Alright, so now let's take what we've learned about game theory and apply it to an oligopoly situation. Right, so what we've learned so far, we've seen that in an oligopoly, a firm's profit will be dependent on the decisions, on the output decisions of their competitors, right? They're going to be dependent on each other, and this is called interdependence. The firms are said to be interdependent because they depend on each other to make their best choices. They can't make their best choice without considering what the other people are going to do. Okay, so let's dive into an example here. We've got Jack and Jill who own the only wells in a small town, right? So Jack and Jill are the only producers. We've got two producers, so this is a duopoly, a form of an oligopoly. Okay? So in our duopoly, Jack and Jill, they have no cost of pumping water, right? No cost. We're just keeping it simple, so their marginal cost is equal to 0, and average total cost is equal to 0. We're just not going to deal with cost here because it's just going to complicate anything in our discussion. Okay, so we've got a table here with our demand schedule and notice we've got some quantities and prices and just like we would expect, as the quantity increases, the price decreases, right? Or as the price decreases, quantity increases. This is what we expect with a demand curve, right? We've got the law of demand, a downward-sloping demand curve, and then we have these quantities and prices and then a column for our revenue. And in this case, the revenue is going to be the same as profit because there are no costs. We're just leaving that out. So let's go ahead and figure this out. So, this total revenue, right, this is just our price times our quantity, right, so all we did was multiply across, so 0 times 120 was 0, 10 times 110, 120 times 100 was 2,000, right? We just multiplied it across our price times our quantity to get our total revenues. Okay, so I want to point out some key points here.

First, let's talk about the maximum revenue. Notice here when the quantity is 60, the price is 60, we have the maximum revenue of 3,600, right? And this is what a monopoly would produce right here. So, whether or not you studied monopolies, monopolies have significant market power, and they can produce wherever they're going to maximize their profit. They're the only producer in the market, so they're going to maximize their profit just like this, right? They would produce here 60 quantity at a price of 60 to maximize their profit. Compare that to perfect competition, right? Remember when we learn perfect competition, they reach efficiency. There are so many competitors in that market, right? There would be so many suppliers that they would keep driving the price down because there's still money to be made, so more competitors would join and drive it all the way to a situation where price equals marginal cost, right? That's a situation that occurs in perfect competition, so we would basically end up where there's no profit, right and we're supplying this maximum amount of 120 here. Perfect competition would reach some efficient quantity where our marginal benefit equals our marginal cost, perfect competition, right, down here.

Okay, and if you're confused, you see a price of 0, don't get hung up on that. That's because we have no cost in this situation. We're just saying that the condition of perfect competition is going to be a greater quantity. So, how are we going to find what's the best situation for an oligopoly? The first thing we have to consider is collusion, right? If Jack and Jill were able to work together, well they could essentially act as a monopoly. They could each produce half of the monopoly quantity. So that could be probably the ideal situation for them would be something where they're colluding. So let's start here in this left column where we have some collusion where they both say, "Let's produce 30 gallons to get the maximum profit in total." The total maximum profit will be highest, or the total profit will be highest.

So let's see what happens. If they're both producing 30 gallons, well the total quantity is going to be 30 that Jack produces, the 30 Jill produces, we're going to have 60 total gallons, right? So what's the price when there's 60 gallons on the market? 60 gallons on the market, a price of 60, right? That's what we have in our demand schedule, so the price equals 60. Knowing this, we can calculate their profit. We've got no costs, so their revenue will be their profit in this case. Let's go ahead and check that out. So Jack's profit is going to be the 30 units he sells times the $60 price. Well, that's going to give him 30 times 60 is 1800 in profit. Jack's profit is 1800. Jill also sells 30 units at a price of 60 and she also gets 1800.

Let's go underneath this table right here, let's do a column for, or a row for total profit. What's the total profit between the two of them? Well, that's the sum of the 1800 plus the 1800, that's gonna give us 3,600 in total profit, right? 3,600 total profit, and guess what? That's equal to our monopoly profit right here. That's what we expected. They took that monopoly profit and split it down the middle by each producing 30 gallons. But remember when we're colluding, there's that incentive to cheat. Jill can consider expanding her output. Knowing that Jack plans on cooperating, Jill can say, "Hey, if instead of producing 30, maybe I can make more money if I produce 40 gallons instead." So let's see what happens if Jill decides to cheat. This is going to be a situation where Jill cheats on their collusive agreement to each produce 30. So now let's see what happens. Jack produces 30. Jill produces 40. Well, that's going to be a total quantity of 30 from Jack, 40 from Jill, gets us to a total quantity of 70. So now the price is going to change. There's a higher quantity on the market, there's got to be a lower price to clear that and what do we see? When there's a quantity of 70, our price is 50 over here. So the price now is 50. Jill produced more than the collusive agreement and now it dropped the price down to 50.

So let's see what happens in this situation. Jack still produced 30 gallons, right? So Jack's profit is going to be the 30 gallons times this price of 50. He's no longer getting $60 per gallon, he's getting 50, and he's going to have 1500 in profit. 30 times 50 is 1500. What about Jill? Well, Jill produced 40, right? Her quantity is 40 that she sold at this $50 price, and guess what? Jill comes out with $2,000 in profit. Jill got more profit by cheating here, right? So this is that incentive to cheat we were talking about. By increasing her quantity, she took a little bit from Jack, and now she has a higher profit, but notice our total profit in the industry. The total profit is going to be the 1500 plus the 2,000, well total profit is now 3,500. The total profit decreased. There was a better situation for the producers in total when they colluded, and there was 3,600 in total profit. Notice at a quantity of 70, we've got a price of 50 and a profit of 3,500 just like we saw there, except now it's split between Jack and Jill, 1500, right?

So now what about this final situation? Jill thought about cheating. What if at the same time Jack had thought about cheating too? They both considered cheating. Alright, so now we're in this final column where both cheat, and they both. Well, we've got 40 plus 40 equals 80 in total quantity, right? What price do we have when 80 is the quantity on the market? Well, here's 80, a price of 40 when there's a quantity of 80. So we're going to have a price of 40. So let's check this out. What's going to happen to profit now? Let me get out of the way here, so we can fill in these boxes. We've got Jack's profit, right? Jack produced 40 units and he's selling them at a price of $40, and he's going to get $1600. 40 times 40 is 1600 and the same thing for Jill. 40 units at $40, and she's also going to get $1600. So what's the total profit in this case? Well, the total profit is 1600 plus $1,600. So notice that the total profit for the industry keeps decreasing, and in this case where they both cheat, we end up where both of them are worse off. If they had colluded, they would have both had 1800. If they both cheat, they're both down to 1600. What does this sound like to you? This is something we've gone over before. This sounds like a prisoner's dilemma. So let's pause here, and then in the next video, we'll fill out a payoff matrix using this information and see how the whole game theory relates to everything we just talked about. Alright, let's do that now.