[MUSIC] Market forces, the forces of supply and demand, lead us to an equilibrium, where quantity supplied is equal to quantity demanded. That's the power of markets, to converge to this equilibrium. But there's a result that's really fascinating. And that is that this equilibrium also maximizes total surplus, it makes the pie as big as possible. I'm going to go ahead and prove this, and I'm going to do a proof by negation. I will start with a quantity that's bigger than the equilibrium quantity. And I'll prove to you that that reduces total sublease. Then I will choose a quantity that's less than the equilibrium quantity and I'll prove to you that, that too, reduces total surplus. And as a result we will conclude that the market equilibrium is the best of all possible worlds. Let's start, so suppose we're talking about the market for bread, and suppose that in equilibrium, where supply is equal to demand, the price is equal to $4. So that this quantity here is the equilibrium quantity at a price of 4. But what happens if we produce more loaves of bread than this equilibrium quantity? We'd be moving in this direction, so we'd be somewhere out here. Let's call this Q1. I want to prove to you that Q1 is not a loaf of bread that we want to produce. But it's very easy to see why. The demand curve reflects the marginal benefit of this loaf of bread. It tells us how much consumers value this loaf of bread. And we can see from the fact that demand is downward sloping that they value it at less than the equilibrium price. If the equilibrium price is 4 the marginal benefit of this loaf of bread is something less than 4 for the sake of this example, let's say it's $2. So that is the marginal benefit of this loaf of bread. But how much did this loaf of bread cost to make? Well, we can read that off of the supply curve, because the supply reflects the marginal cost of making this loaf of bread. So this last loaf of bread, this Q1, had a marginal cost up here. And we can see that this is something greater than $4. Maybe this is a marginal cost of 5. In other words, to make this loaf of bread, we spent the extra cost of making this loaf of bread was $5, and the person who consumed it got a benefit of $2. In other words, as a society, what we did here is we took $5 and we converted them to $2. We took $5 bills, scrambled them up, and out came $2. Obviously, as a society, this is not a very efficient thing to do. If I asked you, how many of you are willing to give me $5, and I will automatically immediately with no risk give you $2 back. I don't think a lot of people would agree to that trade, and yet that is the trade that we're asking society to do at this quantity. We're asking society to spend more money than society is getting back. And that's the case for any quantity that's bigger than the equilibrium quantity. For any quantity bigger than the equilibrium quantity, the marginal cost is greater than the marginal benefit. So, any quantity to the right of Q* is a quantity that we do not want to produce.