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Main content
Current time:0:00Total duration:11:19
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PRD‑3 (EU)
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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 do ah Polly 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 this is 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 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 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 one way to think about it pick and pick an arbitrary and arbitrary marginal cost so for one firm what can they produce at or what quantity will they be at that marginal cost well there'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 at that 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 that the exact same cost structure could produce two 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 farms and the average that that will also be true for the average total cost if if at this price right 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 provide twice the quantity of that average total qua cause 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 markets average total cost curve is going to look something like this it's going to be twice as fat the exact same logic it's going to look something something like that so that is the average total cost curve for 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 the equilibrium per hour let what of what what the right price should be if they were able to coordinate if they were to able be able to coordinate together if they were essentially combined 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 market demand demand curve so if both of these firms operated together if they and I have often 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 we're 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 it would look something like that so that is the this right over here is the market this is the market marginal revenue 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 will 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 the 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 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 we're behaving 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 is right this this height is their economic profit per unit and if we if we multiply that times the total number of units you would get you would get their total economic profit if they coordinate perfectly essentially behaving essentially behaving like a monopoly and let's just say for argument that this height right over here let's say that that is ten and let's say that this quantity this quantity that they would 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 total economic economic profit if they coordinate if they coordinate is 500 if they coordinate and so they see this and they say look why don't we agree to each produce exactly how of this and we would we would split the economic profit and to see that let's just say one firm says okay 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 they're going to and they're their costs are right here now we're going to each individual farm and that makes sense because this cost is just twice as far away as this cost and that 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 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 250 250 per firm 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 one firm in particular so the other firm holds at two at 25 units but the other firm says hey I like this price I'm already making economic profit let me produce ten more units so the other firm says I'm not going to produce 25 I am going to produce I am going to produce 35 units and if that guy produces 35 units and the other firm the other the other firm in the market the other dwop a list I guess we could say it continues to produce at 25 then the total market production is now going to be 60 the total market production is now going to be 60 now what is the total economic profit so we can go 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 the new economic profit is this area in this bluish purplish color that I just drew and we 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 high this height right over here is eight and it's going to be eight eight eight dollars of economic profit per unit times sixty 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 sixty units for the whole market times eight dollars of economic profit per unit you're going to have total economic profit total economic profit profit of four hundred and eighty your total economic profit went down and that makes sense because now is 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 all of this is essentially you're creating economic loss because each of these incremental units as a market you're creating the cost is higher than the revenue or and you have an economic loss and so that's why your total economic profit as a market went down from five hundred to four eighty but how much is this character how much is this character going to be making the one that decided to cheat well he now has 35 units he's producing thirty five units and he's getting an economic profit of eight dollars per unit so he gets this entire area right over here so let's multiply let's multiply thirty-five times eight I'll do it right over here thirty-five times eight five times eight is forty three times 8 is 24 plus four is 280 so now the cheating firm the cheating firm cheat has 280 dollars 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 we'll have the rest non the non-cheater is going to have the non-cheater is going to have the balance of the economic profit and the total economic profit was 480 the cheaters getting 280 the non-cheater is only going to get two hundred 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 and it really hurt the non cheat right over there