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.

nice

It's more likely that when one firm cheats, the other will as well; so each firm will face a highly inelastic demand curve below the original cooperative price and quantity of $10 and 25 units each. If the competitor matches a price decrease, neither firm will gain much market share and total revenues and profits will decrease for both firms. The incentive, therefore, is to cooperate and maintain the original price. This is what the kinked demand curve model illustrates.

FUCK THE CORPORATIONS

Sounds like Coke vs. Pepsi

LOL.. I though he meant the Mexican Cartel

@Superfresh602 Fruity Pebbles?

seems like it would apply to quality as well in some form

I believe there are some errors.

In the case of non-equal share of the market (one party is cheating), average total cost is not just 2 times fatter (for example one produces 0 as an extreme case).

Also for cheating scenario, average total profit of 8$/unit is for 60 units total, and company can get 8$/unit if it produce (lets say) 30 units. The cheating party is producing 35 units, ([email protected] < [email protected]), thus getting more than 8$/unit, while non-cheating is getting less then 8$/unit.

However, when a firm changes their quantity to 35, does the price change instantaneously? Because if not, one could argue that for a short period of time they'd still be selling it for 10$ and so one firm would still be doing 250$ and the other would be doing 300$. Also, do the marginal cost and the average total cost curves change over time? If you can predict those changes, won't it affect your decision?

Thank you so much!! Totally make sense now

Thank you for making this video!!

ths helpful when it come in study

Once you understand this though doesn't it just seem…obvious?

Thanks…Really helped me a lot