas stations in town collude to keep prices high. If this were true, where would you expect this conspiracy against the public to work best? Why?

6. Suppose you have a suit that needs altering, and you take it to three different tailors in the same mall to get an estimate of the cost of the alterations. All three tailors give you the exact same estimate of $25. What are two different explanations for the similarity of the price quotes? (Hint: One is consistent with competition and one is not.)

1. Usually, we think of cheating as a bad thing. But in this chapter, cheating turns out to be a very good thing in some important cases.

2. Firms in a cartel each have an incentive individually to lower the prices they charge.

3. In the late fifteenth century, Europe consumed about 2 million pounds of pepper per year. At this time, Venice (ruled by a small, tightly knit group of merchants) was the major player in the pepper trade. But after Portuguese explorer Vasco da Gama blazed a path around Africa into the Indian Ocean in 1498, Venice found itself competing with Portugal’s trade route. By the mid-sixteenth century, Europeans consumed 6 to 7 million pounds per year, much of it through Lisbon. After da Gama’s success, the price of pepper fell.

4. In 1890, Senator Sherman (of the Sherman Antitrust Act mentioned earlier) pushed through the legislation that bears his name, which gave the government significant power to “bust up” cartels, presumably in order to increase output. More than a century later, economist Thomas J. DiLorenzo examined the industries commonly accused of being cartels and found those industries increased output by an average of 175% from 1880 to 1890—seven times the growth rate of the economy at the time.

Suppose the industries were conspiring. Indeed, let’s suppose that these cartels grew ever stronger in the decade before the Sherman Act became law. If that were true, would we expect output in these industries to grow by so much? In other words, is DiLorenzo’s evidence consistent with the standard story of the Sherman Antitrust Act?

5. In 2005, economist Thomas Schelling won the Nobel Prize in economics, in part for his development of the concept of the “focal point” in game theory. Focal points are a way to solve a coordination game. If two people both benefit by choosing the same option but cannot communicate, they will choose the most obvious option, called the focal point. Of course, what’s obvious will vary from culture to culture: whether to wear business attire or just shorts and a T-shirt, whether to use Apple or Microsoft products, whether to arrive at meetings on time or late. In all these cases, having a group agree on one focal point is more important than which particular focal point you all agree on. Therefore, people will look for cultural clues so that they can find the focal point. (Note: Schelling wrote two highly readable books that won him the Nobel Prize: Micromotives and Macrobehavior and The Strategy of Conflict.)

6. Suppose the five landscapers in your neighborhood form a cartel and decide to restrict output to 16 lawns each per week (for a total of 80 lawns in the entire market) in order to keep prices high. The weekly demand curve for lawn-mowing services is shown in the following chart. Assume that the marginal cost of mowing a lawn is a constant $10 per lawn.

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7. Looking for dominant strategies is a great way to find an equilibrium in many games. However, there are also a lot of games where this won’t work because not all players have dominant strategies. If one player has a dominant strategy but the other doesn’t, game theorists remove the first player’s dominated strategies (the strategies that are always worse than some other strategy) and then continue to work toward solving the game with what’s left. Let’s take a look at an example of this. Consider the following payoff table, where the outcomes are written in the form {A’s payoff, B’s payoff}. Each player has four choices, which might make this game seem intimidating, but it’s not.

Start off by trying to figure out whether any player has a strategy that is never best, and then eliminate it. The first one is done for you; no matter what move A makes, B’s best response is never to play Red. Since B will never play Red, we don’t even have to consider that as part of the game. Next, figure out if there’s a move A will never make, then B, and so on. What is the equilibrium?

1. The French economist Antoine Cournot developed an interesting model of competition in an oligopoly that now bears his name. In a Cournot oligopoly, all of the firms know that the total output from all firms will determine the price (based on the downward-sloping market demand curve), but they make independent and simultaneous decisions about how much output to produce. Cournot developed this model after observing how a spring water duopoly (two firms) behaved. So let’s look at a duopoly example.

For each firm to decide how much to produce, it must make a guess about how much the other firm is going to produce. Also, the firms basically assume that once the other firm has decided how much to produce, it can’t really change its decision.

Here’s an example. Suppose the market demand curve for gallons of fresh spring water looks like the one in the next table and, to keep things simple, the marginal cost of spring water is zero. If Firm X believes that Firm Y is going to produce 100 gallons of spring water, for example, then Firm X knows that if it produces 0 gallons, the price will be $2.75; if it produces 100 gallons, the price will be $2.50, and so on. Basically, Firm X will face its own demand curve where all of the quantities are lower by 100.

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Based on this demand schedule, calculate the demand schedule that Firm X would face if it suspected Firm Y was going to produce 0, 200, 400, or 600 gallons of spring water. Then, figure out the profit-maximizing amount of spring water for Firm X to produce in response. Fill in the table.

What you have just constructed is what economists would call Firm X’s reaction function. Even though Firm X thought about the different choices Firm Y could make, Firm Y is not actually going to choose just any random level of output. In fact, Firm Y has its own reaction function, where it considers how best to respond to what it thinks Firm X is doing. Because both firms have the same zero marginal cost, the two reaction functions are symmetrical. (Thus, Firm Y’s reaction function looks the same, only with “X” and “Y” switched.)

Graph the two reaction functions. Do you notice any points that stand out? Describe why this point represents an equilibrium for both firms.

2. The following diagram shows the monthly demand for hot dogs in a large city. The marginal cost (and average cost) is a constant $2 per hot dog.