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Why parties to cartels cheat

In this video, we explore a conflict that duopolists (and other oligopolies) face: there is a tension between cooperating and forming a cartel or cheating on that cartel once it is formed.  Created by Sal Khan.

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  • mr pants teal style avatar for user jyd.chang
    How does OPEC maintain stability if there's an incentive to cheat?
    (26 votes)
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    • male robot hal style avatar for user Brandon Sanders
      In the past the price has remained the same because Saudi Arabia has reduces their output of oil to keep the price artificially high. Saudi Arabia has the largest reserves of oil still in the ground, so they have a higher incentive to keep the price high. The incentive is that in the future, when these other countries start to run out of oil, Saudi Arabia will still have untapped oil that can be sold at an artificially high price.

      I hope that makes sense.
      (59 votes)
  • leaf green style avatar for user Jon Dough
    Wouldn't the honest firm figure out the cheating firm is cheating if the product started being sold at $8.00 instead of $10.00? Also, why would the honest firms marginal cost go up if the honest firm is not cheating? If they're sharing MC you'd think they'd share MR. I keep getting stuck on if the cheating firm's MC is greater then their MR, they'd have less of a profit even though they sold more.
    (13 votes)
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    • spunky sam blue style avatar for user Enrique Penson
      1st Question: Yes, it would eventually realize it´s being conned. It´s explained in the next video in more detail.
      2nd Question: The "honest´s" firm marginal cost would not go up, It´s the "market´s" that would do so.
      3rd Question: MR does not have to be greater than MC for the firm to be making profits. The difference of these values represents the profit that would result from producing an additional unit. In this example there is a "global" loss of profit by producing more units; however, the cheating firm is forcing (by cheating) the "honest" firm to bear the complete weight of that loss.
      (16 votes)
  • blobby green style avatar for user Wayne Turner
    Doesn't this only hold true if the cartel parties are only interested in their economic interests above all else? i.e., if a cartel forms as a means to exact revenge, then the desire for all the members to have revenge on the outside parties would be stronger their their collective economic interests, therefore there would be less incentive to cheat. If a cartel forms as a means of social change, then the members' desire to bring about that social change may be stronger than their individual desires to make more money. My point being, cartels may form for many reasons but economics may not always be the main reason so cheating can be mitigated by stronger incentives than financial gain.
    (6 votes)
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  • leaf green style avatar for user adam keller
    Wouldn't the equivalent of both firms cheating essentially be "legal", or at least result in a competitive market? What happens to each firm's MR if both cheat?
    (4 votes)
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  • blobby green style avatar for user Kelly Kuo
    Why do the cheating firm and non-cheating firm have the same average total cost of $8? I would expect that if the cheating firm produces 35 units and the non-cheating firm 25, they would be at different points along their (identical) ATC curve and hence have a different average total cost. (though the price they get per unit of good will be the same)
    (6 votes)
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  • piceratops seedling style avatar for user Paul Christian
    This is a wonderful lecture, but I'm confused by one of the pre-conditions: Why would the marginal production cost increase with the number of units created. Wouldn't economies of scale drive per unit cost the opposite direction?
    (3 votes)
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    • mr pants teal style avatar for user Wrath Of Academy
      In reality marginal cost "curves" are not curves at all. They are usually jagged and sometimes discontinuous functions. They may go down over some sections (and usually do), but ultimately they must go up at the end. Eventually at large enough scales you will being to bid up the cost of factors of production such that they increase your cost per unit.
      (3 votes)
  • leaf green style avatar for user enilopene
    The video is a very clear explanation, thanks. But here's what I don't get: parties to cartels have strong incentives to cheat, but in reality, cartels or duopolies I've come across seem to never cheat? Also, this explanation assumes the price is based on produced units, but don't cartels often collude a fixed price and it's up to each firm to coordinate production costs and control the output flow so that they maintain high profit margin?
    (1 vote)
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    • blobby green style avatar for user Michael O'Donnell
      The short answer to your question about cheating is that cartels, etc. have an incentive to cheat in a non-repeated game but that incentive may be reduced in a repeated game. In other words, in real life most cartel members have to deal with each other in the future, and not just in one period.

      It gets somewhat complicated mathematically, but intuitively, in a repeated game, the colluding firms will have to coordinate in the first period as well as future periods. Every firm must have as its strategy set something like: "if a firm cheats in period 1, I will produce the competitive quantity (as opposed to the smaller cartel quantity which would give each firm a larger profit) in every period thereafter." So the cheating firm will get relatively large profits in period 1 (from cheating) but relatively small profits in each period thereafter (because every other firm will start producing the larger competitive quantity).

      It is important to note, that the other firms must be willing to utilize the punishment strategy - in other words, the threat of producing the relatively larger competitive quantity must be credible. The credible threat will keep the other firms from cheating provided the stream of future profits is greater for the firm when it doesn't cheat compared to the stream of future profits when cheating.
      (7 votes)
  • blobby green style avatar for user Anders Søgård
    Is this what xbox and playstation are doing? They essentially have a duopoly when it comes to consoles, are they therefore on purpose causing stock shortages to manipulate pricing and earnings?

    Same thing might be said about Nvidia and Amd when it comes to stock shortages of their new graphics card?
    (3 votes)
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  • aqualine ultimate style avatar for user QUIDES
    Is there any real world example of such a case happening?
    (2 votes)
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  • female robot grace style avatar for user 🅗🅐🅝🅝🅐🅗 😜
    Sneaky, which reminds me of Amazon, because I believe they try to intimidate small businesses and all others around them to force them to cooperate and sell their products through them.
    Not cool. >:(
    They literally made a warehouse and never used it and never sold it, a total waste of money and land.
    A big bruh!
    (1 vote)
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Video transcript

What I want to do in this video is analyze why it makes sense for two companies that make up a duopoly to coordinate. To get into an agreement, which may or may not be legal-- probably would be illegal-- and restrict quantity. But also think about why there's a strong incentive for either or both of the parties to cheat their agreement and produce more quantity than they agreed to produce. So let's say that both of our players in our duopoly-- and this would actually apply to an oligopoly generally, but the analysis would be a little bit more difficult if we had more than two players-- but let's say each player has an identical-- they're identical companies. And they both have a marginal cost curve that looks something like that. So they both have an individual marginal cost curve that looks like that. And they both have an average total cost curve that looks something like this. And they are identical. So I'll just draw it once. This is the marginal cost and average total cost for both firms. Now let's think about what it would look like for the market. Well, one way to think about it-- pick an arbitrary marginal cost. So for one firm, what can they produce, or what quantity will they be at that marginal cost? Well, they'll be at this quantity for that marginal cost. But if you have two firms that are just like that, they could have twice as much quantity to be at that point in marginal cost. So two firms will be over there. And if you picked this marginal cost, one firm would produce that quantity to be right at that marginal cost, for that next incremental good. But two firms could produce two, especially if they have the exact same cost structure. So what you're going to have is you're essentially adding this curve to itself in the horizontal direction. So if you look at the marginal cost curve for both firms together, you're essentially going to get a curve that is twice is fat as the marginal cost curve for one firm. So it will look something like this. And I'll do it in yellow. So it will look something like that. So that is the marginal cost for the market, where the market in this example is both of these firms. And that will also be true for the average total cost. If at this price-- or actually, I should say, if the average total cost is up here for one firm-- that means that they are producing this quantity. But two firms together could produce twice the quantity of that average total cost. So two firms would produce twice. And so what you're going to have is an average total cost curve that is twice as fat as the average total cost curve for one firm, if you talk about the market. So the market's average total cost curve is going to look something like this. It's going to be twice as fat. It's the exact same logic. It's going to look something like that. So that is the average total cost curve for the market. So, so far, the convention that I've ended up using is orange for an individual firm, and then this dotted yellow line for the market as a whole. Now let's think about what a good equilibrium-- or what the right price should be if they were able to coordinate together. If they were to essentially combine their firms and almost behave like a monopoly. And to think about that, we're going to have to draw a demand curve. So let me draw the market demand curve. Let's say the market demand curve looks something like that. It's really big, so it's hard for me. And we'll assume that this is a line. So it's not-- well, that's pretty good. So this is the market demand curve. So if both of these firms operated together, if they-- I drew the market demand curve. I also want to draw the market marginal revenue curve. Now remember, we're going to assume that both of these firms are acting together. If they perfectly coordinate, they can join their capacities and act essentially like a monopoly. So if they did act like a monopoly, their marginal revenue curve would be twice the slope of this market demand curve. So it would hit the horizontal axis right over there. And so it would look something like this. So this right over here is the market marginal revenue curve. So if they were to behave like a monopoly, you could view this dotted line as their marginal cost curve. This would be their average total cost. And now this is their marginal revenue. If they were to behave as a monopoly, what would be the optimal quantity? Well, it would be right there, right where marginal revenue is equal to marginal cost. Before that, they would keep wanting to produce because marginal revenue is higher than marginal cost. And then after that, they don't want to produce, because marginal cost is higher than marginal revenue, and they're going to take economic losses on each of those incremental units. And so this is the quantity that they would produce. And the price they would get for that-- they just have to go to the market demand curve-- they would get this price right over here. Let's say they would get that price right over there. And the actual-- their average total cost per unit-- once again, we have to go to the market here. It's this dotted line right over here. That is their average total cost per unit. So their average economic profit per unit is going to be their revenue per unit, minus their average total cost per unit. So this height is their economic profit per unit. And if we multiply that times the total number of units, you would get their total economic profit if they coordinate perfectly, essentially behaving like a monopoly. And let's just say for argument that this height right over here-- let's say that that is 10. And let's say that this quantity that they would want to produce as a monopolist is 50. So what is the total economic profit here? Well, their total economic profit is 500. Total economic profit if they coordinate is 500. And so they see this, and they say, look, why don't we agree to each produce exactly half of this, and we would split the economic profit. And to see that, let's just say one firm says, OK. They both decide that they're going to produce 25. They're going to get this price for it up here, which was the market price. They're going to get that price for it, and their costs are right here. Now we're going on each individual firm. And that makes sense, because this cost is just twice as far away as this cost. And the dotted line yellow average total cost for the market is just a fatter version, twice as fat as the orange line. And so each firm will make this much economic profit per unit, times 25 units. And so each firm would make this orange area in terms of economic profit, or half of the entire 500, or 250 per firm. Now let's think about why there is an incentive for one or both of the firms to cheat. Let's say one firm in particular-- so the other firm holds at 25 units. But the other firm says, hey, I like this price. I'm already making economic profit. Let me produce 10 more units. So the other firm says, I'm not going to produce 25. I'm going to produce 35 units. And if that guy produces 35 units, and the other firm in the market-- the other duopolist, I guess we could say it-- continues to produce at 25, then the total market production is now going to be 60. Now what is the total economic profit? So we can go up the demand curve right over there. That's the new price. That right over there is the new price. The cost per unit is this right over here, and then the number of units that they're producing is 60. So the new economic profit is this area, in this bluish purplish color that I just drew. And even visually this is true-- looks like the demand curve and the average total cost curve have gotten closer together. So let's say that this height right over here is 8. And it's going to be $8 of economic profit per unit, times 60 units. So if they cheat-- let's talk about the cheating circumstance. This was coordinate, now let's think about if they cheat. Now we have 60 units for the whole market times $8 of economic profit per unit. You're going to have total economic profit of 480. Your total economic profit went down. And that makes sense, because now as a market, you're producing beyond the point where marginal revenue is equal to marginal cost. Now marginal cost as a market is higher than marginal revenue. And so all of this is essentially, you're creating economic loss because each of these incremental units as a market-- The cost is higher than the revenue, and you have an economic loss. And so that's why your total economic profit as a market went down from 500 to 480. But how much is this character going to be making? The one that decided to cheat? Well, he now has 35 units. He's producing 35 units, and he's getting an economic profit of $8 per unit. So he gets this entire area right over here. So let's multiply 35 times 8. I'll do it right over here. 35 times 8. 5 times 8 is 40, 3 times 8 is 24, plus 4 is 280. So now the cheating firm, Cheat, has $280 of economic profit in this period. And then the honest firm, or the fair firm-- what they're both doing might be illegal by even attempting to coordinate-- the non-cheater, I guess I could call them-- the non-cheater will have the rest. The non-cheater is going to have the balance of the economic profit. And the total economic profit was 480. The cheater's getting 280. The non-cheater is only going to get 200. So the cheater definitely benefited by increasing quantity past that optimal one. He went from 250 to 280. So it made sense for him. It reduced the total economic profit, and it really hurt the non-cheat right over there.