We have been constructing measures of efficiency and we've measured the consumers' rent. Words that economists like to use is the rent that what consumers are getting above and beyond what they need to. We've measured producers' rent, what they're getting above and beyond what they need to. We call those consumer surplus; excessive value above what you actually had to pay to get that product and producer surplus; excess of price or revenue in excess of what you really would have needed given your cost structure to offer that unit. Now we need to combine these two and so to make this happen, we're going to introduce a new player to our lecture series. This person is called the benevolent dictator, okay? Now the benevolent dictator is just exactly what it sounds like. A dictator can do anything he or she wants, okay? The dictator can say "Here's the resource allocation I think which had happened and here's how many units are producing and here is who gets what." That's what dictators can do. But this dictator is a special one. This dictator is a benevolent dictator. So the benevolent dictator he's down out to push people around, the benevolent dictator wants to see society get the most efficient outcome. There's that word again, efficient. So let's think about this. We need to come up with a goal then. I want you to see what is it that drives a benevolent dictator. So we'll call this BD is just shorthand for the benevolent dictator and our benevolent dictator wants to maximize social gain. You say well what's that Larry? That sounds okay. The benevolent dictator wants to make society better. Well, I'm going to define social gain, which we'll call SG, is defined as the sum of gains to all parties. So right now we've only got two parties, consumers and producers, but we will pretty soon have the government enter in because the government might decide they are going to for example manipulate the market. So examples of the government decide that they're going to hold the price of milk up. By holding the price of milk up, they're giving more revenues to milk producers, but they're also using a lot of taxpayer's dollars to buy that milk and produce vast warehouses of government cheese for distribution based on some rules that who gets what in terms of passing out free cheese. So we're going to have to put that in when we bring the government back into the game, but right now we only have consumers and producers and so what we're going to say then is that social gain is equal to the sum of consumer surplus plus producer surplus. So social gain is the size of the pie. Now what do I mean by that? Well I want you to think about this, the transactions in a market whether it's stickers or jars of mayonnaise or whatever it is, consumers voluntarily hand our money to get something and they do that because they get something that's a greater value than the green sheets of paper. The green sheets of paper don't really have any value themselves, but they embody in your head, you know what you're missing out because you no longer have that green sheet of paper to give for something else. So consumers are handing over voluntarily green sheets of paper to get products that they value in excess of those green sheets of paper. So that's good for society. That net return to consumer surplus is good stuff for society and producers are doing the same thing. They're voluntarily selling you products for money that turns out that they would have more money than they actually have to have to do it because that supply curve shows us. When we did the producer surplus for any given unit of output, if the market price is here there could have been the marginal cost is down here, which is the supply curve is the sum of marginal cost, firms would have sold that same unit for a much lower price. But the market prices don't look this was what was on the market. We need a market clearing price and so producers and consumers together get some excess happiness because of the existence of a market, and we say that the pie that's generated. The size of the pie is this big. Now what's important for you to understand is that when we talk about resource allocation, we mean to talk about the way the market is clearing, however might not be a market, maybe it's a dictator, maybe it's the king. The way the market allocator, let's say that, has passed this out we're going to be able to measure how much benefit to consumers and how much benefit to firms, and if that pie is bigger, by definition is more efficient. Now it's important that you remember one thing. The benevolent dictator has no stake in the game. The benevolent dictator does not say "I value consumers better than producers." No. The benevolent dictator can't tell who gets what. The benevolent dictator only wants to make the size of the pie as large as possible. Now you might say "No. I don't like that Larry." I think we ought to wait consumers at 80 percent and producers at 20 percent. Okay, if we're going to divide it up that way. The benevolent dictator says "No. That's not efficient. I want the whole size of the pie to be great" and you say "Well, sometimes that means that a lot of the wrong people are getting it." Well that's a different issue. The benevolent dictator will tell you if he or she was to sit down with you right now and talk about this, the bigger the pie is, is unambiguously more efficient. If you don't like the distribution, you as a society can come back later with a very sharp knife and cut up the pie and push things over to different people, which is exactly what we do. Okay. We as a society want that pie to be as big as possible and then later we'll put policies in place where we take money away from wealthy people with a higher tax rate. We have what's known as a progressive income tax rate in this country. People who make more money, pay greater taxes, and we use some of those taxes to give vouchers to people with less income. We give him vouchers to send their kids to the different schools. We give them vouchers to be able to compete in housing markets. We give food stamps to people who don't have enough money because of the system for all reasons to get to have food. That is a transfer from other taxpayers to different taxpayers or non taxpayers depending on what their income level is. So the point from the benevolent dictator is get the pie as big as possible. That's unambiguously better and if you as society don't like the distribution later, go back and cut it up. Redistribute anything you want, but it's always better to have a pie of size 100 than a pie of size 99 because there's less to cut up and hand around. So what we're going to do now is we're going to think about growing the size of that pie and so I want you to think about this exercise. Again remember, the benevolent dictator doesn't care who gets what. The benevolent dictator just wants. Just wants this to be maximized. Well, let's draw a graph and see what that looks like. The first thing I'll do is to draw my axis system. Put price on the vertical axis and quantity on the horizontal axis. I'm going to draw a demand curve, it looks like this and a supply curve that looks like this. Bear with me while I repeat this point again. Some of you will always say, "Why do you know where those are, Larry?" I don't. I know the supply curve is upward sloping, and the demand curve is downward sloping. I've drawn that. You and the company you work for, if you work in a statistics part of that company, you can get the data to figure out what these look like. I'm just showing you the general shape of these. Now, given these general shapes, I'm going to pick an output level and let's just call this output level Alpha. Now at Alpha, it turns out, producers would have produced this for two dollars and consumers would play, there is somebody up here whose marginal willingness to pay is exactly here, let's say $10. So the consumers would pay, the marginal willingness to pay. I should put that one here because I like that phrase; marginal willingness to pay. There is a person standing exactly at this spot who says, "I would pay up to $10 for that." Right now, we don't know what the price is and we're not really interested in that. We're thinking about how the benevolent dictator would look at this. So the benevolent dictator says, "Okay, I want you to produce unit Alpha." So let's suppose that, let say well, at that unit of Alpha, the only way I could figure out consumer surplus and the only way I could figure out producer surplus is what? Pick back to our definition of consumer surplus. Our definition of consumer surplus was, consumer value, net of what they have to spend, that's price. Producer surplus was, producer value, net of what they have to cause it. So their revenue is price. So the price is a very important strike point for us. We need to know something about price. Suppose right now, bear with me, let's assume that price is eight dollars. Let's suppose price is eight dollars. That means consumer surplus would be, remember consumer surplus is difference between the demand curve and price. So if it was eight, in this particular case, it would be like right here, and consumer surplus would be, 10 minus 1 is 8. Consumer surplus is 10, and they would have paid 10 but they only had to pay eight. So the consumer surplus nets out to be two and producer surplus, they said, "Well, I would have given that to you for two dollars. But now you're going to give me eight, that's great." I get 8 minus 2 which is equal to 6. That makes social gain be equal to consumer surplus plus producer surplus; 2 plus 6 is equal to 8. Now, that's not too hard but let's just for the moment, try a different price. I'll use blue here. Let's assume the price is actually five dollars, like a midpoint in there. The prices is five dollars, what's happening here? Well, consumer surplus would be 10 minus 5, which is 5. Producer surplus would be equal to the $5 they get minus the $2 that they would have done it for, which is 3, and that makes social gain be equal to 5 consumer surplus, plus 3 producer surplus which is 8. Notice something here, as I hope you can see. No matter what price I choose as the strike price, I chose an example of eight dollars, I chose an example of five dollars; any price I want to choose, pick any price here, what's going to happen is the difference between the consumer value and that price, plus the producers value in that price minus the cross is always going to be that vertical gap. The strike price just decide who gets what share. But remember, in the eyes of the benevolent dictator, the benevolent dictator doesn't care who gets what. The benevolent dictator just knows that the size of the pie is going to grow by eight because of the existence of that unit. Value to society, to consumers is 10. Cost of resources burned up is just two. Who gets what share of it? Benevolent dictator doesn't care. But the benevolent dictator knows for sure that that total gap would be the sum of consumer surplus and producers surplus for that particular output level Alpha. Now, in our next step is to try and figure out what the whole size looks like. Thanks.
