I was thinking about modeling collusive arrangements. How do they pull these things often? We used as an example, OPEC, 1973. OPEC had been into existence for a decade, but they had not really exercised their quite significant economic strength up until the oil embargo of 1973. So we know that cartels have to figure out three tasks. The first is the cartel has to figure out what is the right market output? Then of course that also implies some price under the fix. Task number 2 is they need to come up with some quota rule. The quota rule basically tells each member how much they can actually produce. It tells each member what level of production is okay for that particular member. Each member has a different quota. But the sum of those quotas were such that if you summed up the quota of each of the N players in the industry, and that was their quota for each of those i firms, it would sum would be the amount of that fix. Now, we have one last problem we have to think about, and that's going to be task 3. We need three tasks. The first two are done, they were hard. But now, the third one, we're going to go back and think about what's really happening in this market. So I've drawn here the typical picture. In this picture, you can see that the competitive outcome was originally here, and price was at three dollars for years, and years, and years, and individual players produced about this amount. We're going to call that q_c, the competitive outcome. It had been that way for decades, three dollars a barrel. Now, the cartel gets together and they come to an agreement that, "What we really want to do, we want to price, we want to reduce output to this level." We'll call this Q star sub fix, and that's going to increase price to this level. We'll call this P star sub fix. In fact, when they put it in place, it raised the price of oil from our three dollars to $12 in a matter of a week, because the demand curve is actually even steeper than the one I drew here. The demand curve for energy is pretty steep. So you don't have to do too much reduction, and that price is going to go up by a lot. Now, this is the new new price. The problem is that in order for this arrangement to hold, it's incredibly important that everybody sticks to their quota. If they stick to their quota, then the market output will in fact stay here, and they'll continue to earn this nice price. But if in fact they don't stick to their quota, they say, "Well, I know that they told me I have to reduce my output by 10 percent or 15 percent or wherever, but I really wanted to produce more." You think about the incentives here. We go back to this picture. At this price, the firm says, "Hey, I'm currently being told by the group that I have to have a quota back here." That's my fixed output. At that output, my marginal cost is this, but each barrel of oil I'm selling is giving me this. That's what this says. This says that if the market would reduce its output, if we got together as a group and reduced our output from Q_c to Q_fix, price is going to climb all the way up to here. As long as we hold this low output, price is going to remain up here, and I'm going to be making a lot of money on extra barrel of oil. So let's think about this, suppose this is $12. I'm making $12 on every barrel of oil, and my marginal cost here looks like it might just be two dollars, because it used to be three, the price. So I'm basically making a $10 killing on each barrel of oil. That's great. But on the other hand, if I could just run out a few extra barrels, and so you have this problem where each firm has this great desire. You see this gap here? This gap goes by a very important name in economics, it's the incentive to cheat. The very nature of a cartel is that you are trying to manipulate a market and force everybody to produce less. Of course when everybody produces less, we know enough economics by now to know that whenever the produce is less, price is going to go up. When price goes up, everybody who's doing nothing, who's producing less, they're all producing their quota because that's the only way we can make market output go down. Because if we all take turns holding our own output down, they're going to see that there's a huge markup on the last barrel of oil. So we have what in the time of OPEC was called midnight oil shipments. So the question was, you're only supposed to be pumping out let's say 250,000 barrels of oil a day as your new [inaudible]. That's not hard. You've oils, you can just turn the spigot a little bit, and you reduce how much oil is coming out of your pipeline into the tankers to go to the rest of the countries in the world. Suppose you could just somehow squeak out, even though your quota was 250,000, suppose you could squeak out just maybe, let's go to 300,000. 50,000 barrels extra a day. Who's going to know that? At 50,000 barrels extra a day with a $10 per markup on each barrel, we're talking about a $0.5 million every day. Even after just a couple of weeks of this, that's pretty good. I've been making that. The problem is, this incentive to cheat is in every single member's mind. Because every single member who's taking their share, and remember some of them took a bigger share than others, every single member who's taking their share, they can see that they have this incentive. Because they're reducing their output, therefore their marginal cost is falling, but yet market price is screaming up because of the relative steep demand curve in the oil industry. So we're going to add now task number 3. This is the last one. Task number 3 is you have to construct a policing mechanism. You have to figure out a mechanism to make sure the members stick to their quota. Because if the members don't stick to their quota, then output is not going to go all the way back here, it's probably going to stop somewhere here, maybe here, or maybe just collapse completely, and we'll just go back to the way it was in the old days, three dollars a barrel. So the policing mechanism is extremely important. The incentive to cheat is in every firm's mind. Even firms who maybe didn't get a quota at all. Imagine somebody said to me, "Well, you know what? Because you really are such a team player and I know you're currently struggling, we're not even going to give you a quota. You just don't even have to cut back." They're still going to have an incentive to put more out there, because if the rest of them still put this much out, price is going to go up. If price goes up, even if you didn't change what would've been producing, you're going to want to produce more. So constructing the quota mechanism requires two parts. Part 1 is you have to detect cheaters, and then you have to deter cheaters. So detection issue and deterrence issues are two required components of a policing mechanism. Detection, it's pretty straight forward. You have to have some technique, some methodology to actually know how many barrels of oil each of the members are really shipping out. There has to be some way that you can monitor their actual shipping levels. If you can't monitor their shipping levels, then they're just going to go ahead and cheat. If the person who's setting that is thinking, "Should I cheat or not? Well, nobody's going to catch me. There's no way. They don't know how many barrels of oil actually are on my tanker." Now, it turns out they figured out how to do detection. They figured out from satellites in the sky. Satellites in the sky can take pretty good level of detection. Even back in the early 1970s, they were strong enough that they could see how low the tanker was riding on the water, or how high the tanker. The more oil it's in there, the heavier the tanker is, but the water level, it's lower and lower in the water. Given that they all know exactly what the underlying characteristics of those oil tankers are, they can see that just as a simple computer model to show that that tanker must be carrying around 480,000 barrels for it to ride that low in the water, that's it. So they could track who was actually shipping out too many barrels a day, and they could go back and say, "Okay, we have caught you." Well, once you catch them, you have to come up with a deterrence mechanism. The original deterrence mechanism they came up with wasn't very good. The original deterrent mechanism was that they said that if any of you cheat, we're all just going to go back to our regular levels. Now, the problem is, that's what economists would say that's not a credible deterrence mechanism. Because what happened is, suppose you're a small player in the market, suppose you're one of those people who only puts out 250,000 barrels, and you decide that your quota is 250,000 barrels, and you say, "Well, I'm going to put out an extra 20,000 barrels." The Saudis find out about it because they have access to those defense satellites too, and they say, "Hey, you're cheating. You know what the rules are, if we catch you cheating, we're going to go back to what we were doing in the old days." The cheater would look at them and say, "Really? You're going to go from 7.5 million barrels back to 15 million barrels, and watch the oil price drop from 12 all the way back to three again?" So those types of deterrence mechanisms where you think you're going to try and you announce that if I catch you cheating, I'll just go back to the old days. Well, they're not very credible, because people didn't think the Saudis correctly. So the Saudis wouldn't want to kill the goose that lays the golden egg, and just return the giant free-flowing oil. So they had to come up with much more clever ones, and those are the subject of many different economic treatises. We're not going to go into them. But the point is you have to have a good program that will allow you to to detect cheaters, and you have to have a good program that you can get them. If they know they're going to get caught, they have to also believe that the penalty is going to hurt. You have to have some penalty function in there that's really going to hurt them, to keep them from wandering down that line and collapsing this whole problem. Because if you can't stop cheaters, this thing will end up going right back to the original point. Thanks.
