Why parties to cartels cheat Why duopolists would benefit to form a cartel and why it makes sense for them to cheat
Why parties to cartels cheat
- 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 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 - they're identical companies
- and they both have a marginal cost curve that looks something like that.
- So they both have a marginal cost curve, an individual marginal cost curve that looks like that,
- and they both have an average total cost curve that looks something like this.
- So they both have an average total cost curve that looks something like that,
- 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 the 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 had 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 as 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 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 gonna have is an average total cost curve that is twice as fat
- as the average total cost curve for one firm, if you're talking 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 to - well assume that this is a line.
- Well, that's pretty good.
- So this is the market demand curve.
- So if both of these firms operated together -
- and oh, if 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 it would 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 keep wanting to produce because marginal revenue is higher than marginal quantity -
- or 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.
- The 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.
- 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.
- Their total economic profit - if they coordinate - is 500.
- 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 to talk about 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, 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, 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.
- 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 blueish, 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, if they cheat -
- 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 - the cost is higher than the revenue and you have an economic loss,
- and 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, that's 280.
- So now the cheating firm 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 him,
- 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 is 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.
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