[User] Please transcribe this text

[Assistant] Then I would have, be able to lock in a profit. How could I lock in a profit? Because I would just


[User] Please transcribe this text

[Assistant] He's willing to give this to me for a low price of 90 cents instead of 91 cents. So what can I do? Let's say he's willing to, uh,


[User] Please transcribe this text

[Assistant] He would, he'd pay me, let's say more likely, let's say he'd pay me 93 cents.


[User] Please transcribe this text

[Assistant] Say, some guy came to me, I'm the banker, and he says, I'll pay you 93 cents today to get, uh, a dollar in year three. In other words, for three years zero. Well,


[User] Please transcribe this text

[Assistant] I'd say, that's wonderful. I'll, I'll sell him this promise in year three of a dollar for 93 cents.


[User] Please transcribe this text

[Assistant] And I'll go out and buy the three year zero, uh, three year treasury. I'll sell some of the two year treasury. And I'll sell a little bit more of the one year treasury. And by doing that, and, and, and that portfolio which I've done by doing that will pay me exactly a dollar in year three enabling me to keep my promise to him.


[User] Please transcribe this text

[Assistant] But it will only have cost me 91.7 cents. I've made a 1.3 cent profit for sure with no chance


[User] Please transcribe this text

[Assistant] Okay, because I've done all the transactions today, and all the government's gonna keep its promises. I don't have to worry about the government giving me the money, and so I'll be able to turn the money over to that guy in your, uh,


[User] Please transcribe this text

[Assistant] In year three. And meanwhile, he's given me his 93 cents.


[User] Please transcribe this text

[Assistant] So if you want to do an arbitrage and make your profit, you have to figure out what the replicating portfolio is. And the replicating portfolio also tells you the price.


[User] Please transcribe this text

[Assistant] But it takes a long time to figure out what all these arbitrage replicating portfolios are.


[User] Please transcribe this text

[Assistant] And maybe nobody's coming to you and offering a stupid deal like that. So, you don't need to figure out, so the principle of the duality is, you don't need to figure out the replicating portfolio to figure out what the pi 1, pi 2, pi 3, pi 4, and pi 5 are. I can find those numbers now just by clicking a button in Excel.


[User] Please transcribe this text

[Assistant] You know, bad trader comes to me and offers me 93 cents for the three or zero coupon.


[User] Please transcribe this text

[Assistant] Then I'll figure out the replicating portfolio and take advantage of that offer to make a pure profit for sure.


[User] Please transcribe this text

[Assistant] So what I want to show you now is how to get pi 1 through pi 5 without having to go through this complicated calculation. And it just reasons backwards. Okay, so, please interrupt if you're not following this logic. So, you reason like this. We don't know what pi 1 through pi 5 are, but if you did know them, you'd be able to price the very bonds that the market is trading. So you'd know that 100.1


[User] Please transcribe this text

[Assistant] times pi of one. And you know that 100.2, the two-year


[User] Please transcribe this text

[Assistant] Zero coupon bond whose price is 100.2 would have to be 2 times pi of 2, uh, 2 times pi of 1 plus 102 times pi of 2.


[User] Please transcribe this text

[Assistant] Right? Because pi of one, remember, is the price you pay today for a dollar one year from now. 101 dollars one year from now. Cost, 101, if you knew pi one, this would be the price.


[User] Please transcribe this text

[Assistant] Okay, if you knew pi 1 and pi 2, you could figure out the price of the zero-coupon bond. I mean, the two-year treasury bond, because $2 at time 1 costs 2 pi 1, and $102 at time 2 costs pi 2. And then the three-year is 100.3 equals 3 times pi 1 plus 3 times pi 2 plus 103 times pi of 3.


[User] Please transcribe this text

[Assistant] Okay, and the last one is 100.5 equals


[User] Please transcribe this text

[Assistant] Okay, so you don't know the little pi's, but you do know these prices, because the market tells you, and you know the payoff of all the bonds, because that's just written on there.


[User] Please transcribe this text

[Assistant] You know, that's, that's written on them, literally, so you can just read what the payoffs are, and you know the government's gonna keep its promise.


[User] Please transcribe this text

[Assistant] So, rather than doing this complicated stuff trying to figure out the pi's, assume you had the pi's.


[User] Please transcribe this text

[Assistant] And then, if you have the pies, it would tell you what the prices of everything were. If you guessed the wrong pies, you'd get the wrong prices.


[User] Please transcribe this text

[Assistant] But basically you're solving five equations and five unknowns, and that's what Excel is so good at. It's gonna start with a wild guess of the pi's, and then it's gonna move around the pi's until you match all these prices. And since it's five equations and five unknowns, and they're all linearly independent, it'll be a unique set of pi's that it'll calculate.


[User] Please transcribe this text

[Assistant] And solve these equations, namely the ones you got by the replicating argument. So we can figure out the pi's by solving five equations and five unknowns. So that's what I do. So if you write, if you guess the pi's, one one one one one, any questions about what I'm doing?


[User] Please transcribe this text

[Assistant] You write 1-1-1-1-1, you're going to get prices


[User] Please transcribe this text

[Assistant] For the third one, with all the pi's 1, which is obviously not the right thing, it would be 3 plus 3 plus 3, that's 100.


[User] Please transcribe this text

[Assistant] You know, 109, so those are bad prices. We're trying to match what the market says the prices are.


[User] Please transcribe this text

[Assistant] Okay, so all I do is I subtract the market prices we're trying to match from the actual prices.


[User] Please transcribe this text

[Assistant] And which of the cells do I want to change? I want to change the pi. Those are the ones that are wrong. So I do that. So I'm minimizing the squared error by changing the pi.


[User] Please transcribe this text

[Assistant] I got the same prices that I told you about before by replication.


[User] Please transcribe this text

[Assistant] 9-9-1, 9-6-2, and 9-1-7. 9-9-1, 9-6-2, 9-1-7. Et cetera. Okay, so we got the pie. So that's step one. Alright, so that's what every single financial


[User] Please transcribe this text

[Assistant] Firm, and the entire world does, every single morning and sometimes every single hour.


[User] Please transcribe this text

[Assistant] So, are there any questions about what we just did?


[User] Please transcribe this text

[Assistant] You think you could do, you have to do this in the problem set. Is there any quiz, is there anything puzzling you about this?


[User] Please transcribe this text

[Assistant] Okay, now I'm gonna start deducing all kinds of surprising things from this. I hope that you'll be surprised.


[User] Please transcribe this text

[Assistant] So, but I want to make sure you've got the concept of what we've done now. Anybody puzzled by it?


[User] Please transcribe this text

[Assistant] You know, deducible from market to what's going on in the markets every day.


[User] Please transcribe this text

[Assistant] Alright, so let's ask one more thing that's deducible. Suppose I go to a bank and say,


[User] Please transcribe this text

[Assistant] Uhm, I promise to give you a dollar in year two. How many dollars will you give me in year three?


[User] Please transcribe this text

[Assistant] Every bank will give me the same answer if that yield curve, you know, given


[User] Please transcribe this text

[Assistant] We're, you know, this morning, and that was this morning's yield curve. So I ask every bank in the world, I'll give you a dollar in year two, you tell me how many dollars you'll


[User] Please transcribe this text

[Assistant] You know, be willing to give me, so I'll give you today, what am I doing? I'm saying, I promise today to hand over to you a dollar in year two, and you know I'm going to keep my promise, and in exchange I want to promise from you to give me a certain number of dollars in year three.


[User] Please transcribe this text

[Assistant] How many dollars is the bank going to offer to give me in year three? Every bank will give the same answer, and what will that answer be? So the thing I'm asking is I'm asking for what's called the forward interest rate.


[User] Please transcribe this text

[Assistant] Okay, so we've got these things for obviously very important numbers. Those are the most important things. Fisher would say those are the prices you use to get everything, but now I want to say something.


[User] Please transcribe this text

[Assistant] I'm going to ask another important thing, almost as important, I want the forward rate. So, 1 plus I1, you can't see that, I'm glad you pointed that, can you see this?


[User] Please transcribe this text

[Assistant] Cameraman told me this board was great. But anyway, uhm, so, how about one plus, okay, so I'll write


[User] Please transcribe this text

[Assistant] Okay, so we agreed today that you're gonna pay this many dollars at time t plus one in exchange for one dollar at time t. So why, this is like the interest rate that you might pay at time t. You give up a dollar at time t, how much do you get at time t plus one? The interest rate. But we're not there yet. We're agreeing to it today. So today we're agreeing to this interest rate.


[User] Please transcribe this text

[Assistant] Okay, so what is the interest rate we'd agree to today? So we've locked in the rate. When it comes to time t, one guy's gonna hand over the dollar, and when it comes to time t plus one, the other guy's gonna give back.


[User] Please transcribe this text

[Assistant] So what is the rate we would lock in today? It's called the period T interest rate forward because we're locking it in today for a forward period of time. But it's really just the normal time T interest rate for one year, but we're locking it in today. So what would we lock in today?


[User] Please transcribe this text

[Assistant] What's that? How do we compute that? We already know what that number is. What is it?


[User] Please transcribe this text

[Assistant] Well, I put t here. So, something like that.


[User] Please transcribe this text

[Assistant] Okay, exactly. That's pi t over pi t plus one. That's it exactly. So why is that?


[User] Please transcribe this text

[Assistant] Right, so all we're doing is this forward rate. We're exchanging time t dollars for time t plus one dollars at this ratio. But, we're committing to do it today.


[User] Please transcribe this text

[Assistant] But today we already know what the ratio is, it's time t dollars to time t plus one dollars. We know that pi two


[User] Please transcribe this text

[Assistant] 962. That's a bigger number than pi 3. Two, you know, from today's point of view, a dollar times two is worth more than a dollar times three.


[User] Please transcribe this text

[Assistant] We already know how much more a dollar at time T2 is worth than a dollar at time 3.


[User] Please transcribe this text

[Assistant] It's the ratio pi 2 over pi 3. That ratio, as he says, pi 2 over pi 3 has to be exactly the exchange rate that the people are agreeing to today. That's what pi 2 and pi 3 mean. And if you express it as an interest rate, it's 1 plus the forward interest rate at that ratio is 1 plus IFT.


[User] Please transcribe this text

[Assistant] If the yield curve is downward sloping, yes.


[User] Please transcribe this text

[Assistant] Okay, so you've made a little mistake in your premise.


[User] Please transcribe this text

[Assistant] Good question, but let me phrase your question a little differently so you see the answer to it. The yield curve was, uhm, almost flat in year 2000.


[User] Please transcribe this text

[Assistant] Okay, so in the year 2000, the yield curve was almost flat. In fact, there are moments where the yield curve seems to go down.


[User] Please transcribe this text

[Assistant] Okay, so what is that, uh, if the yield curve goes down, what does that mean? Does that mean that that's like


[User] Please transcribe this text

[Assistant] Between year 6 and year 7, the yield curve went down a little bit. Does that mean that pi 7 is less than pi 6?


[User] Please transcribe this text

[Assistant] Maybe, but it couldn't really be that way.


[User] Please transcribe this text

[Assistant] Okay, so let me translate his question. He's saying, look, yield curves very often are flat, mostly they go up, very often they're flat, sometimes they even start to go down. And he said, that worries me that maybe pi 7 is less than pi 6. Okay, but that shouldn't


[User] Please transcribe this text

[Assistant] So that could never happen. That would be crazy, because that would mean that there would be a negative interest rate in the future, and with money that can never happen. You can store the money. No one's ever gonna ask for a negative interest rate. He could just keep the dollar and keep it in his pocket, okay? So why is that? To remember, pi 6


[User] Please transcribe this text

[Assistant] equals one over one plus the sixth year yield to the sixth power and pi seven


[User] Please transcribe this text

[Assistant] Equals 1 over y plus the 7 year yield to the 7th power.


[User] Please transcribe this text

[Assistant] And yet pi 7 is still small. Could be that y7 is less than y6, as it is over there, but because you're taking this to the 7th power and this to the 6th power, you still have pi 7 less than pi 6.


[User] Please transcribe this text

[Assistant] So just because the yield curve is downward sloping doesn't mean that the pi's are going down. The pi's could never go down. The pi's are always going to go up. Okay, so, excellent question. Any other questions?


[User] Please transcribe this text

[Assistant] The i's will typically be going up. Suppose the yield curve is going up, by the way. Will the i's be going up faster or slower than the, than the, uh, than the yield?


[User] Please transcribe this text

[Assistant] Yeah, if this is the yield curve and I calculate the forward,


[User] Please transcribe this text

[Assistant] Do you think the forwards will be going up faster or less fast than the yields?


[User] Please transcribe this text

[Assistant] So let's just go back to our example that we were doing. Uhm, yield curve spreadsheet. Okay. So maybe I did it here. Hopefully I've solved it all.


[User] Please transcribe this text

[Assistant] Okay, so here we got the, uh, the actual pi's. You see the pi's are always declining.


[User] Please transcribe this text

[Assistant] Okay, and if we, uh, now look at the yield curve.


[User] Please transcribe this text

[Assistant] You can figure out the yield. How can you figure out the yield?


[User] Please transcribe this text

[Assistant] Because you solved that formula we gave at the very beginning. You take the price.


[User] Please transcribe this text

[Assistant] Okay, you, you know what the price is to figure out the yield on the three-year, we just plug in


[User] Please transcribe this text

[Assistant] 1 plus y of 3, 1 plus y of 3 squared, 1 over 1 plus y of 3 squared, 1 over 1 plus y of 3 cubed, and that gives us the yield. Remember that's how the newspaper reporter figured out the yield. So I figured out the yields in the spreadsheet, okay, down here, and here are the yields. So this is what would appear in the newspaper.


[User] Please transcribe this text

[Assistant] The one year yield is a little under one percent, the two year yield is a little under two percent, the three year is a little under three percent, the four year is a little under four percent, and the five year is a little under four, under five percent. Those are the yields.


[User] Please transcribe this text

[Assistant] So what if we did the forwards? The forwards, remember, are just the ratios of these pi's. What are the forwards? They're down here. So, what do they do? Sorry, I don't know how I did that. Here are the forwards, over here.


[User] Please transcribe this text

[Assistant] So the forwards have gone up much faster than the yields. Okay, they went from


[User] Please transcribe this text

[Assistant] 0.008%, which is the same as that one, to 2.9, which is bigger than 2.8, to 5, which is way more than 3.8, to 7.2, which is way more than that, to 9.6, which is way more than that. So the forwards went up much faster.


[User] Please transcribe this text

[Assistant] So why is that obviously going to be the case whenever the yield curve is upward sloping? So if we go back to our picture here.


[User] Please transcribe this text

[Assistant] If the yield curve were completely flat, what do you think the forward yield would be? This is just common sense just to see if you have any idea what's going on. If you think about batting averages and how somebody's average changes each time he bats,


[User] Please transcribe this text

[Assistant] If the yield curve is flat like in 2006, the forwards are going to basically be flat. But if the yield curve is


[User] Please transcribe this text

[Assistant] Upward sloping, then the forward yields are going to go up much faster. So why is that?


[User] Please transcribe this text

[Assistant] When you do a five year coupon bond, you're discounting all the cash flows, the previous four cash flows. You're using the same yield to discount them all. So if you go from year four to year five, okay, and you have to raise the yield a lot,


[User] Please transcribe this text

[Assistant] It means, you know, like if you're a batter and your average goes up, it means the last thing you did was better than the average of what you've done before. So it's gonna be even higher. You know, if your average was 300 and then you played a series against the Red Sox in which you did very well and your average went up to 320,


[User] Please transcribe this text

[Assistant] In that series against the Red Sox, you obviously did even better than 320 because you had to average what you did then with what your previous 300 to get 320. So if the average sort of is going up, remember the yield is the same thing over the whole history. If when you take a longer history, the average has gone up, it must mean that the most recent thing went up really much more.


[User] Please transcribe this text

[Assistant] Okay, so the four-year yield is sort of averaging the payoffs of the first four years. The five-year yield is averaging it over five years. So if that yield, the five-year yield has gone up,


[User] Please transcribe this text

[Assistant] Everybody can look at these pictures every single day. From these pictures, they can deduce the pi's. That's the crucial variable in the whole economy, the pi's.


[User] Please transcribe this text

[Assistant] But a second crucial variable is the forward yields, the 1 plus i f, which you can just get by the pi's. Now why are the 1 plus i f so important? We know the pi's are critical because they evaluate every project by multiplying the cash flows by the pi's. Why are the forwards so important? The forwards are so important because suppose you believed that


[User] Please transcribe this text

[Assistant] So, the forwards, let's go back to what we got.


[User] Please transcribe this text

[Assistant] Okay, so let's just look at the numbers here. Here are the forwards, remember? Down here. Okay, suppose I said to you,


[User] Please transcribe this text

[Assistant] You tell me, you don't know anything about the economy maybe, but you can read the newspapers and do mathematics that we've just been doing. What do you guess the interest rate's gonna be in year two?


[User] Please transcribe this text

[Assistant] Zero year forward, the one year forward, the two year forward, the three year forward, and the four year forward.


[User] Please transcribe this text

[Assistant] If I say in year two, what do you think the interest, guess what you think the interest rate's gonna be, what would you guess?


[User] Please transcribe this text

[Assistant] Yes. Right. I could do this real interest rate by doing it for tip. Fisher would say do that.


[User] Please transcribe this text

[Assistant] Trouble is that tips are not traded as, they're becoming more and more freely traded in the market. They used to be traded very, people didn't want to trade them.


[User] Please transcribe this text

[Assistant] So my classmate Larry Summers, uh, introduced TIBs, uh, Treasury, no, Treasury Inflation Protected Securities.


[User] Please transcribe this text

[Assistant] And he, you know, announced this was a fantastic idea and it's going to change radically the whole market.


[User] Please transcribe this text

[Assistant] And then nobody traded them, and they, they offered astronomical, uh, interest rates, real interest rates, to get anyone to buy them. And so they were nicknamed, really bad on camera, but their nickname became, totally illiquid pieces of, and so that was, so, so.


[User] Please transcribe this text

[Assistant] The market has not used the tips. To do most of its pricing, it uses the treasury bonds, but yes, Fisher would say if the tips were a reliable market,


[User] Please transcribe this text

[Assistant] You would, uh, use the tips to get the real interest rate, and that's really what you should care about is the real interest rate, not the nominal interest rate.


[User] Please transcribe this text

[Assistant] If I asked you to predict on the basis of the yield curve in this example and what we've been able to deduce, what would you predict the interest rate was going to turn out to be two years from now, the one year interest rate, what would you predict?


[User] Please transcribe this text

[Assistant] Year two. In year two, what do you think? The interest rate will be between year two and year three.


[User] Please transcribe this text

[Assistant] It's today and we're asking what do you predict the market rate of interest will be in year two between year two and year three?


[User] Please transcribe this text

[Assistant] Okay, and I2F happens to be right here, five percent. Okay, so that's the forward. So five percent you'd predict.


[User] Please transcribe this text

[Assistant] Okay, so let me refine that a little bit. If the world were one of total certainty


[User] Please transcribe this text

[Assistant] So everybody trading today had a perfect forecast of what was going to happen in the future. Then of course, the forward rates in the market today would have to be exactly equal to the forward interest rate. Because suppose that you knew for sure the interest rate was going to be 4% in year two.


[User] Please transcribe this text

[Assistant] How could the market get to a 5% forward? That means that some guy is promising today, I'll give you a dollar in year, you give me a dollar in year two, and I'll give you a dollar five in year three. And we're agreeing to that deal. But that's a ludicrous thing for him to do, because when he got to year two,


[User] Please transcribe this text

[Assistant] When he got to year 2, right, when he got to year 2, he could simply, if he knew for sure what was going to happen in the future and that the rate was going to be, uhm, 4%, he would just, uh,


[User] Please transcribe this text

[Assistant] I said it backwards. Suppose he knew for sure the rate was going to be six percent, he would be a, uh,


[User] Please transcribe this text

[Assistant] Oh yea, if he knew for sure the rate was only going to be 4%, he'd be a fool for promising to give the guy 5% today, because in the future, when he got the dollar, what would he do with it? Put it in the bank and get a dollar 4 next year? That wouldn't cover his promise. He'd be screwed.


[User] Please transcribe this text

[Assistant] Okay, so if he knows for sure that the rate two years from now is going to be four percent, the forward


[User] Please transcribe this text

[Assistant] That would be exactly equal to what everyone is expecting to happen in the future.


[User] Please transcribe this text

[Assistant] Let's go back to our picture now, uhm, the picture of the zero yield curve.


[User] Please transcribe this text

[Assistant] So what do you think this blue curve means?


[User] Please transcribe this text

[Assistant] What are the traders convinced is going to happen in the future? Assuming the traders, so the second half of the course is going to be dealing with uncertainty. We're now assuming like Irving Fisher that everybody trading today has no doubt about what's going to happen in the future. So what is, what do we think the, uh,


[User] Please transcribe this text

[Assistant] What do you think these traders think about these prices? About the interest rates?


[User] Please transcribe this text

[Assistant] What do you think, traders? What does this curve mean? Making the assumption that traders today are convinced about what's going to happen next, you know, in the future 10 years and 30 years, what do we know that they are convinced of? Yup.


[User] Please transcribe this text

[Assistant] That interest rates are going to go up and go up a lot. They're not just going to go up to 4% because that's the four, that's the, you know, the 30 year yield. They're going to go up, the forward rates are going up much faster than that. So we could have computed what they think. So they think rates are going to go way up in the future, okay? Much higher than that.


[User] Please transcribe this text

[Assistant] Because you're starting so low, so you're going to have, you know, you're staying low for a while, so the rates have to go up the floor and rate really sharply to pull the average that high.


[User] Please transcribe this text

[Assistant] So people are convinced that rates are gonna go up in the future. That's what that tells you. And why would they be convinced of that? Well, for the two reasons that you gave at the beginning. One of you said the market is gonna get more productive.


[User] Please transcribe this text

[Assistant] Irving Fisher has already told us that when the market gets more productive, you know, you're more optimistic about what's going to happen later, the real interest rate goes up. And if inflation's constant, the real interest rate goes up, the nominal interest rate goes up.


[User] Please transcribe this text

[Assistant] The other possibility is that the real interest rate stays the same, but there's inflation in the future. The real interest rate plus the inflation is the nominal interest rate. That's another explanation for why people might expect the nominal interest rate to go up.


[User] Please transcribe this text

[Assistant] Okay, so you know that the market is predicting rates going up and the two obvious explanations according to Fisher is that either the inflation is going to go up or the real rate is going to go up and why might the real rate go up? Well, there are a bunch of reasons, but most likely because productivity is going up. Okay, so I got one more surprising conclusion to end this. Okay, so if you were certain about the future and you had a, uh,


[User] Please transcribe this text

[Assistant] You had a five year, you took the five year coupon bond.


[User] Please transcribe this text

[Assistant] Could you tell me what the price of the five-year coupon bond was going to be next year?


[User] Please transcribe this text

[Assistant] Assume that everybody is convinced that the five year coupon bond, that they know the future for sure.


[User] Please transcribe this text

[Assistant] So therefore, from the zero curve, I erased my graph. This is the last question, so I'll let you go as soon as you answer this. You need to answer this to do the problem set. Uhm, uh, so wrong graph. Shit. Sorry. Okay, it's only taken one second to answer this. Okay.


[User] Please transcribe this text

[Assistant] I'm telling you now that this is what everybody's looking at in the morning. Okay, these numbers


[User] Please transcribe this text

[Assistant] They're getting all the forward rates and stuff like that. They're making all the deductions we made. Now if you suppose that those people are convinced, they don't have any doubt about what's gonna happen in the future. Because they don't have any doubt about what's gonna happen in the future, you can infer from these prices what they think about the future.


[User] Please transcribe this text

[Assistant] So the question is, can you infer what the price of the 5 year treasury, which is now 100.5, that 5 year bond is 100.5. Next year it will only be a 4 year bond. Do we know what its price is going to be next year? Yup?


[User] Please transcribe this text

[Assistant] Those pies, but those pies are something slightly different from those pies. It's gonna be a year later, remember.


[User] Please transcribe this text

[Assistant] Okay, so what you both said is absolutely correct. Unfortunately, we're two minutes, uh, we're ending now. So let me just end by saying, in the problem set, that's exactly the question. What is the five-year coupon going to be priced next year? If there's a world of certainty, you're going to know what all the interest rates are.


[User] Please transcribe this text

[Assistant] In the future. And if you know what all the interest rates are in the future, obviously Fisher tells you you can figure out what the price is. However, to get the exact formula would take a few minutes, and I unfortunately am a few minutes behind, so you're gonna have to figure out what the right formula is. But it's what he said and what you were getting to.


[User] Please transcribe this text

[Assistant] Yeah, tell us everything you know! Keep it coming!


[User] Please transcribe this text

[Assistant] I'll just add one point, which is, Meg typically says that trading is, or, you know, eBay is in the DNA of people. And, you know, it seems like a strong statement.


[User] Please transcribe this text

[Assistant] If you look across our 27 countries, there's a lot more similarities than there are differences.


[User] Please transcribe this text

[Assistant] A new, a whole new experience, you need a new UI and a new trading platform, but you don't. You actually can deploy very much


[User] Please transcribe this text

[Assistant] Uh, the user experience that we have at eBay, you just have to customize it for the local community in terms of language, in terms of message boards. If there are competitive sites, you have to try to match their functionality. So in Taiwan, for example, when we launched, we ended up competing with Yahoo.


[User] Please transcribe this text

[Assistant] So in many ways the feedback system came from his desire to make the community work, but also from his desire to get out of the middle. I mean he really felt very strongly that


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[Assistant] And that's a really unique, uh, I think business objective given what happened in the 1998 and 99 boom when people were just throwing money.


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[Assistant] Alright, well today I'm gonna talk about Social Security again. There's gonna be one more, uh, discussion of Social Security later. I'm gonna defer most of my plan until later.


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[Assistant] But, uh, I wanna finish the discussion so that we totally understand


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[Assistant] The subject, it'll also allow me to talk about demography.


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[Assistant] There's someone named Maurice Allais, a French economist.


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[Assistant] And it was sort of rediscovered by Samuelson in the 1950s.


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[Assistant] I'm not sure whether Samuelson had read outlay, I think Samuelson may well have read outlay, but anyway, Samuelson


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[Assistant] Uh, so these were 1947, something like that, 1958, in which Samuelson rediscovered it. And it, it's, uh, you'll see it's a very basic thought.


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[Assistant] And it seemed at first to challenge everything that we've learned so far.


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[Assistant] So the idea of the overlapping generation model is that time doesn't have a beginning and an end like we've assumed so far. Uh, time might go on forever. Now, whether or not you believe time


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[Assistant] Whether there's scientific proof that time goes on forever, or scientific proof that the universe has to come to an end,


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[Assistant] Let's face it, many of our institutions presume that time goes on forever.


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[Assistant] Most important among them is social security, which is the most, uh, which we'll see is the easiest thing to, that the model is designed to, to understand.


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[Assistant] The idea of social security is every, the pay as you go social security.


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[Assistant] The idea of Francis Perkins was that every young generation was going to, uh, give money to the old, but they shouldn't worry so much about it because when they got old, the next young generation would give them money.


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[Assistant] Obviously if you thought time was going to come to an end, the last young generation, knowing that they were the last generation, would refuse to give money to the old because they weren't going to get anything back when they were old.


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[Assistant] But then the second to last generation, knowing that when they got old they'd get nothing from the last generation's young, they wouldn't give anything either to the old.


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[Assistant] And working backwards like that, if everybody's rational and it's common knowledge that the world is going to end, nobody would ever participate in the social security scheme.


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[Assistant] So it's clear that there's some thought that the world might end or at least there's a thought that it's not worth bothering about the world, uh, ending.


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[Assistant] So, the overlapping generations model is meant to take that idea extremely seriously.


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[Assistant] And imagine life going on forever. So let's take the simplest example, where there's a generation that begins, generations last when they're, uh, young and old. So let's say we're at time, uh, one here.


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[Assistant] Okay, so there's an old generation and a young generation and the endowment of the old generation is one. The young generation has three when it's young, one when it's old, three when it's young, one when it's old, three when it's young, one when it's old. So, when you're young you have three


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[Assistant] Three apples, when you're old you have one apple, the next generation when it's young has three apples, when it's old it has one apple, and so on forever. So this will be t equals one here, two here, three here, four here, etc.


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[Assistant] Now what did Allay and Samuelson both basically say?


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[Assistant] They both basically said, look, everybody when they're young is incredibly well off. They're working, they're productive. When they're old and retired and feeble, they don't have very much.


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[Assistant] But what is it that the, but what can you do? Where can you trade according to Sandelson? What does the old have to trade? You know, it doesn't look like there's any trade that can take place.


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[Assistant] So it seems like it would be very helpful if the old would give the new something, if the young would give the old something, and when they got old, the next generation's young could give them something. So the young could constantly be making gifts to the old, that was


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[Assistant] Uh, I lay in Samuels idea and it's very closely related to social security. So Samuels got a little carried away with his idea.


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[Assistant] And he said that social security was the greatest and only true


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[Assistant] Uh, beneficial Ponzi scheme ever invented because


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[Assistant] You know, in a Ponzi scheme, this has gotten a lot of attention lately thanks to our


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[Assistant] So a Ponzi scheme is basically, uh, an investment strategy where


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[Assistant] You take the money that people give you, and you buy yachts with it, and then when they ask for their money back...


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[Assistant] When they ask for their money back, you tell them that you've gotten great returns and you just hand them money that new people have given you so they think you've gotten great returns.


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[Assistant] And when that second generation of people wants their money back, you tell them, well you've invested it brilliantly, you've gotten great returns, but all you're doing is giving them the money that the next, the third generation is giving you, and you keep going like that until finally you owe so much money you can't find new people fast enough to pay the people off, and then everybody discovers the Ponzi scheme and it all unravels.


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[Assistant] And, uh, the people at the beginning have made out very well, and the people at the end who, uh, you know, the second to last generation, they've lost all their money, and then lawsuits go, you know, lawsuits accumulate, and, uh, it's quite interesting that in the Ponzi scheme, the very first generation


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[Assistant] You know, that benefited are not free, because the whole thing was a ski, you know, the whole thing.


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[Assistant] But the guy Madoff running it knew from the beginning what was going to happen, and so those first generation of people, there's no reason why they deserve to make their great returns. They benefited from the Ponzi scheme. So the last generation suing Madoff are effectively suing the first people as well, and so we'll see how the courts decide it.


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[Assistant] Often the people who get out of the Ponzi scheme early


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[Assistant] In general, but Samuelson said, well, when life is going on forever, then there might not have to be an end to the scheme. It just keeps going. This guy gives to this guy, this guy gives to this guy, there's no reason for the Ponzi scheme to end, if you really think that the world is going to go on forever. And therefore, social security is a great Ponzi scheme, which is actually beneficial. So, Samuelson even wrote this as in,


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[Assistant] Little boy when he was writing the stuff and I remember some of the articles and I've gone and found them.


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[Assistant] But it certainly sounds plausible. Another thing he said was he said that in the social security, you know, money you could think of as a Ponzi scheme. Money too.


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[Assistant] Because, you know, you have worthless pieces of paper, you know, but, but you're willing to hold them when you're young, you'll accept them for, for good, because when you get old, you can find the next guy who's willing to give up goods for your money, and that guy's willing to take the money for it, because when he gets old, he can find the next generation's young who's willing to give up goods for his money. So, the money, which is a worthless piece of paper, never gets, uhm,


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[Assistant] So these are fascinating topics that Samuelson, uhm, discussed.


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[Assistant] But I don't want to discuss them in this class. I want to discuss social security. And so I'm going to do a variant of the model that Samuelson never thought about.


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[Assistant] Which I think is a much more realistic model, so I'm gonna do overlapping generations with land.


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[Assistant] And you'll see that in this model, I'm going to add land to it. It's a, I think a more interesting model.


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[Assistant] And we're gonna, and I'm not going to discuss the paradoxes of infinity because once you put land, even though time goes on forever, the paradoxes disappear. So rather than spending all the time on the paradoxes and how they come about and do they make sense, I'm just gonna add land from the beginning and we're gonna, it's gonna,


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[Assistant] You know, it will recapitulate in a nice way almost everything we've done this semester and there won't be any paradoxes. So what do I mean by land? I mean suppose that land produces one, this is land output.


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[Assistant] This produces one every period. So there's another output called


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[Assistant] Apples that just, you know, a tree that's gonna live forever, let's call it land, produces one every single period. So here are the periods, you know, this is what's happening in every period.


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[Assistant] Okay, now land seems to make the situation much more complicated, but in fact it will turn out that we can analyze this pretty easily. So, let me, let me summarize again the model. The model is that every generation


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[Assistant] Has endowments. So every generation T has endowments.


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[Assistant] Generation T, so it's an endowment at time T and at time T plus 1.


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[Assistant] Equals 3, 1. And let's say they all have utility, and the utility of every generation t, which only depends on what they consume when they're young and old, let's say is log, uh, x t plus log y, uh, x t plus 1.


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[Assistant] Okay, so, everybody cares about consumption when they're young, consumption when they're old, they don't care about consumption any other time, they begin with three apples when they're young, they know they're gonna have one apple when they're old, everybody's like that for generation t greater than or equal to one, but generation, uh, zero just has u, so I can call that u t, generation zero is only cares about consumption when old.


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[Assistant] Okay, but I also have to talk about the land. Generation 0 owns the land.


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[Assistant] Okay, so that's the economy. Very simple economy but it looks


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[Assistant] Much more complicated than anything we've done before, but it will turn out not to be, but it looks at it at first glance.


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[Assistant] Every generation has three apples, one young, one apple, one old.


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[Assistant] Except the very first generation which has land, and that in addition to is one apple when old. And that, uh, land produces one apple forever.


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[Assistant] So we have to figure out what equilibrium is, and then we have to look at social security.


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[Assistant] And by doing this, we're gonna understand Social Security much better than we did before. Okay, so any questions about this? What's going on? I'm gonna try and...


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[Assistant] Write down what equilibrium is, and then solve it, and then we're gonna talk about Social Security. Yup.


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[Assistant] Oh, well you know, if you only can eat one good, if I put log x1 here, it would be the same thing. Remember?


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[Assistant] If I take a monotonic transformation, if I double the utility or take the utility E to the utility, like that,


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[Assistant] Which is just equal to x1, it describes the same utility. The guy's not trading anything off, there's only one good. So more of the good is better for him. It doesn't matter whether we call it log x or x1, it's the same thing.


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[Assistant] That's a good question. Let's call it log x1, make him symmetric.


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[Assistant] Alright, well how, how would we define equilibrium?


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[Assistant] So there's financial equilibrium, and then we're going to see if we can solve this. So what's happening in financial equilibrium?


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[Assistant] Well, it's kind of interesting here. There's going to have to be a price of goods every period, QT. That's the contemporaneous price of apples.


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[Assistant] There's going to be the price of land every period, pi, let's call it t. So this is apple price.


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[Assistant] Contemporaneous apple price, land price.


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[Assistant] Well, we have to decide what everybody's going to consume every period. For Generation T, what they're going to consume when young and when old.


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[Assistant] Okay, and there's generation zero, what they're gonna consume when old.


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[Assistant] What else do I need to describe equilibrium?


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[Assistant] Probably it. So what's the budget set everybody's gonna face?


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[Assistant] Okay, so that's what you can, so generation T is going to consume something when young and when old, such that what? What's the budget constraint? Well, when they're young, if they want to consume goods, they have to spend QT to consume goods. So this is young, call that Y.


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[Assistant] Okay, and when they're old, they're going to have to consume...


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[Assistant] Sorry, when they're younger, what else would they want to do? They might want to old land. We could call that pi t.


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[Assistant] Okay, pi t plus theta, that's how much land they hold. Remember how we did this? Okay, and then what, what have they got? Well they've got their endowment, time t, uh, this is


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[Assistant] Time t, let's say, this is generation t, so they're endowment.


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[Assistant] Everybody comes into the world with just apples when young and apples with old. So when they're young, they've got three apples they can sell. Okay, they, you know, they can consume something, so three minus Q, the stuff they don't consume, they sell, and they can buy land with it. Ah. Got all this time, this never happens.


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[Assistant] Okay, and then when they're old, what can they do? Well, when they're old, at qt plus one, okay, times z,


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[Assistant] Now, are they gonna bother to hold the land when they're old? No, because they're gonna be dead and they don't care about their children. All they care about is eating as much as they can. So they're gonna sell all their land. So that's gotta be less than or equal to what? And so here's the, uh,


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[Assistant] What are they going to get when they're old? Well, they have 2t plus 1 when they're old and they're endowment of 1 plus


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[Assistant] What? They can sell their land, pi t plus one, times theta,


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[Assistant] Whatever they bought the first time, they can now sell when they're old. Plus, what else do they have?


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[Assistant] One last term, what else is there? So see what they do, why would you buy land? Well, because when you're young, you're so rich.


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[Assistant] You know, you don't want to consume everything when you're young, so instead of consuming your whole three, you consume less, you buy the land because the land's gonna be worth something next period. So what is it gonna give for you next period? What do you get next period from the land? Well, if you own the land, you get what?


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[Assistant] We have to multiply by the price, which on the one of the early classes I forgot, and the dividend is one. That's the dividend.


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[Assistant] But how many dividends do you get? How many apples? It depends on how much of the land you had. So if you had theta units of the land, you get, you know, if you had three acres of land, you get three apples.


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[Assistant] Which you can sell for a price QT plus one. You also still have the three acres of land, which you can sell off when you're old.


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[Assistant] Okay, so that's the revenue you get by selling off the land.


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[Assistant] And you also sell off some of your endowment maybe, and that's how you can buy when you're old. So that's what the budget set is of the young, of every generation. The budget set for generation T equals zero.


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[Assistant] Well, q1v has to be less than or equal to


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[Assistant] What does he have? Q1 times 1 plus he's got all the land. So he's got one acre of land. That's all the land there was. So he's got pi times, uh, pi 1.


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[Assistant] He's got all the land, so I've normalized the land to be one acre. Okay, so pi one times, uh, all land. So that's what that guy can do.


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[Assistant] Did I write theta? I forgot to write theta in the definition of equilibrium here.


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[Assistant] So I have to write a theta t, they're also having to keep track of what, uh, what, how much land they're gonna have. This is t equals one to infinity.


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[Assistant] Now how much does that very first generation consume? It's obvious they're going to sell all their land to consume as much as they can. So the budget's set. So x1, uh, solve z equals x1 and yz theta equals that.


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[Assistant] Uh, best for generation t in this budget set, and z equals x1 is best for generation 0 in this budget set.


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[Assistant] Okay, so, to say it in words, it's very simple in words, and then we have this mathematics, and it looks complicated, but we're just gonna...


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[Assistant] Say, it's gonna be very short to solve, even though it looks very complicated. So, the problem is this.


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[Assistant] We've got generations who are rich when young, poor when old. There's land that lasts forever.


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[Assistant] The only way people can save is by holding the land, that's like holding stock, that's holding something real, so when they're young, they're gonna take some of their extra endowment, cause they're so rich when young, they've got three when young, and they're gonna use it to buy land, and when they get old, they're going to, uh, sell the land.


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[Assistant] And eat the endowment from the land, the dividend from the land, and sell the land.


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[Assistant] And use that sale proceed to also increase their consumption when old.


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[Assistant] And the question is how do we solve for this equilibrium? And so why is it, so just to go back to Samuelson and all that, why is it so interesting? Well, one of the reasons it's interesting is that people, when they're young, have to think about the price of land


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[Assistant] Next period when they're old, because they know they're buying the land today, they can see the price today, but when they get old, they have to, you know, why are they buying the land today? Partly for the dividend next period, when they're old, but also for the resale value of the land. So everybody is thinking to themselves, what's the value of land going to be next period?


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[Assistant] And of course the value of land next period depends on what the young in that period are willing to pay. But they're thinking about what they're willing to pay on the basis of what they expect to happen the period after.


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[Assistant] Everybody has to think about the guy after him and what the guy after him is thinking, but what the guy after him is thinking, and it looks very complicated.


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[Assistant] Okay, and we want to solve for an equilibrium in which everybody can rationally anticipate what the guy in front of him is going to do, which means rationally anticipate what that guy is rationally anticipating the guy in front of him is going to do, and you have to solve for the whole equilibrium and see how it turns out. Okay, any questions about this?


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[Assistant] It looks very hard, but it's gonna turn out to be very, very simple. Yes.


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[Assistant] By the way, I haven't said what happens to the, uh, dividend in period zero. So actually I think that was a good, uh, point. So he gets one. He also gets the dividend in period zero.


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[Assistant] So to answer your question, remember the convention that we've made, which holds in the market, you know, and it's one of the reasons for the breakdown of the market. One of the reasons why the market


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[Assistant] Seized up in the last year or two is because, or the last, you know, last year,


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[Assistant] So the convention is, that we always use, is that if you buy the land at time zero, you don't get the dividends at time t, if you buy the land at time t, you don't start getting the dividends until time t plus one.


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[Assistant] So, if the young generation buys the land at time one, they don't get the dividend.


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[Assistant] So the very first dividend at time one is going to go to the old guy at time one, which I had left out here. So the old guy does get a dividend, it's the dividend at time one, because he began owning the land. So he had it before, so he gets that piece of land. Even though he's selling the land,


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[Assistant] At time one, he still gets the dividend at time one.


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[Assistant] And the generation that bonded at time one doesn't start getting dividends until time two.


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[Assistant] That's an excellent question, it was an oversight of mine, so exactly right.


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[Assistant] Okay, and that's how it happens in real life. Of course, you know, the length of time might be three days, or it might be one month, or it depends on the security, what the settlement rules are.


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[Assistant] So in, in, uh, in the settlement for, so they say t plus three is a very common kind of settlement, or t plus one, that means


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[Assistant] You know, in three days or in one day, and so if you're desperate for cash, and you have to give a, so anyway, I won't get into, we'll come back to this when we talk about the crisis and what happened, but.


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[Assistant] Okay, so people who are desperate to get stuff, you know, it doesn't start coming for a little while, so. Okay, any other questions? Yes.


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[Assistant] Alright, now how do you solve this? Well, let's, uh, figure out how to solve this. So, the first thing you can notice is that as, so Fischer never thought of having infinite time and thought about social secu, maybe thought about social security, I'm not aware that he had any


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[Assistant] I think, something like that. So, right around the time Allé wrote his paper. So, what is it that, uhm,


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[Assistant] What is it that, uh, he said, all his lessons are going to hold true. The first thing he said is that, look, in every period, there's a cue, there are cues on every, uh,


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[Assistant] Here are qt, you know, qt, qt plus 1, qt plus 1, qt plus 1. So if you just double, there's no loss in generality by taking all the qt's to be 1. We have no theory of inflation yet because there's no money or anything. So you might as well assume we're measuring everything in terms of apples and take qt to be 1. So without less of generality, as they say, you know, qt is equal to 1.


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[Assistant] And of course that means we have to, we can divide every equation by qt. So pi t divided by qt would go here and we'd have a 1 and a 1. We divide this one by qt plus 1, so it's an equation. We have z less than or equal to 1.


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[Assistant] Plus pi t plus one over two t plus one plus one times one times theta. So we just re-normalize all the prices. Okay, so re-normalize


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[Assistant] Okay, so one simplifying thing is we can get rid of, so think of pi t as the price of land in terms of apple. So we just get rid of all the q's here. Just assume that they're one. And so we have this equation. Okay, and now that means that pi t


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[Assistant] Okay, so that was a normalization we did many times before. We said that, you know, we might as well assume the contemporaneous price. We can't figure out what inflation is, so let's figure there's no inflation. The price of apples is always one, and we're going to measure the price of land in terms of apples.


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[Assistant] So we get the same equation, it now looks a lot simpler. So the q's you don't have to really worry about, we're just worrying about the pi's every period.


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[Assistant] Okay, so how did, what did Fisher say to do? Who's gotta worry about, what did Fisher say to do? What was his...


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[Assistant] Whenever you have an economy, a stock market economy like this, what do they say to do?


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[Assistant] What was his advice? He said turn it into general equilibrium, how?


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[Assistant] By doing what? Yup. Okay, so Fisher said, Fisher's lesson,


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[Assistant] into the endowment. That's the first lesson.


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[Assistant] Okay, so you see this is a good summary of what we've learned so far, and the second lesson was, look at present value prices.


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[Assistant] Okay, so he says, forget all these pi's and things like that, just look at


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[Assistant] The present value, so we're looking at P1, P2, P3, dot, dot, dot, where PT


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[Assistant] So once you knew the presence of the endowment then, I'm not gonna write all this, the endowment of all generations one and above stays the same, three one three one three one, but the endowment of generation zero is now one one one one one one one forever.


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[Assistant] Okay, and the budget set, everybody's gonna have a budget set determined by the p's.


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[Assistant] Okay, so now we're just one step from solving this. So there's one more thing to notice before we can solve it. So by symmetry, so observe


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[Assistant] You know, every generation is the same. The only relevant price for a generation is the trade-off between the price of goods when they're young and the price of goods when they're old. That's what Fisher said.


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[Assistant] The veil of the, of the stock market is just a means of transferring wealth between when you're young and when you're old. And really you should calculate. All these guys have to calculate. If I buy the stock now when I'm young, it's gonna cost me a certain amount of money, and I'm gonna be able to get a return, so the real rate of return,


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[Assistant] Well, they're gonna, by putting in pi t dollars today, they get out pi t plus one, plus the dividend. One tomorrow.


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[Assistant] Alright, so tomorrow they're gonna get pi t plus one plus one. So for every, if they, if they put in, buy one share of stock, it costs them pi t, and tomorrow they get, you know, pi t apples, we're measuring in terms of apples, and in the future they get pi t plus one plus one apple in the future. So that's the real rate of return, that's like one plus r, one plus r t,


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[Assistant] Okay, but we're gonna assume that that's a constant. 1 plus r, we're gonna guess it's a constant, and that's, you know, just 1 over this t that I told you about before. The ratio, pt plus 1, the present value,


[User] Please transcribe this text

[Assistant] So this ratio is just the interest rate between time t and time t plus 1.


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[Assistant] So Fisher says you don't have to think about all the stock market, what the return on the stock market, and all that's gonna be. Really, you're just trading off, by doing all that calculation, you're figuring out what's the trade off between time t goods and time t plus one goods.


[User] Please transcribe this text

[Assistant] In the Fisher economy, you don't look at the stock market. You assume that everybody knows the present value prices, and therefore the trade-off between time t and time t plus one goods, and we're going to assume that's a constant. Because the thing's so symmetric, how else could it turn out except a constant?


[User] Please transcribe this text

[Assistant] Okay, so now we're ready to solve it. We've done all the tricks, almost, to solve it. So what is equilibrium going to be?


[User] Please transcribe this text

[Assistant] At every generation, you're going to have an old and a young.


[User] Please transcribe this text

[Assistant] Right, if you look at any generation like this one at time two, there's that one, no not that one, a little less. The one in the middle, that's the one for the old guy. Then there's the young guy who has three. Right, and then there's the apple that the land produces. So this is young apple.


[User] Please transcribe this text

[Assistant] Well, there's gonna be an old guy eating apple, and there's gonna be a young guy eating apple. So how much is the old guy going to eat?


[User] Please transcribe this text

[Assistant] Old guy's gonna spend half his money, and how much money does he have? Well from his point of view, he's just trading off when he's young against when he's old. So from his point of view, he's got three apples when he's young, plus one apple when he's old, but that's worth


[User] Please transcribe this text

[Assistant] To him, the trade-off between apples when he's young and when he's old is just given by P.


[User] Please transcribe this text

[Assistant] Okay, divided by t. Alright, so this, this is the whole trick. Okay, so we have to spend a minute, so this dawns on you why this is true.


[User] Please transcribe this text

[Assistant] And now what's the young going to do? The young generation, what's their income? Well, they only care about the trade-off between prices when they're young and when they're old.


[User] Please transcribe this text

[Assistant] Okay, so when they're young and when they're old, they don't care about land according to Fisher. They don't have to think about that. They just have to know the price, which we're assuming is P for everybody, the tradeoff between young apples, which are worth more than old apples.


[User] Please transcribe this text

[Assistant] You know, these p's refer to different time periods, but we're assuming they're the same. Here's the young. This is the young.


[User] Please transcribe this text

[Assistant] This is the young, so this is divided by one. So this is the young, and this is the old.


[User] Please transcribe this text

[Assistant] And once I solve this equation, we'll have the whole equilibrium. But we need to understand this equation. So where did I get this equation?


[User] Please transcribe this text

[Assistant] Okay, so let's take any time period too, like t equals two for example.


[User] Please transcribe this text

[Assistant] We know the total apples around that can be eaten are five. That's on the right hand side. The old guy's apple, the young guy's three apples, and the land producing one apple. Five apples in all. Now who's gonna be eating the apple?


[User] Please transcribe this text

[Assistant] They're gonna be old guys, and they're gonna be young guys eating apples.


[User] Please transcribe this text

[Assistant] So the old will be the generation one.


[User] Please transcribe this text

[Assistant] They've got three apples at time two, so they're looking at three. But they've got expectations in their head. They're gonna think ahead. What's the price of stock market today versus tomorrow? Fisher says, okay, they do all that thinking. They realize the tradeoff between


[User] Please transcribe this text

[Assistant] One apple when I'm old is not worth the same. In present value terms, it's just 3 plus 1p, because the old apple's not worth as much at time t as it is at time t plus 1. It's 3 plus 1p. I'm gonna spend half of my income, and the price when I'm young, I've assumed that's 1. Okay, so that's what the young are doing.


[User] Please transcribe this text

[Assistant] The old guys, now the old guys, what they're doing at time t, depended on what they did when they were young. But when they were young at time 1.


[User] Please transcribe this text

[Assistant] And so they did the same calculation. When they were young, they were gonna spend half their money, this time one generation's gonna have to spend half its money when it's young, half its present value when young, okay, divided by


[User] Please transcribe this text

[Assistant] We'll figure out all the prices and everything in the whole economy and, uh, so we're at the end. But this is a, this requires a little bit of thought. So, go ahead.


[User] Please transcribe this text

[Assistant] Okay, the dividend, that's a good question. The dividend fit in here, because yes, there's a dividend. Here's the dividend that got produced, so there's an apple to be eaten from the dividend. Okay, right? Now you're saying,


[User] Please transcribe this text

[Assistant] So very important question you're asking. So it's correct what I wrote, but it doesn't sound correct. So what he's saying, the question is, what happened to the dividend? This guy, this generation say, this young,


[User] Please transcribe this text

[Assistant] Because that's precisely the point of what Fisher did. Fisher said yes, in the real world, everybody is thinking to themselves, like Generation 1, I'm young now, I'm buying the land because when I get old I'll be able to resell it and I'll also get the dividend. But Fisher has


[User] Please transcribe this text

[Assistant] Thought ahead. Fisher's saying, okay, the guy's gonna think about pi t plus one. That's what he'll be able to sell the land for. And he's gonna think about the dividend he's gonna get.


[User] Please transcribe this text

[Assistant] Okay, and his rate of return is therefore divided by how much he had to pay for the land today. That's his rate of return. But see the top thing is how many, the bottom thing is how many apples he had to give up.


[User] Please transcribe this text

[Assistant] High C there is how many apples he had to give up to get the land. The numerator is how many apples he gets next period after selling the land and taking the dividend.


[User] Please transcribe this text

[Assistant] So that ratio is the trade-off between apples today and apples in the future for him. So if he says to himself what Fisher says, the only thing the guy cares about is that ratio, that trade-off.


[User] Please transcribe this text

[Assistant] Which we're calling P, 1 over P. That's the trade-off he's gonna have in his mind. Okay? And so...


[User] Please transcribe this text

[Assistant] You know, only zero began with the land. Everybody else buys the land only as a means of getting to more consumption when they're old.


[User] Please transcribe this text

[Assistant] So the whole point of Fisher's insight is you don't have to keep track of how the guy's managing to get the payoff when he's old.


[User] Please transcribe this text

[Assistant] All he's doing is he's recognizing a trade-off of 1 plus r, or 1 over p, that trade-off between consumption when young and consumption when old. And all he can do is turn his endowment when he's young into more endowment when he's old at that ratio.


[User] Please transcribe this text

[Assistant] It doesn't matter how he does it as long as we have the right ratio. So Fisher says forget about the assets, just keep track of the present value prices.


[User] Please transcribe this text

[Assistant] And these will tell you the ratio of transformation of goods when young to when old, and that's all you need to know to make a decision. The whole point of Fisher says you don't need to think about the F's. Now after we get the P's, we'll go back and figure out what the price of land is. Any other questions?


[User] Please transcribe this text

[Assistant] Right, cause this ratio, so for every apple I have down here, I can get p apples at time t plus one.


[User] Please transcribe this text

[Assistant] So that ratio is the only thing that, so I might as well call, you know, if the ratio of two prices is p, it doesn't matter what their levels are. So I might as well think of one of them as 1 and the other one as p. I could think of the first one as 2 and the second one as 2p. That would be the same thing.


[User] Please transcribe this text

[Assistant] Alright, so if I thought of the first price is 2 and this price is 2p, I'd put a 2 here, a 2 here, and a 2 here, and it wouldn't change anything. So remember,


[User] Please transcribe this text

[Assistant] Learned that the very, this is why the lessons of general equilibrium, they seem so obvious, and then you put them in a slightly different context and you realize how clever Fisher was. If you double


[User] Please transcribe this text

[Assistant] That he's measuring the prices when he's young in terms of one and the prices when he's old in terms of p.


[User] Please transcribe this text

[Assistant] When we go back to the original equilibrium, you'll, you'll, it'll be clearer I think. But so that's the only equation that we have to satisfy.


[User] Please transcribe this text

[Assistant] So we can solve that equation now. Any other questions?


[User] Please transcribe this text

[Assistant] Okay, let's solve that equation. That equation is, I'm going to multiply by 2p, so I'm going to get 10p on the right hand side.


[User] Please transcribe this text

[Assistant] Alright, because if I multiply by 2p, I get 5 times 2p is 10p. On the left hand side, I'm just gonna get 3 plus 1p plus, uh, 3p plus p squared.


[User] Please transcribe this text

[Assistant] Okay, and so if I multiply, you know, I rearrange, I just get p squared. Uh oh, my usual problem's here.


[User] Please transcribe this text

[Assistant] P squared minus six P plus three equals zero.


[User] Please transcribe this text

[Assistant] P squared minus 6 P plus 3 equals 0, so P equals 6 plus when I'm using the quadratic formula, which you might have to, which I assume you know, minus P squared minus


[User] Please transcribe this text

[Assistant] So 6 squared minus 4 times 1 times 3 minus 12 over 2, which equals 6 minus the square root of 24 over 2.


[User] Please transcribe this text

[Assistant] So this is gonna be a little bit more than one, uh, sorry, a little bit less than five.


[User] Please transcribe this text

[Assistant] So this will be a little bit more than one, so the whole thing will be a little bit more than a half. Let's say it's .55.


[User] Please transcribe this text

[Assistant] Okay, now how did I know, okay, so here's a crucial step. How did I know when I said 6 plus or minus, why did I take the minus? Because if I had taken 6 plus this, I would have gotten a gigantic


[User] Please transcribe this text

[Assistant] Well let's come back to that, okay? So how did I know to take 6 minus that instead of 6 plus this? So if this is the P,


[User] Please transcribe this text

[Assistant] Then what are the prices? What are Fisher's prices? We've just solved for equilibrium. And these prices are going to be point, uh,


[User] Please transcribe this text

[Assistant] You know, we'll call this one one maybe, .55, .55 squared, .55 cubed, et cetera. That's what Fisher says the prices are.


[User] Please transcribe this text

[Assistant] Okay, we can, we can now figure out everybody's consumption, y and z. What's y going to equal?


[User] Please transcribe this text

[Assistant] You should check, I'm going a little fast here for myself. 3.55 divided by 2.


[User] Please transcribe this text

[Assistant] Okay, P is .5, I'm going too fast for you, aha! P is .55, right? I just got P.


[User] Please transcribe this text

[Assistant] So if I wanna see now, go back to consumption, what's the consumption gonna be when you're young? It's going to be...


[User] Please transcribe this text

[Assistant] Right, 3 plus .55, that's the guy's income, and he consumes a half when he's young. So it's 1.775. And when he's old...


[User] Please transcribe this text

[Assistant] He's gonna have the same income, uh,


[User] Please transcribe this text

[Assistant] You can see, uh, no, that doesn't look right. Uh, divide, not to divide by, yeah, 1.7, that divided by t, and that's gonna be a little bit more than 3. And so, in fact, if you solve it out, it turns out to be 3.225.


[User] Please transcribe this text

[Assistant] So I'm just solving, I'm plugging in 0.55 there. So it's 3.55 divided by half, that was that number, 1.775, divided by P, which is 0.55. So you can see it's a little bit more than 3.


[User] Please transcribe this text

[Assistant] .55 into 1.7 is, you know, a little bit more than 3. In fact, if you solve it out to some decimal places, it's that.


[User] Please transcribe this text

[Assistant] Okay, so we've solved what everybody does. Everybody now, we know what everyone's gonna do. The young are gonna spend 1.775


[User] Please transcribe this text

[Assistant] They're going to consume 1.775 here. They have an endowment of three apples, they're not going to eat them all. They're going to consume 1.775 of them.


[User] Please transcribe this text

[Assistant] Okay, and what are they gonna do with the, and then the old, at the same time, what are they doing? They're consuming 3.225. But you notice that those things add up to 5. So the consumption when the young, plus the consumption when they're old,


[User] Please transcribe this text

[Assistant] Okay, so the consumption of this old guy there is 3.225, and you add the consumption of that, yeaah, I went too high. The consumption of the young guy just under him is 1.775, the two of them add up to five. That exactly clears the market. So at time two, you repeat the same thing at time three, et cetera.


[User] Please transcribe this text

[Assistant] Okay, so you see we've already cleared all the markets. Except the one at time one, which looks more complicated.


[User] Please transcribe this text

[Assistant] But we've cleared all the markets. Now what's the price of all land going to be? What's the price of land? I want to write that. Let's write it here. What's the price of land? Which is going to be a constant. How do we figure that out? How would Fisher say you figure out the price of land?


[User] Please transcribe this text

[Assistant] So the price of land at time one, say, what would Fisher say? Yep.


[User] Please transcribe this text

[Assistant] Now, that's not the way Fisher suggested finding out the price of land. What did he say you should do? What's the fundamental theorem?


[User] Please transcribe this text

[Assistant] And what is that? So the land pays one apple every period.


[User] Please transcribe this text

[Assistant] So it's saying 1 plus 1 times p squared plus 1 times p cubed plus 1 times p to the fourth, right? Because looked at from the point of view of time 1, you get an apple next period relative to the apples today that's worth p. An apple in two periods is worth p squared at time 1 because, you know, an apple at time 1


[User] Please transcribe this text

[Assistant] At time two is worth p apples at time one and worth p squared apples at time zero, so you just keep doing this.


[User] Please transcribe this text

[Assistant] But this is a perpetuity, and so therefore it's equal to


[User] Please transcribe this text

[Assistant] Yeah, 1 over r, okay, we didn't, so it's equal to 1 over r. Okay, and so what's r?


[User] Please transcribe this text

[Assistant] So we know that, so what's R? How do we figure out what R is?


[User] Please transcribe this text

[Assistant] 1 over 1 plus r equals t, right? Equals .55.


[User] Please transcribe this text

[Assistant] Okay, and so this is a little less than 2, minus 1 is gonna be like .81 or something. Okay, and you take 1 over .81 and you get the same number.


[User] Please transcribe this text

[Assistant] Alright, so that's how Fisher, so let's go back. So Fisher solved everything. He said, I mean, the Fisher method solves it all. It says,


[User] Please transcribe this text

[Assistant] Well, we haven't, let's worry about time, uh, zero, time one, we haven't done that. So, okay, so what happens every period? Every period, like from two onwards,


[User] Please transcribe this text

[Assistant] The young guy says, aha, I've got three, uh, apples. What am I gonna do with them? He says to himself, well, the price of land is 1.225, so I could, you know, I could, uh, I could eat some of the apples or I could buy some land. And what does he decide to do? He says, let me eat 1.225.


[User] Please transcribe this text

[Assistant] So I'm gonna be getting a rate of return, we just calculated, of 81%.


[User] Please transcribe this text

[Assistant] At that rate of return of 81%, so this ratio up here, okay, this is another thing, this also.


[User] Please transcribe this text

[Assistant] Plus 1 divided by 1.225. Okay, that's also equal to, uh, 1.81. Remember R we just calculated over here. Where did I do R? R was 81%. That's the same number here. 81%. Okay, so everybody says to themselves, given that there's an 81% rate of interest,


[User] Please transcribe this text

[Assistant] I'm happy to hold the whole unit of land because at that rate of interest I'm just trading off consumption today for consumption when I'm old at the rate that I want to.


[User] Please transcribe this text

[Assistant] Okay, and at time zero the market clears also. So we clear the market for every time two through infinity. Okay, and that was by this equation.


[User] Please transcribe this text

[Assistant] That was up here. By picking the right P, we know every marker from 2 equals 2 onwards was clearing. And Fisher would say, by Valroslo, we don't have to worry about time 1, that's going to clear as well. And sure enough it does.


[User] Please transcribe this text

[Assistant] You know, it's a little bit different now, it's just the old guy, but the old guy with his land, which is 1.225, plus his dividend of one


[User] Please transcribe this text

[Assistant] His land, which is worth 1.225 and his dividend of, uh,


[User] Please transcribe this text

[Assistant] Okay, so the old guy, what does he do? He has his...


[User] Please transcribe this text

[Assistant] He has his one apple, plus he has the land, so he's gonna consume... The old guy has his...


[User] Please transcribe this text

[Assistant] Oh, I see. The old guy, so what happens at time uhm, one, the old guy has his dividend that he had before.


[User] Please transcribe this text

[Assistant] Okay, so he's got the dividend of the land because he's owned the land, you know, forever. So he gets the dividend of one plus


[User] Please transcribe this text

[Assistant] So that's one, plus he has an endowment of one, so he's consuming two now, plus he sells the land for 1.225. So that all adds up to 3.225, and then if you add the young generations, 1.775, that indeed clears the market at time one.


[User] Please transcribe this text

[Assistant] Complicated model with land and people having to look forward and expect what the price of land was going to be depending on what the next generation wanted to hold, which depended on what they were going to, they were going to think the generation of that were going to hold, etc. Very complicated stuff.


[User] Please transcribe this text

[Assistant] And we saw that to solve it was very simple. You just do the Fisher thing. If everybody's rational, you can always turn everything, you can forget about the assets and the land and turn everything into present value prices and put the endowments so you forget about


[User] Please transcribe this text

[Assistant] All the assets and just put the dividends into people's endowments and look at all the present value prices.


[User] Please transcribe this text

[Assistant] Okay, and the present value prices by symmetry we're assuming just grow exponentially, decline exponentially.


[User] Please transcribe this text

[Assistant] Okay, and then we could solve the one equation and figure out what that price was, the x, the, the, the exponential number p that's


[User] Please transcribe this text

[Assistant] You know, to the nth power gives the nth price as present value of the price. So solving for that P, we then


[User] Please transcribe this text

[Assistant] Clear the market. We found out what everyone was going to do when young and when old, and by plugging in now, Fishers


[User] Please transcribe this text

[Assistant] So in this formula, the price of every acid is the present value of its dividend, we figured out what the, uh, we figured out what the price of land was every period. So we solve for the whole equilibrium, and sure enough it clears. And in equilibrium, everybody's doing this calculation. If I buy land today, I'm gonna get that rate of return on the land, which corresponds to the P. It's gonna be 81%. And so everything works out.


[User] Please transcribe this text

[Assistant] The way I solved it is I ignored the assets. So I didn't pay attention to what the assets were. I just put the dividends in the endowment. I didn't pay any attention to what people were holding of the assets.


[User] Please transcribe this text

[Assistant] Because Fisher says, forget the assets altogether, just do the present value prices and augment the endowments.


[User] Please transcribe this text

[Assistant] And I found the present value prices by getting this factor P, and then it was just P to the N.


[User] Please transcribe this text

[Assistant] And I found what everyone was going to consume. That was it as far as Fisher's concerned. But then Fisher says, okay, once we found general equilibrium, we can go back


[User] Please transcribe this text

[Assistant] So financial equilibrium, and figure out what the price of land is, which is, uh,


[User] Please transcribe this text

[Assistant] The present value is a dividend, so its price is 1.225, and the step I left out, which you're asking about, you can also figure out what assets everybody's holding.


[User] Please transcribe this text

[Assistant] So Fisher's saying, okay, what assets are they holding? Well, the guy, you know, he's spending, he's consuming 1.775 here. We figured out the price there of 1.225.


[User] Please transcribe this text

[Assistant] So it must be that he's holding exactly one unit of the asset.


[User] Please transcribe this text

[Assistant] And so the asset market is clearing too. But that's no accident. Fisher's saying, if you, if you clear all the markets, doing the present value, general equilibrium stuff, and you go back to the financial equilibrium, you're automatically going to be clearing all those markets too.


[User] Please transcribe this text

[Assistant] So I did, I left out the step that, you know, once, because


[User] Please transcribe this text

[Assistant] Somebody a- somebody anticipated all that and got me to calculate the price of one in a cheating way. He said assume fate is one, then figure out how much money you're spending on the asset. What I should have done, so he did that, what I should have done is done Fisher's trick of figuring out the price of the asset, which is 1.225, and then of course we know the guy must have bought


[User] Please transcribe this text

[Assistant] One asset in order to use up his budget set, but that clears the


[User] Please transcribe this text

[Assistant] Market for assets. But Fisher knew that was going to happen. It always has to happen. That's the beauty of what he did.


[User] Please transcribe this text

[Assistant] Yes, so the point is, so thank you, I'm coming back to exactly that point. So the point is when you look at the present value of land, it's gonna be P plus P squared plus P cubed plus P to the fourth. The present value of land had better be finite. Okay, so in other words,


[User] Please transcribe this text

[Assistant] P has to be less than 1, otherwise the value of land would be infinite. And it wouldn't make any sense, because the very first old guy with an infinite amount of land, infinite value of land would buy more apples than there possibly were in the world.


[User] Please transcribe this text

[Assistant] So you know that the interest rate, the real interest rate has to be positive. If the real interest rate were not, were less than zero, you would have to, uh,


[User] Please transcribe this text

[Assistant] And you had some asset that paid a constant dividend forever, that asset would have an infinite value. So the presence of land, which pays a constant, uh, asset forever,


[User] Please transcribe this text

[Assistant] It forces the rate of, the real rate of interest to be positive.


[User] Please transcribe this text

[Assistant] So Sanderson and all his talk of negative real interest rates, it can't really happen if you think that land is going to, you know, land is going to pay some dividend probably forever. So there's going to be a positive real rate of interest.


[User] Please transcribe this text

[Assistant] Okay, and so it means in social security, if, if like the young give up one, and the, uh, the young give up one to get one back when they're old, they're always gonna be losing. Because there's a positive real rate of interest, and so every generation has to lose.


[User] Please transcribe this text

[Assistant] Okay, so we're exactly the point of all, so it's precisely the point. Because of the presence of land, you know that the real rate of interest is going to have to be positive. You know, Fisher never made this argument. He said it's impatience and you know, maybe if people are incredibly patient, it could even turn out to be negative.


[User] Please transcribe this text

[Assistant] But not so when you have land with a constant dividend forever. Then if the interest rate is constant, it better be positive, otherwise the land would have infinite value. Okay, so it's a new argument for a positive rate of interest. You have to have the, the, uh, land has to have a finite value.


[User] Please transcribe this text

[Assistant] Uh, easily. Now, uh, and after we've done it a couple times, this will


[User] Please transcribe this text

[Assistant] I know it seems a little confusing now, but let's just do a couple more thought experiments. Suppose we do Social Security. What will happen with Social Security? How does that work? What does Social Security mean?


[User] Please transcribe this text

[Assistant] And until now, we talked about it as if the young


[User] Please transcribe this text

[Assistant] Could give the old part of their endowment, you know, the young pay taxes and the taxes get handed over to the old guy that pays you go. And we talked as if it wouldn't change the equilibrium.


[User] Please transcribe this text

[Assistant] The giveaway was on the spot, was bigger than GNP for a year. You know, 17 trillion compared to 12, 14 trillion. So clearly it's going to have an effect on the interest rate.


[User] Please transcribe this text

[Assistant] So, we ought to take that into account if we're doing a more careful analysis of social security.


[User] Please transcribe this text

[Assistant] So what would Social Security do? How would I take into account Social Security? Suppose every young person gave one unit, you know, one apple to the old guy at the same time. How would I figure out what happened in the new equilibrium?


[User] Please transcribe this text

[Assistant] All I would do is I would change this to a two. Every young guy now only has two apples when he's young because he's given one of them to the old. And the old would have two. So all the way through here, I would just change all this to, uh, two, two, two, two, two, two, two. Okay, that's what I would do. So that's the change. Then I'd have to re-solve the equilibrium. So how would that change?


[User] Please transcribe this text

[Assistant] The apples in the economy, the young apples, the guys only got two, but the old apples,


[User] Please transcribe this text

[Assistant] The old's got two, and there's still one apple coming from the land. So that's still five. But now every generation's gonna be behaving a little bit differently. They're gonna have two when they're young, and two when they're old.


[User] Please transcribe this text

[Assistant] This guy will have two when he's young and two when he's old, and otherwise it's the same thing. So I just re-solve for the equilibrium.


[User] Please transcribe this text

[Assistant] Okay, and so if I resolve for the equilibrium multiplying by 2p, I'll have 2 plus 2p plus 4p.


[User] Please transcribe this text

[Assistant] So, no, I might get, sorry, I just confused myself. I multiply by 2p, I've got, uh,


[User] Please transcribe this text

[Assistant] 2 plus 2p, multiplying by 2p, I have 2p here.


[User] Please transcribe this text

[Assistant] Okay, plus multiplying by 2p, I have 2p squared here. Hope I'm doing this right. Okay, I've got 10p on the right, like I had before.


[User] Please transcribe this text

[Assistant] 10p and that's 4p so it's still 6p it looks like plus 2 equals 0 and so p equals 6 plus or minus 36 minus 8.


[User] Please transcribe this text

[Assistant] Okay, so 6 minus square root of 28, uhm, okay, so it's like, so it's working out pretty much. Okay, so, uhm, so 0.38 is the new price.


[User] Please transcribe this text

[Assistant] Okay, so therefore the interest rate, 1 over 1 plus r,


[User] Please transcribe this text

[Assistant] Equals .38. So what do you think happens to the interest rate? So r now equals


[User] Please transcribe this text

[Assistant] Okay, before I write it, you can figure out what it is yourself in a second. Do you think the interest rate went up or down in the new economy? What would Fisher have said?


[User] Please transcribe this text

[Assistant] Okay, so the interest rate went from 81% to, uh, no that can't be right, went to, uh, 161%.


[User] Please transcribe this text

[Assistant] So, the loss is even worse than it seemed before. Remember in present value terms, when you're young you give up one, and when you're old you get one, and so you lose the present value, so the present value of that trade is this.


[User] Please transcribe this text

[Assistant] What's that over one plus r? Well now that r has gone up, you're losing any more. So social security at the current interest rate looks bad for every generation. After you do the social security and everybody understands what's happening, it's going to be even worse in terms of present value. Okay, so social security hurts


[User] Please transcribe this text

[Assistant] So, social security again, everybody is giving something when they're young to the old. So the guy at the very beginning, at the very top, gains a lot. Everybody else, every other generation loses, and you can compute the utility after social security compared to before social security.


[User] Please transcribe this text

[Assistant] And it goes from something like 2.7 to 2.3. So there's a substantial loss for every one utility except for the first generation. On the other hand, we rescued the first generation. Now, there are two more experiments I'm not going to be able to finish today, but I'm going to mention them.


[User] Please transcribe this text

[Assistant] Experiment one is, suppose we had more and more children every generation. How would we take that into account? Well, it's very simple to take into account.


[User] Please transcribe this text

[Assistant] The same thing, with a trivial change, you can figure out what happened with more and more generations, with more and more children.


[User] Please transcribe this text

[Assistant] Okay, so if we had more and more children in every generation, so every 30 years, let's say the population doubled, that's not such a high growth rate, you know, per year, you'd have 6 and 2 here. Okay, and then it'd go up to 12 and 4.


[User] Please transcribe this text

[Assistant] Okay, and we have to, but, but again, it's, it's, it's all exponentially growing, and the dividends would also be growing. So this would be 2, and 4, and 8, and 16, etc.


[User] Please transcribe this text

[Assistant] Okay, but as you'll see in a second, the way, I won't do it this time, next time, you'll see that it's very easy to solve for the new equilibrium. You just put a, you put a double here thing, because the young are twice as many young. Okay, you just solve it and you do the whole thing. And what happens is,


[User] Please transcribe this text

[Assistant] Social Security isn't solved. Even though, Samuelson was in a way wrong again, even though there are two, okay, even though there are two young people for every old person, so every young person only has to give up half an apple, you only have to give up half an apple when you're young,


[User] Please transcribe this text

[Assistant] Okay, and when you're old you still get a whole apple back. Sounds like now you surely should gain, but the point is you don't because the rate of interest gets higher.


[User] Please transcribe this text

[Assistant] And then we're gonna have generations that alternate in size. But all these are very easy to solve once you figure this out. So today, on Thursday, you have to solve a problem just like that so you get the hang of it. Just one problem to do for Thursday.


[User] Please transcribe this text

[Assistant] Guys, those are the nicest things anyone's ever said to me. You guys are the best. Gotta go now, bye!


[User] Please transcribe this text

[Assistant] Okay, today we're going to talk a little bit more about Social Security. Social Security remembers the biggest


[User] Please transcribe this text

[Assistant] Uh, program the government runs, this annual


[User] Please transcribe this text

[Assistant] Expenditures are slightly bigger than the military expenditures every year and those two things are way bigger than everything else.


[User] Please transcribe this text

[Assistant] It's been the biggest program the government's run since


[User] Please transcribe this text

[Assistant] Uh, the New Deal, Franklin Delano Roosevelt put it into effect in the late 1930s. Uh, and it seems to be broke.


[User] Please transcribe this text

[Assistant] So it lasted for 70 years and now it seems on the verge of going broke. So what happened and how can we fix it?


[User] Please transcribe this text

[Assistant] And as I said, this has been a topic of conversation, presidential conversation, at least since 2000. There were a bunch of commissions before that looking at the problem and the


[User] Please transcribe this text

[Assistant] What I said last time was the general public and our politicians seem completely confused about what's going on. So we need to figure out how could it be that the program went broke. Was that a, should that have been a surprise and how can we fix it? And the three standard things everybody says is President Bush and many people like him say


[User] Please transcribe this text

[Assistant] Well, the system's going broke. The rate of return young people like you are gonna get is, you know, less than 2% a year. That's terrible. Any bond, any stock, you can expect a much higher return than that. So the program's just awful. Uh, we should stop it or privatize it.


[User] Please transcribe this text

[Assistant] I'll explain what privatizing means, in that way your money instead of going to old people will be put in the stock market and you'll get a higher rate of return and you'll do much better.


[User] Please transcribe this text

[Assistant] And then a second thing people say is, well, the thing lasted all this time. I mean, what's really gone different? What could possibly have caused the change? It must be those dastardly, uh, baby booms.