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[Assistant] It's all about scale. Having impact is all about how you do something that scales. And by scale I mean things that can have broad impact, potentially things that have decreasing marginal cost, things that can scale beyond the one-to-one interaction you have as a person. And so I'm going to talk to you today about scaling three things. About scaling a vision for a company.


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[Assistant] About scaling a product, and then about scaling yourself.


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[Assistant] And some of these lessons apply to different people at different times, but I think these three things together are what enable people to be great entrepreneurs and great leaders.


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[Assistant] When designing a layer for a confnet, you might have to pick, do you want a 1x3 filter or 3x3 or 5x5, or do you want a pooling layer? What the Inception network does is it says, why don't you do them all? And this makes the network architecture more complicated, but it also works remarkably well. Let's see how this works.


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[Assistant] Let's say for the sake of example that you have inputs a 28 by 28 by 192 dimensional volume.


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[Assistant] So, what the inception network, or what an inception layer says is, instead of choosing what filter size you want, uh, in a conv layer, or even do you want a convolutional layer or pooling layer, let's do them all. So, one of you can, uh, use a one by one convolution,


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[Assistant] And that will output a 28 by 28 by something. Let's say, uhm, 28 by 28.


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[Assistant] By 64 outputs, and you just have a volume there. But maybe you also want to try a 3 by 3.


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[Assistant] And that might output a, uh, 20 by 28 by 128. And then what you do is just, uhm,


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[Assistant] Let's stack up this second volume next to the first volume, and to make the dimensions match up, let's make this a same convolution, so the output dimension is still 28 by 28, same as the input dimension in terms of height and width, but 28 by 28 by, in this example, 128.


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[Assistant] And maybe you might say, well, I want to hedge my bets. Maybe a 5x5 filter works better. So let's do that too. And have that output a 28x28x32.


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[Assistant] And again, you use the same convolution to keep the dimensions the same. And maybe,


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[Assistant] You don't want a convolutional layer. Let's apply pooling.


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[Assistant] And that has some other output, and let's stack that up as well. And here, pooling output is 28 by 28 by 32.


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[Assistant] Now in order to make all the dimensions match, you actually need to use padding for max pooling. So this is an unusual form of pooling because if you want the input to have height and width 28 by 28,


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[Assistant] So if you have the output, you know, match the dimension of everything else, also by 28 by 28, then you need to use the same padding as well as the stride of one for pooling.


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[Assistant] So this detail might seem a bit funny to you now, but let's, let's keep going. And we'll make this all work later.


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[Assistant] But with a inception module like this, you can input some volume, and output in this case, I guess you can add up all these numbers, 32 plus 32 plus 128 plus 64, that's equal to 256.


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[Assistant] So you will have one inception module, input 28 by 28 by 129, and output 28 by 28 by 256.


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[Assistant] And the basic idea is that instead of you needing to pick,


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[Assistant] One of these filter sizes or pooling you want and committing to that, you can do them all and just concatenate all the outputs and let the network learn whatever parameters it wants to use, whatever combinations of these filter sizes it wants.


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[Assistant] Now it turns out that there's a problem with the inception layer as we've described it here, which is computational cost. On the next slide, let's figure out what's the computational cost of this 5x5 filter resulting in this block over here. So just focusing on the 5x5


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[Assistant] Part on the previous slide, we had as input a 28x28x192 block and you implement a 5x5 same convolution with 32 filters output 28x28x32.


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[Assistant] Uhm, on the previous slide I had drawn this as a thin purple size, but I'm just gonna draw this as a more normal looking blue block here.


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[Assistant] So let's look at the computational cost of, uh, outputting this 20 by 20 by 32.


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[Assistant] Uh, because the output has 32 channels and each filter is going to be 5 by 5 by 192.


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[Assistant] And so the output size is 20 by 20 by 32.


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[Assistant] By 32 numbers. And for each of them, you need to do, you know, this many multiplications. Right? 5 by 5 by 192.


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[Assistant] So the total number of multipliers you need is the number of multipliers you need to compute each of the output values times the number of output values you need to compute.


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[Assistant] And if you multiply out all these numbers, this is equal to 120 million. And so,


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[Assistant] While you can do 120 million multiplies on a modern computer, this is still a pretty expensive operation.


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[Assistant] On the next slide, you see how using the idea of one by one convolutions, which you learned about in the previous video, you'll be able to reduce the computational cost by about a factor of 10 to go from about 120 million multipliers to about one tenth of that.


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[Assistant] So please remember the number 120 so you can compare it with what you see on the next slide, 120 million. Here's an alternative architecture for inputting


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[Assistant] 28x28x192 and outputting 28x28x32, which is following. You're gonna input the volume, use a 1x1 convolution to reduce the volume to a


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[Assistant] 16 channels instead of 192 channels. And then on this much smaller volume, run your 5x5 convolution to give you


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[Assistant] So notice the input and output dimensions are still the same.


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[Assistant] 28 by 28 by 32, same as the previous slide.


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[Assistant] But what we've done is we've taken this huge volume we had on the left and we've shrunk it to this much smaller intermediate volume, which is only, uh, has 16 instead of 192 channels. Sometimes this is called a bottleneck layer.


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[Assistant] Because a bottleneck is usually the smallest part of something, right? So I guess if you have a glass bottle that looks like this, then you know, this is I guess where the cork goes.


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[Assistant] Then the bottleneck is the smallest part of this bottle.


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[Assistant] So in the same way, the bottleneck layer is the smallest part of this network, where you shrink the representation before increasing the size again.


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[Assistant] Now let's look at the computational cost involved. To apply this one by one convolution, we have 16 filters.


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[Assistant] Each of the filters is going to be of dimension 1 by 1 by 192. This 192 matches that 192. And so the cost of computing this 28 by 28 by 16 volume is going to be, well, you need this many outputs. And for each of them, you need to do


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[Assistant] 192 multiplications. I could have written, uh, 1 times 1 times 192, right? It's just this. And if you multiply this out, this is 2.4 million. It's about 2.4 million.


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[Assistant] How about the second, so that's the cost of, uhm, this first convolutional layer.


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[Assistant] The cost of this second convolutional layer will be that. Well, you have this in the outputs. So 28 by 28 by 32.


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[Assistant] 5 by 5 by 16 dimensional filter. So 5 by 5 by 16. And we multiply that out, is equal to, uh, 10.0.


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[Assistant] And so the total number of multiplications you need to do is the sum of those, which is 12.4 million multiplications. And if you compare this with what we had on the previous slide, you reduce the computational cost from about 120 million multiplies down to


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[Assistant] Very similar to the number of multiplications you need to do, so that's why I'm just counting the number of multiplications.


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[Assistant] So to summarize, if you're building a layer of a neural network and you don't want to have to decide, do you want a one by one or three by three or five by five or pulling layer, the inception module lets you say, let's do them all and let's concatenate the results.


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[Assistant] And then we ran into the problem of computational cost, and what you saw here was how using a one by one convolution, you can create this bottleneck layer, thereby reducing the computational cost significantly.


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[Assistant] Now, you might be wondering, does shrinking down the representation size so dramatically, does it hurt the performance of your neural network?


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[Assistant] It turns out that so long as you implement this bottleneck layer sort of within reason, uhm, you can shrink down the representation size significantly and it doesn't seem to hurt the performance, but saves you a lot of computation.


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[Assistant] So this is the key of the, uh, these are the key ideas of the inception module. Let's put them together and in the next video show you what the full inception network looks like.


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[Assistant] Figure out how to deploy the model somewhere in the cloud and make inferences. And that can work pretty well, but it was just a lot of work to go through that process. And also for every task, such as sentiment versus extracting names versus something else, you have to train and deploy a separate model.


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[Assistant] One of the really nice things about a large language model is that for main tasks like these, you can just write a prompt and have it start generating results pretty much right away. And that gives tremendous speed in terms of application development.


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[Assistant] And you can also just use one model, one API to do many different tasks rather than needing to figure out how to train and deploy a lot of different models.


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[Assistant] And so with that, let's jump into the code to see how you can take advantage of this. So here's a usual starter code. I'll just run that.


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[Assistant] Which is actually seems pretty right. This lamp isn't perfect, but this customer seems pretty happy. Seems they're a great company that cares about the customers and products. I think positive sentiment seems like the right answer.


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[Assistant] If you wanted to give a more concise response to make it easier for post-processing, I can take this prompt and add another instruction to


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[Assistant] Give your answers a single word, either positive or negative, so it just prints out positive like this, which makes it easier for a piece of text to take those outputs and process it and do something with it.


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[Assistant] Let's look at another prompt, again, still using the lab review. Here,


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[Assistant] I haven't identified a list of emotions that the writer of the following review is expressing. Include no more than five items in this list.


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[Assistant] So large language models are pretty good at extracting specific things out of a piece of text. In this case, we're expressing the emotions. And this could be useful for understanding how your customers think about a particular product. Uhm, for a lot of customer support,


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[Assistant] Is the right to the funny review expressing anger because if someone is really angry, it might merit paying extra attention to have a customer review.


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[Assistant] With supervised learning, if I had wanted to build all of these classifiers, there's no way, you know, I would have been able to do this with supervised learning in the just a few minutes that you saw me do so in this video.


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[Assistant] I'd encourage you to pause this video and try changing some of these prompts. Maybe ask if the customer is expressing delight, or ask if there are any missing parts, and see if you can get a prompt.


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[Assistant] Let me show some more things that you can do with this system, uhm, specifically extracting richer information from a customer review.


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[Assistant] Information extraction is the part of NLP, of natural language processing, that relates to taking a piece of text and extracting certain things that you want to know from the text.


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[Assistant] So in this prompt, I'm asking it, identify the following items.


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[Assistant] Figure out positive and negative sentiment to track trends about positive or negative sentiment for specific items or for specific manufacturers.


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[Assistant] Your response is a JSON object with item and brand as the keys. And so if I do that.


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[Assistant] Uhm, to then do additional processing on this output.


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[Assistant] In the examples we've gone through, you saw how to write a prompt to recognize the sentiment.


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[Assistant] Figure out if someone is angry and then also extract the item and the brand. One way to extract all of this information


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[Assistant] But it turns out you can actually write a single prompt to extract all of this information at the same time. So let's say, identify the fine items, extract sentiment, uhm, as a reviewer, expressing anger, item purchase, completely made it, uhm, and then here


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[Assistant] I'm also going to tell it to format the anger value as a, as a boolean value. And let me run that. And this outputs a, uhm, JSON.


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[Assistant] Uhm, they extracted the item as a lamp with additional storage instead of lamp. Seems okay. But this way you can extract multiple fields out of a piece of text with just a single prompt.


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[Assistant] Now, one of the cool applications I've seen of large language models is inferring topics. Given a long piece of text, you know, what is this piece of text about? What are the topics?


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[Assistant] Here's a fictitious newspaper article about how government workers, uh, fear about the agency.


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[Assistant] You know, and so on, uh, results of using NASA was a...


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[Assistant] Determine five topics that are being discussed in the following text.


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[Assistant] It's about governance survey, it's about job satisfaction, it's about announcer, and so on. So overall, I think pretty nice, uhm, extraction.


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[Assistant] Python lists with the five topics that, uh, this article was about.


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[Assistant] And if you have a collection of articles and extract topics, you can then also use


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[Assistant] So let me use a slightly different topic list. Let's say that, uhm, we're a news website or something and, you know, these are the topics we track. And also local government, engineering, employee satisfaction, federal governments.


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[Assistant] Which of these topics are covered in that news article? So here's a prompt that I can use


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[Assistant] Uhm, give your answers and this is zero one for each topic. And so, great. So this is the same story text as before.


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[Assistant] So this thing's a story. It is about announcer, it's not about local government, it's not about engineering, it is about employee satisfaction and it is about federal government. So with this,


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[Assistant] In machine learning, this is sometimes called a zero-shot learning.


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[Assistant] Algorithm because we didn't give it any training data that was labeled so that zero shot and with just a prompt it was able to determine.


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[Assistant] And so if you want to generate a news alert, say, so that process news and, you know, I really like a lot of work that NASA does, so if you want to build a system that can take this


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[Assistant] So very quickly, take out the article, figure out what topics it is about, and if the topic includes NASA, have it print out, alert, new NASA story.


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[Assistant] Oh, just one thing. I'll use this topic dictionary down here.


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[Assistant] This prompt that I use up here isn't very robust. If I wanted a production system, I would probably have it output the answer as a, in JSON format rather than as a list because the output of the launch language model can be a little bit inconsistent. So this is actually a pretty brittle piece of code.


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[Assistant] But if you want, when you're done watching this video, feel free to see if you can figure out how to modify this prompt to have it output JSON instead of a list like this and then have a more robust way to tell if a bigger article is a story about NASA.


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[Assistant] So that's it for inferring. And in just a few minutes, you can build multiple systems for making inferences about text that previously this would have taken days or even weeks for a skilled machine learning developer.


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[Assistant] And so I find this very exciting that both for skilled machine learning developers, as well as for people that are newer to machine learning.


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[Assistant] You can now use prompting to very quickly build and start making inferences.


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[Assistant] On pretty complicated natural language processing tasks like this.


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[Assistant] In the next video, we'll continue to talk about exciting things you can do with large language models, and we'll go on to transforming. How can you take one piece of text and transform it into a different piece of text, such as translate it to a different language? Let's go on to the next video.


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[Assistant] A pace and not a size that we've never seen before. It wasn't possible to hit 200 million users. I'm sure the Standard Oil Company didn't get there.


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[Assistant] But the other thing that's happened is that along with the ability to scale, the fundamental economics of distribution, not of everything, we still have to distribute water bottles. In many ways the old fashioned way have fundamentally changed.


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[Assistant] Are the newspapers going away? Many have gone out of business. Many still are struggling more. What's happening to magazines? What's happening to TV? What's happening to the music industry? And when you think about these business models,


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[Assistant] These, all of these companies produce very high quality content. Content that's very important. I mean, I think we all enjoy music. I think it's fundamental to democracy that we have reporting in a I-check-facts kind of way. The kind of reporting that can break watergate, that can take down a president.


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[Assistant] And so we lived in a country, and we still do, where there were about, uhm, a thousand magazine and newspaper companies publishing about 6,700 titles.


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[Assistant] And today because distribution of words is free on the web.


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[Assistant] 15.5 million compared to a thousand magazines and newspapers. Pretty amazing.


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[Assistant] The reason that's happened is that distribution is free. And when distribution became free,


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[Assistant] And then you had to compete for that shelf space, and they made a lot of money. Because people would compete for which shelf space they would, and that's the way people had to buy music. Anyway, they were making money not on the content, but on the distribution. TV shows the same thing.


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[Assistant] There were a very limited number of TV shows, cable channels opened up, and yes, you got from like, you know, I don't know, 5 channels or 10 channels to hundreds, but that's still really limited.


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[Assistant] And so when you think about products that scale, you have to think about what that scale entails and what the basic business model is of distributing your product or service.


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[Assistant] Like yeaah, make a product people want. Fantastic.


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[Assistant] Uhm, and just, you know, please use the learnings from your first project to build about the second project and, you know, maybe even about the third project, so on. Uhm, that's kind of how I have kind of grown over time using these models myself as well.


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[Assistant] Uhm, or if you have an idea for a bigger project already, just, just go for it.


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[Assistant] Uhm, and, you know, as a reminder, uhm, these kind of large language models are a very powerful technology, so it kind of goes without saying that we ask you to use them responsibly and please only build things that will have a positive impact.


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[Assistant] Thanks for having me. I'm really excited to be here. LangChain started as an open source framework for building LLM applications. It came about when I was talking to a bunch of folks in the field who were building more complex applications and saw some common abstractions in terms of how they were being developed.


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[Assistant] And, and we've been really thrilled at the community adoption of, of LangChain so far. And so look forward to sharing it with everyone here and look forward to seeing what people build with it.


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[Assistant] Blankchain is an open source development framework for building alum applications.


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[Assistant] We have two different packages, a Python one and a JavaScript one.


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[Assistant] They're focused on composition and modularity. So they have a lot of individual components that can be used in conjunction with each other or by themselves.


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[Assistant] And so that's one of the key value adds. And then the other key value add is a bunch of different use cases. So chains of ways of combining these modular components into more end to end applications and making it very easy to get started with those use cases.


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[Assistant] In this class, we'll cover the common components of LangChain, so we'll talk about models.


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[Assistant] We'll talk about prompts, which are how you get models to do useful and interesting things. Uh, we'll talk about indexes, which are ways of, uh, ingesting data so that you can combine it with models. And then we'll talk about chains, which are more end-to-end use cases along with agents, which are a very exciting type of end-to-end use case, which uses the model as a reasoning.


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[Assistant] Very involved. I think most VCs think we're dumb money, because we're a corporation, but in reality we're not. Don't tell them I said that. I promise.


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[Assistant] But, uh, but we do a lot to help. In fact, that's one of the things that we've focused on, you know, the past four or five years especially. There's so many venture capital firms in the world now. I mean, I think there's some consolidation going on. I've got some great slides to show you to that point, but for some reason we're not, we're not projecting, but, uh,


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[Assistant] We bring a number of things. I'll give you a couple of things that we bring.


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[Assistant] One thing we do annually is what we call the Intel Capital CEO Summit.


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[Assistant] Sea level people in various industries, oil and gas, manufacturing, you know, high tech, etc.


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[Assistant] The objective there is to create a forum for them.


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[Assistant] To make pitches, essentially, to these prospective customers and prospective partners.


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[Assistant] So that's one major event. We do a smaller version of that.


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[Assistant] About 75 to 80 times a year called Intel Capital Technology Days. And these are specifically customer forums where


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[Assistant] We have our business development organization, they have access to Intel customers, end user customers, like Shell, like IBM, etc., name your Fortune 1000 company.


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[Assistant] They're interested in finding out what's happening in technology.


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[Assistant] They don't have an external R&D department, right? They don't have anybody that's kind of out purveying, surveying technology companies.


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[Assistant] So what we do is we bring the technology innovators together with these Fortune 1000 companies.


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[Assistant] They select the categories they're interested in, whether it's cloud computing or mobile software, or software as a service.


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[Assistant] And we literally do a full day where those companies, the CEOs from those companies pitch to C-level decision makers around technology and strategic partnership. They pitch their idea, their wares, and in many cases we get proof concepts, we get closed sales. So what this does for the portfolio companies


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[Assistant] And to close a deal literally, or at least the concept of a deal.


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[Assistant] In a day, just unheard of. We take months for these companies to close deals. So that's a forum that we create.


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[Assistant] In addition to that, we've got advisory boards, we've got what we call acquisition ITDs, where if a company is approaching the point of liquidity, we line up, you know, prospective buyers. Because we've got relationships with all the major ISVs.


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[Assistant] So those are some of the things that we do. It's unprecedented because we've got, as I say, this very large organization. We've got resources in every geography. So even if they want to enter a new market.


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[Assistant] You know, if they're launching their business from the U.S. and want to start to, uh, make inroads into other developed regions, like Western Europe, for example, we've got a team of people that already have relationships in those areas and can help open doors for them. So I think, you know, if you compare it, it's super smart money in a corporate and, you know, maybe less smart money in a rich firm.


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[Assistant] Lesson 89 A Slip of the Tongue People will do anything to see a free show, even if it is a bad one.


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[Assistant] When the news got round that a comedy show would be presented at our local cinema by the P&U Birdseed Company, we all rushed to see it. We had to queue for hours to get in.


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[Assistant] Those who failed to get in need not have felt disappointed, as many of the artistes who should have appeared did not come.


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[Assistant] The only funny things we heard that evening came from the advertiser at the beginning of the programme.


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[Assistant] He was obviously very nervous and for some minutes stood awkwardly before the microphone. As soon as he opened his mouth, everyone burst out laughing. We all know what the poor man should have said, but what he actually said was


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[Assistant] This is the Poo and E Seed Bird Company. Good ladies evening and gentlemen.


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[Assistant] One of the most common complex applications that people are building using an LLM is a system that can answer questions on top of or about a document.


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[Assistant] So, given a piece of text, maybe extracted from a PDF file or from a webpage or from some company's intranet internal document collection, can you use an LLM to answer questions about the content of those documents to help users gain a deeper understanding and get access to the information that they need?


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[Assistant] In fact, embeddings and vector stores are some of the most powerful modern techniques. So if you have not seen them yet, they are very much worth learning about. So with that, let's dive in. Let's do it.


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[Assistant] So in this video, we are going to learn WebBroker and we have some sample applications for WebBroker and Datasnap. What is WebBroker?


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[Assistant] In WebBroker, you can programmatically construct HTML or XML documents, and you can transfer to the client side. So, now it's time of time.


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[Assistant] So we can start by creating a new project, delhi projects, and we got this web broker.


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[Assistant] And also we got web services and this SOAP server application.


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[Assistant] It all uses the web broker, but it adds some functionalities and some components to the service and we can name it SOP or Datasnap services.


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[Assistant] The WebBroker is a plain web browser application that we can programmatically, customly change all of the stuffs in this app. So, put this.


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[Assistant] And I wanna choose the only windows. And we can choose the standalone GUI application or CGI standalone executable. And also we got a page dynamic link model. But I wanna choose the standalone GUI application. So next.


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[Assistant] And only there we see all applications. And we have to test this port.


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[Assistant] So, in a web module, this web module can be a data module that means we drag and drop some non-visual components.


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[Assistant] So here is the, another sample application. This is created using the Datasnail and WebBroker. And we got this edit in a button.


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[Assistant] So we got server methods and server container. In the server container, we got data snap components. For example, DS server, DS server class, transport, proxy generator, and it's all the components connected to each other. For example, DS server. This is the DS server class. And server, this DS server one.


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[Assistant] We got only the generated default codes. In the server methods, we got FireTag components. For example, WaitCursor for GUI and the MySQL driver link. So this assemble, this application connects to MySQL database in the localhost.


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[Assistant] So, in the MySQL driver link, we have to show the lip-micycle-dll-pass to connect to the MySQL database, and to connection.


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[Assistant] In this video, I'm going to show you how to make database web application using Unity UI framework. So, let's get started.


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[Assistant] The main form. Main form is a single form implementing the SBA which is created and shown after successful login or if no login form exists.


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[Assistant] In general, a main form is the application form used to navigate to other forms using menus or other navigation tools. For instance, main menu, buttons, etc.


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[Assistant] The server module. Each Unity UI web application contains a special data module named server module, which is the core module of the application. It's singleton, which means that it's created only once per application.


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[Assistant] It is mainly used to configure various server settings.


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[Assistant] So main module. Main module can be considered the heart of the session. It is a special propose, the data module which is automatically created and added to the project each time a new project is created.


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[Assistant] Main module has many important roles in a Unity Y application.


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[Assistant] Some of these roles are not visible to the developers. For developers, main module can be used to place resources shared by a session, such as database connections, shared variables, etc.


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[Assistant] For instance, you can declare public variables in main module's public section and then access them from other forms in the session. So, it's time to demo.


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[Assistant] So here is the FishFacts demo application created using the UniGUI. So here is the uniform. And we have a data source.


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[Assistant] And, uh, uni-labels, uni-gb components that you can connect to database using this uni-gb components.


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[Assistant] So, this is the unitdb edit component and unitdb image and this is the unitdb demo and main menu, media list, native media list. So here is the unitdb grid.


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[Assistant] So, as you can see, these components have data source and data fields properties.


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[Assistant] So, in the main module, we have to connect to database. I'm going to add client data set component. And we can open this context menu and load from my base table. And uh, fmsoft, framework, new GUI.


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[Assistant] As you can see, there is no code. It's all generated by, uh, ng-wife framework. And they come back to main. And, ehm, we have to select the data source. And in database, dataset, we have the unimainmodule.client.dataset1.


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[Assistant] So first of all, we have to add main module to our users clouds on this main.pass or main form. So then we can connect to client dataset and we can select this and


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[Assistant] So, we can select this data source, and we have events, and you can see there is a onDataChange, so we can open it. So, onDataChange event, the UnistouchBar panels 0, the text object gets data source 1, data set, and


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[Assistant] So now we can save it and run without debugging.


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[Assistant] And this is our FishFacts demo application. You can click this next button.


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[Assistant] And rotate again. Here are the results.


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[Assistant] Alright, so I'm going to finish talking about overlapping generations today. I'm going to defer my plan to save Social Security, uh, to a couple lectures from now.


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[Assistant] And I'm gonna start to introduce uncertainty in this class. The exam will only cover the


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[Assistant] Up to basically the last problem set. So you can, uhm,


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[Assistant] There are a few things about overlapping generations I might say today, which will clarify what you already know, but you don't have to know anything beyond the problem you turned in on Thursday, on uh, you're turning in today.


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[Assistant] So you, I think, are better informed now than you were yesterday. I think it's a big help to be doing the problems.


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[Assistant] Those of you watching on screen at home, you know, do the problem.


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[Assistant] The, uh, remember we had a situation where there were


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[Assistant] There were generations, each of whom was rich when young and poor when old, that looked like that.


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[Assistant] And then there's generation, cause I forgot the generation here, generation 0, generation 1,


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[Assistant] Now this model, I've been told, is the hardest thing you do the entire class.


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[Assistant] Things are going to get much more complicated, but since they build up slowly, I think this model is the hardest thing that you have to do the entire


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[Assistant] So I realize it's a little bit confusing, but in the end I don't think it's that complicated. And it reveals all the subtlety of Fisher's thinking. Not that Fisher understood about overlapping generations, but his ideas you can see here. So what are his ideas?


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[Assistant] You've got a complicated model in which you've got people trading apples when they're young


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[Assistant] Uh, against land. So the two, the objects in the economy are land, which you're supposed to think of as a stock market.


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[Assistant] Okay, so we've got land, and we've got, uhm, we've got land, yes, and we've got apples.


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[Assistant] So the young here are gonna buy the land, but when they get old they're gonna sell the land. So the land is constantly changing hands. It's not that one person buys it at the beginning and holds it forever.


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[Assistant] So Fisher's formula, remember, was that the price of any asset


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[Assistant] And the logic seemed to be at the time that the price


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[Assistant] But you see, in this example, it's a little more complicated. Nobody's gonna hold the land.


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[Assistant] So we never used the fact, in Fisher's argument, that the same person had to hold the asset till the end.


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[Assistant] Get rid of assets. Put dividends into endowment.


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[Assistant] And transform it into general equilibrium, the very thing you solved in the first couple days of class.


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[Assistant] Okay, and then go backwards and figure out what the financial equilibrium is.


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[Assistant] So, although it seemed very easy before, it's a little subtler this time, but it's the same principle. Whose endowment should you put the dividends into?


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[Assistant] The land is changing hands all the time. There's a new guy owning it, a new guy owning it every period. So whose endowments do we increase?


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[Assistant] Okay, so this old person who has the right to the first apple, his own endowment of an apple, and also the right to the first dividend, but he actually has a right to all the dividends. So his endowment,


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[Assistant] The endowment of Mr. Zero, okay, is gonna be two, one, one, one, et cetera. Cause he has his original apple, plus he's got, uh, and


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[Assistant] He has this endowment of an apple, cause, you know, everyone when they're old has an apple. He's also, because he's owned the land before, gotten the right to this first dividend of the apple, that's two. And because he's the original owner of land, he owns all the future dividend stream.


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[Assistant] Okay, so we can forget about land after we've stuck the dividend into the right person's endowment, and now we just trade as if it's general equilibrium.


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[Assistant] We just look for supply and demand and the present value prices, which are P1, P2, P3, etc. Okay? And, because it's symmetric, we know that this is going to equal, uhm, one P, we can always make one of them be, uh, you know, one price can be one, so the present value prices are going to look like this.


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[Assistant] Okay, and the reason I can make this simplification is by symmetry. You know, everything, every generation is the same. So it's obvious that I'll be able to keep repeating the same argument over and over again. Okay?


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[Assistant] This guy bought the land and then he sold the land. So he, you know, it was a fair trade. So he started, you know, he started without it and ended without it. The fact that in between he used the land to save, you can already do that in a general equilibrium. You don't need to think about the land, because the only reason this guy is buying the land is to use it for a means of saving, which is already in Fisher's equations. So, to solve for equilibrium is then quite simple.


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[Assistant] Okay, and so therefore in equilibrium we have to have one half


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[Assistant] Times the income of every generation. Every generation's gonna have three when young.


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[Assistant] Of course, one went old, now from the point of view of any generation T, the prices are


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[Assistant] Okay, if I'm doing any t, like this period 4, the old guy here, you know, that's p4 and p3. He cares about p3 and p4. But he only cares about the ratio of p3 and p4, which is p. So from his point of view, he might as well have thought of them as 1 and p. So his income is 3 plus 1p, and he's gonna spend half his income


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[Assistant] On that good, which for him is a relative price of P. The young guy's gonna spend half his income, which is also 3 plus 1 P.


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[Assistant] In general, if I had prices, the present value prices, this guy's income would be given by that, because he's the old at time t, and the young would be given by that.


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[Assistant] Okay, but I have to do that for every single t, so I have an infinite number of prices and an infinite number of equations. But then you say to yourself, well, hm, you know, this is, if I, if I replace, if I take the ratio of pt over pt minus one to equal p,


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[Assistant] Okay, then the ratio of these two prices is the same as this price, and so I've got,


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[Assistant] You know, I'll have one equation in one unknown variable, and that same equation will get repeated every other generation. Because when I go to generation, you know, S, which is another generation, all that matters is the ratio between Pt minus 1 and Pt, and Pt and Pt plus 1.


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[Assistant] If I, uh, assume every gen- if I assume those ratios are always the same,


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[Assistant] I'm going to be repeating the same equation over and over again.


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[Assistant] So if I can solve it once, I can solve it an infinite number of times. It's basically the same equation written infinitely often, and so, as long as I stick in, keep these ratios constant, I'm just doing it over and over again, so I only have to do it once. So that's the...


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[Assistant] So it doesn't have to work out that it's, you know, that it's just because, you know, every generation has the same endowments and every generation has the same utility. That's why it's such a simple thing to solve. Yep.


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[Assistant] Between time t and time t plus 1, this good is more valuable than that good.


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[Assistant] And then this good here is only worth 55% of that good. So the symmetry assumption


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[Assistant] You know, but the symmetry of the problem suggests that I could guess that the prices are gonna, the present value prices are gonna decline by 50, by the same percentage every period.


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[Assistant] Okay, so let me, any other questions? I mean, we'll keep going with questions, yeaah.


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[Assistant] Yeah, what is the endowment of the original old guy? He's the guy who owns the land.


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[Assistant] So what does he have? He has one apple when he's...


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[Assistant] His endowment, when he's old, like everybody else is old, he has an apple, you know, his own tree in his backyard, uh, gives him an apple when he's old. Okay? Or, you know, when he's an old man or an old woman, he can sort of, you know, barely scrape together one apple. Now,


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[Assistant] He also has the land. The land is his for all time. So the land is paying an apple every year forever. So his own apple when he, you know,


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[Assistant] At time one, plus the land's apple is this two, and the land produces an apple every time in the future. So that's his endowment. I stuck the dividends of the land into his endowment.


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[Assistant] Right, I'm not assuming he lives forever. He doesn't. In fact, he knows he's gonna die in period one. He wants to do all his consuming in period one. But he has in death, so that's another subtle thing about this. You can own endowments that, you know, occur after you're dead.


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[Assistant] You know, if you own a tree, the tree's gonna be, the land is gonna be producing stuff long after you're dead. So when you sell off the land, you're selling off those future dividends. Okay, of course you're not gonna hold the land.


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[Assistant] Because you wanna just consume as much as you can. So you're gonna sell off the land and consume. But you're selling off all of these future dividends.


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[Assistant] Okay, so another thing this model gives us is a new argument.


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[Assistant] So the price of the acid is discounted dividends, that's gonna be 1 over 1 plus r plus 1 over 1 plus r squared plus 1 over 1 plus r cubed plus dot dot dot. By the way, that's equal to p plus p squared plus p cubed, you notice. Okay, so,


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[Assistant] The discounted value of the dividend is the price of land. So the price of land, of course, has to be finite.


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[Assistant] So if the land is producing, you know, I think it's sort of realistic. Land is probably gonna produce forever. As long as the world lasts, if you've got land, you'll get something out of it. Someone will always want the land. And so if it's gonna have a finite price, the whole future dividends


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[Assistant] Okay, so it's another argument that Fisher never would have thought of because he never thought about infinities or anything like that. Another argument for the interest rate, real interest rate being positive.


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[Assistant] Okay, any other questions about this? So we reduce it to one equation


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[Assistant] And I'll put back the P here in just one unknown.


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[Assistant] Okay, equals 5, and we solve it and we get p equals .55.


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[Assistant] Okay, and it's a quadratic equation, so you can all solve quadratic equations.


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[Assistant] Analyze all sorts of things. You could do the same comparative static Fisher does. Suppose we change the utility function and made this, you know, a third instead of a half. That would correspond to doing what? Making people more


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[Assistant] Impatient. Okay, and what would you think would happen to the interest rate?


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[Assistant] Okay, so in the Excel file, we're gonna do just that, we're gonna see it's gonna go up. Instead, we could, uhm,


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[Assistant] We could do the social security thing and we could have every young person give something to the previous old. Which means everybody's endowment goes from say 3 to 2 and 1 to 2.


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[Assistant] Okay, so they get more in the future and less than early on. So again, you could re-solve for equilibrium, and Fisher's saying if you've got more endowment in the future and less in the present, you're gonna have a higher, uhm,


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[Assistant] A higher, uh, real interest rate. You get a higher real interest rate.


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[Assistant] You know, you could make the land more productive and change this to a two everywhere and see what happens. Okay, so, in this Excel file, I do that, maybe I'll come back to that. So, we're gonna do those experiments in a second.


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[Assistant] Uh, but now I do, I wanna do two, two more things before I end this. The first is, I wanna say, suppose we had growth in the economy.


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[Assistant] So what if you had growth? Where am I gonna add growth? Over here, I shouldn't have erased that. Let's have growth.


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[Assistant] Tobin, you know, Yale's greatest economist after Irving Fisher, he said something which was 90% right, but not 100% right.


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[Assistant] He said, you know, I pointed out to him that I got these guys at Social Security. I worked with them.


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[Assistant] Anyway, the people at Social Security and the Social Security Administration calculated who were the biggest beneficiaries of Social Security, and it was Tobin's generation.


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[Assistant] Same generation as my father. And I said, look, it's your fault that Social Security is such a mess. You benefited, and I'm gonna have to pay for it.


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[Assistant] And he, you know, just like your feeling, you're gonna have to pay for it. Uhm, so it's even worse for you, but even my generation's not getting a very good deal. Yours is getting a terrible deal. Tobin's got a great deal. And so, he said to me, not his fault, it's my fault, because I didn't have enough children.


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[Assistant] Okay, so the question is, what happens if you, you know, what does that mean? So what Tobin meant is that if instead of having, uhm, one child for every adult,


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[Assistant] Okay, so every family has two children. In other words, instead of one child for every adult, so it goes three one three one three one, we start


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[Assistant] Doubling the, you know, the generations are growing through time. So since this is 30 years or something, we can think of the generations doubling. That wouldn't be such a fast growth rate. And so Telvin would say, you know, might have meant, if you double the generations, you're going to have


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[Assistant] Six and two is the endowment. You know, two guys at three and one, which means six and two. Then you're gonna have twelve and four. It's gonna be a gigantic, uh, growth. And so each generation, when it's old, the young guys only have, if there's six and two here now, instead of, I should use a different color, if I wrote six and two here,


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[Assistant] That each guy would have to, or two guys at three and one, each three one guy would only have to give up half, uh, would only have to give up


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[Assistant] Our fault, my fault in your generation is probably not going to have any more children than my generation. So what's the, uh, is that true, Tobin's argument?


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[Assistant] Right. Okay, exactly. And so you can't know that until you actually solve a model. So the point is that if the generations keep growing like that, uhm, the interest rate is going to go up.


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[Assistant] And so it's still going to be a loss because although you're going to be trading off


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[Assistant] Minus a half to get one, as opposed to minus one to get one. So this looks like a much better scenario. Once you get to this scenario, there's gonna be a bigger interest rate. So remember the present value of that trade is minus one plus one over one plus r.


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[Assistant] That's why it's negative, because r is positive. Here, it's minus one, minus a half, plus one over one plus r. Okay, but that's a different r. That's an r, I'll put it at the top.


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[Assistant] That's in a new economy, a growing economy, and that R is gonna be a bigger R. So you're gonna, even though...


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[Assistant] It's minus a half instead of one, this thing's gonna be small enough so you still end up losing money. Okay, but you'd never know that unless you solved it.


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[Assistant] And in fact it's still going to depend on a little delicate assumption. So I claim, so Tobin by the way never bothered to work this out, I claim that if you're going to be doubling the population like this,


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[Assistant] There are going to be a lot more people working on the land, and so the dividends of the land are probably going to grow at the same rate. So I would add a 2 here.


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[Assistant] You know, I'd make the dividends of the land also double if the population doubled. Okay, so the land dividends are gonna grow.


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[Assistant] And so now you can see why the interest rate has to go up.


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[Assistant] Because the present value of the land still has to be a finite number. The present discounted value of the dividends. And if the dividends are growing, then the interest rate had better be growing even faster if you're gonna make that a finite number.


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[Assistant] So sure enough, when you solve it, you're gonna get a higher interest rate. Okay? And so how would you solve it? Let's say the growth rate.


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[Assistant] You can just change this equation very simply. What would you do? Well, for any generation, it's the same equation except that you've got


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[Assistant] One plus G times as many old guys as you have.


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[Assistant] Oh, these are young guys. The number of young guys is 1 plus g times the number of old guys. So if it's generation t...


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[Assistant] So this would be 1 plus, at time t, this would be 1 plus g to the t minus 1, and this would get multiplied by 1 plus g to the t, okay, and then the dividend, 5,


[User] Please transcribe this text

[Assistant] So everybody's endowment is also going up, so it would be, well, actually I screwed up, it would be, uhm, the old guy 1 times 1 plus g to the t minus 1.


[User] Please transcribe this text

[Assistant] Times one plus g to the t, or t minus one, whichever.


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[Assistant] Okay, so that's the new equation, then you can multiply, you can divide through by 1 plus g to the t minus 1. So right, so this is for, this is period t market clearing equation, but you see I haven't


[User] Please transcribe this text

[Assistant] Okay, because the number of old guys is, you know, for each one of them is behaving like that, but they're now this many of them. And the young guys are behaving just as before, but they're this many of them. More of them.


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[Assistant] And then the endowments of the old have been grown that far, you know, the old generation has this many endowments, the young has this much endowments when young, and then the land we also assume grew.


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[Assistant] Now divide through by 1 plus g to the t minus 1 and that goes away. And that just leaves that. That goes away.


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[Assistant] And that goes away and that goes away. You'd have that equation. Oh no.


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[Assistant] Okay, so I took my original equation, which didn't have any 1 plus g's in it.


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[Assistant] And I just said, if I had growth in the economy, it's no big deal to take that into account. I'm still gonna have one equation, so I can still solve it. It's just that at every time t,


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[Assistant] How many old guys do I have? I have each old guy behaving the same way as before except that now, you know, there's been a growth.


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[Assistant] By a factor of 1 plus g, so 1 plus g to the t of these guys. So I take their old demand,


[User] Please transcribe this text

[Assistant] You know, the same for each guy, but different number of guys, and the young generation's demand, and I have to set it equal to the supply.


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[Assistant] But that's just the old guy's endowment, so one for each old guy, and there's that many old guys, plus the young guy's endowment, same as before, and there's that many of them, plus


[User] Please transcribe this text

[Assistant] Uh, the land, which I've also assumed has been doubling, 1 plus j is 2, so the land is also doubling.


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[Assistant] And I'm not sure whether I call this t or t minus one, but you know, either one is not going to make a big difference. Okay? Who asked the question? Who followed that, right?


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[Assistant] So now I just say I can simplify, I've got 1 plus g's everywhere, so I can cancel a lot of them out. That's all I did. So if I divide by 1 plus g to the t minus 1,


[User] Please transcribe this text

[Assistant] I just get rid of the 1 plus g to the t minus 1.


[User] Please transcribe this text

[Assistant] I change 1 plus g to the t divided by 1 plus g to the t minus 1, that's just to the first power. I got rid of this one, I made this to the first power, and this to the first power. Okay, so I can solve that perfectly easily. Okay, and I'll do that in Excel in a second.


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[Assistant] And then we can see what happens to everybody's utility. So any questions about what I did here?


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[Assistant] Yeah, it's gonna change the answer, but it's gonna qualitatively be the same.


[User] Please transcribe this text

[Assistant] Well it depends whether when I do this I want to say this is 2, 4, 8, 16 or whether I want to call it 1, 2, 4, 8, 16. So I don't know which is the right thing to, probably I should have done 1, 2, 4, 8, probably the way I have it here, which is t minus 1.


[User] Please transcribe this text

[Assistant] Okay, so the last thing to do is to, uhm,


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[Assistant] And I happen to have written a file that you can use to solve these all automatically.


[User] Please transcribe this text

[Assistant] Okay, so the first one, the first case I did is I say suppose A, that's the exponent for how patient you are, it's half. Okay, that's the first exponent.


[User] Please transcribe this text

[Assistant] Okay, so A I took to be a half, that's just what we were figuring out.


[User] Please transcribe this text

[Assistant] I took the endowments when young to be three and when old to be one and the land output to be one forever. And then whatever, you know, the price is what I'm gonna try and solve for.


[User] Please transcribe this text

[Assistant] And so, I, uh, you know, I solved the market clearing equation, squared it, and, you know, did excel solver.


[User] Please transcribe this text

[Assistant] And I got the consumption, which we figured out was 1775 when young and when old was


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[Assistant] 3.225, which adds up to, the two of them add up to five together, just as we thought.


[User] Please transcribe this text

[Assistant] And so I even calculated the utility of each of the people. I didn't took log utility.


[User] Please transcribe this text

[Assistant] Actually, I wrote a monotonic transformation. I put y to the a, z to the 1 minus a. It's easier for me to get positive numbers. That's just a, that's e to the u.


[User] Please transcribe this text

[Assistant] So I might as well describe utility as the exponent of u. Take e to it, so it's a positive number. When you do logs of small numbers you get negative, so that's easier to look at. So, that's the utility. Okay. Now we can do Social Security.


[User] Please transcribe this text

[Assistant] And then the rest of the model is exactly the same and so of course it's going to give you a different price. P.A. is different. So P.A. is smaller. That means


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[Assistant] Today's price of next year's good is smaller. It must be more discounting.


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[Assistant] So, I did the interest rate, 1 over 1, you know, 1 over 1 plus r equals p, so p, you know, the inverse of p is this thing.


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[Assistant] Okay, so if the forward weight is 161%,


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[Assistant] And if you think of that as 30 years, that's an annualized 3.2% interest rate.


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[Assistant] Before it was only a 2% interest rate annualized, right? Remember we got the one


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[Assistant] Okay, so this Social Security doubled the interest rate from 81% to 161%.


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[Assistant] Huge increase in the interest rate. So social security has raised the interest rate and so, you know, you resolve the whole equilibrium.


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[Assistant] And it had, you know, not, it didn't crush everybody, but everybody's utility went down except


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[Assistant] For the very first generation. We know they, they, they won for free.


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[Assistant] Okay, but now I could do the same thing with, uh, with growth. Okay, I could just solve that equation on the left.


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[Assistant] And so I plug in now the growth rate from generation to generation, one plus growth, and here I've got


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[Assistant] And you see that of course when the generation's growing and land is being more productive and there are more apples and stuff like that, there's just more for everybody to consume. It's actually made everybody better off.


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[Assistant] Okay, but now we see that Tobin and the interest rate is higher, way higher, 247% instead of 161%.


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[Assistant] Every generation, when young, only has to give up half a, uh,


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[Assistant] An apple and get a, you know, and get a whole apple when old.


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[Assistant] So that raises the interest rate from 400 from uhm,


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[Assistant] Okay, so, uh, it's the rate of growth. It's faster now than the growth of the economy, right? The interest rate.


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[Assistant] 247, 300% is faster than the rate of growth, which is 100%. So...


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[Assistant] Again, everybody is going to lose. They're gonna go from 3.06, they're still gonna lose by Social Security to go down to 3. But, Tobin was, I would say, is 90% right. Although,


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[Assistant] More children doesn't solve the social security problem because it's going to continue to, it's going to increase the rate of interest. So you're still going to have losers. Nonetheless, the loss is now much smaller with lots of children than it was before.


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[Assistant] So Tobin, I would say, is 90% right. If only every generation would have more children, we still would have had a crisis in social security, we still would have had, you know, this every generation complaining it was getting a bad deal, but it would be a lot worse, it would be a lot less bad than it was before.


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[Assistant] And then I did this variant depending on, you know, what we said, whether the growth


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[Assistant] I wrote a paper, uh, the newspapers were saying the same sorts of things, and I'll tell you what they were saying.


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[Assistant] Remember those pictures that we showed before of the stock market. If you discount for, if you take out inflation, the stock market seems to go in these waves where prices go up and then they come down and prices go up and they come down and prices go up and they come down. We've had five big waves.


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[Assistant] of stock markets going up and coming down. We're now in a period where they've been coming down. You know, the stock market is lower now than it was ten years ago.


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[Assistant] Correcting for inflation. In fact, even not correcting for inflation.


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[Assistant] So here's an old picture of the stock market. So this, I wrote this paper in 2005. So remember at the first class we had a picture like this. You can see the stock market was going up and down, up and down, up and down, up and down. Five waves have now come down further.


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[Assistant] This is like 2001 or 2002, so it's come down way further than that.


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[Assistant] Okay, so is there any explanation for why that would happen?


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[Assistant] So, here's an explanation I gave in a paper, which a lot of people in the newspapers were giving. I said, the baby boomers.


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[Assistant] I said, you know, all these baby boomers like me, we're getting old, we're gonna start selling our stock, and so the stock market's gonna go down.


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[Assistant] And so my, so that's what newspapers were saying too. The difference is that the economist


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[Assistant] So what I pointed out was that the, if you look at the history of live birth, you get the same cycle. Look, it went up and down.


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[Assistant] Are the, you know, the number of 18-year-olds in the country is, you know, at its all-time high, or is gonna be in two years when my poor son tries to get into college. And so they're, so and then it's gonna go down again.


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[Assistant] So this is a cyclical thing that keeps happening over and over again with baby booms and buts.


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[Assistant] And everybody knows about the baby boom after the war, my generation, the 50s and 60s, when I was born, everybody knows about that, but they don't realize that there's been baby boom after baby boom after baby boom, and this is a cyclical phenomenon. And then the thing they really don't know is that


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[Assistant] It's exactly the same as the stock market. That the stock market followed, those five patterns in the stock market were the same patterns of the baby boom. Okay, so I'm gonna end with that picture. So uhm,


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[Assistant] Okay, so a picture is worth a thousand words, but it's not that compelling an argument. You need a little bit of analytics.


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[Assistant] Suppose everybody knew that generations were gonna get bigger and then smaller and then bigger and then smaller.


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[Assistant] Would the stock market go up and then down and then up and then down as I was saying and as all these newspaper columnists were saying? Or would it just stay the same as the, uhm,


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[Assistant] Less imaginative. Economists crit- crit- you know, critiquers were saying that it couldn't have anything to do with demography because by rationality people would look forward and they'd anticipate it going down and they'd all sell before it went down so it would never go down and okay, so that


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[Assistant] So it turns out it does go up and down, okay, and that argument the economist gave doesn't make any sense.


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[Assistant] And if the rate of interest doesn't stay the same then there's no reason why the stock market has to stay the same.


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[Assistant] Go back to where we were before and change the model a little bit.


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[Assistant] So let's suppose that the model is an alternation between big, between big generations and small generations. So let's suppose that you have 6, 2, 3, 1, and 6, 2.


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[Assistant] Now I hope that wasn't the key to the result. Okay?


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[Assistant] So in the paper, of course, I had, you know, people living 80 years and I had their


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[Assistant] Income, you know, reflecting the sort of trend and income over the lifetime. But anyway, for the purposes of this...


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[Assistant] Class, let's say every generation, there's a small generation where it goes, you know, young, three, old, one. Then the next generation, which is just two guys, so they're both three one guys, so in aggregate they're gonna be six two. The next generation is three one, the next generation is six two, the next generation is three one, and it keeps alternating like that forever. Okay, now, how would you solve for equilibrium?


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[Assistant] Are there any questions here about what we're doing? So it looks way more complicated, but it's not.


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[Assistant] It's a little bit more complicated, but not much. You can still solve for this.


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[Assistant] Okay, so I'm going to not spend too much time on this, but I'm just going to show you what you would do. So what would you do? Well, by symmetry, I claim, you can guess that there are going to be two prices.


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[Assistant] So you notice that every generation only cares about the relative price between when it's young and when it's old.


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[Assistant] So there's this relative price, that relative price between consumption at time one and time two, that's going to affect the generation born at time one. It actually has no effect on any other generation, you know, these generations are born after that. So this interest rate, this relative price between these two periods, affects only one generation.


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[Assistant] Okay, so, this generation is affected by the interest rate between time two and time three.


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[Assistant] This generation is, is, is affected by the interest rate, but times 3 and times 4, every generation


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[Assistant] So by symmetry, I think you could guess, and it turns out to be true, that there's going to be a price, a relative price, I should call them small, relative price


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[Assistant] Okay, and that, the same thing is gonna happen. So this is gonna be, this relative price will be P small. This will be P big. And then we'll get P small again, here. And P big connecting these guys.


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[Assistant] And it's just going to keep repeating itself over and over again. And by symmetry, you could guess that the equilibrium would look like that.


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[Assistant] So what would I have to check to see that there's equilibrium? Well, any genera- so, uhm, let's do a, uh, let's do it over here. Let's do a small generation.


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[Assistant] Oh, okay, so we never did the first, so the first generation, yeaah, depends on whether we start with a small one or a big one. But remember, if we can clear all the markets for all time,


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[Assistant] Except the first market, that one has to automatically clear. That's, Fisher also, that was Vol Ross's insight.


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[Assistant] Okay, so we know that if we can clear all these, the first one's gonna look very different, but it's gonna clear anyway, so I don't really have to worry about it. Uhm, so we'll see why that works.


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[Assistant] What are the generations? So I'm gonna now talk about market clearing at any time except the first one, which is more complicated. The first one seems really complicated because there's this guy, Zero, who owns these dividends that go on forever. But of course, they're just worth the price of land, which he's gonna sell off.


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[Assistant] So, but then we'll come back to that in a second. So, in every generation,


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[Assistant] Every time period, you're either gonna have the, when small generation is young,


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[Assistant] Okay, what do you get? What's the, what's the market clearing equation going to be? Well, the small generation is going to be young, so that means the old generation is big. Alright, so there's a half here. So the big old guys,


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[Assistant] Their endowment is gonna be three, sorry, it's gonna be six, there's two of them, so I can multiply, I can put the two out here. Three plus one P big.


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[Assistant] So this should be p small, not p y, p small. No, I don't, because the old guy...


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[Assistant] The big generation is old, the small generation is young, so the young generation, they're consuming in their youth now, so they're looking at their endowment, the price when they're young is one.


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[Assistant] So their young endowment is three, their old endowment, their, their income is three times the price to them of one when they're young, plus the endowment of one when they're old, times P small.


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[Assistant] Divided by the price when they're young, which they're thinking of as one, right? They only care about the relative price between young and old. And that relative price is be- is determined by P small. So I could call it Pt and Pt plus one, but I know that ratio's gonna be P small. So really it only depends on the ratio, so I might as well just use the ratio, P small. Is this- this is a crucial idea that I've used a hundred times, and I think


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[Assistant] I've used it now, you know, three or four times anyway. So, but I think some of you don't quite know what the hell I'm talking about. So, somebody asked me a question if they don't know why this is right. Whoever just asked it, maybe you still don't know why it's right. Who asked this question a minute ago?


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[Assistant] Yes, you understand how I got this, or you do. Okay, but when the old guys, the old guys, which is the big generation, we're clearing time, we're looking at this time. So the total endowment is three for the young generation, their endowment is two, and the one unit of land, that's where I got the total supply of six.


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[Assistant] So this generation, when it's young, they care about the p small, the relative price between here and here. And so they're, they're, they're looking at p small, the relative price of 1 to p small. The old generation, at the same time, is looking, over their lifetime, at the ratio of consumption here to here, which is given by p big.


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[Assistant] So they've got a P big here, and they're consuming one old, so they're dividing by P big.


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[Assistant] Okay, but now we've got a second equation, which is when the, when, uh, big generation is young. So why don't you tell me what that equation's going to be. How much is the endowment when the big generation is young? So that may be clearing at this time. Here the big generation is young, so what's the endowment?


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[Assistant] Two young, young guys, each have an endowment of three, plus one unit of land. That's eight.


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[Assistant] And you can see that adds up to 6 plus 1 plus 1 is 8.


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[Assistant] Okay, and what's their demand? What's the demand for the two? So there's the old. What are the old going to be doing here?


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[Assistant] It's in this generation we're doing the market clearing. Somebody knows how to answer this. Yeaah.


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[Assistant] So this is the one old guy's endowment, two young guys who have three each, that's endowment of six.


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[Assistant] That's the supply, so what's the demand? Who's trying to buy the stuff?


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[Assistant] Okay, we're doing this one. They make their plans when they're young. They anticipate what the prices are going to be, and so how much do they plan to spend when they're old?


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[Assistant] So there are two equations and two unknowns, P big and P small, and two equations. So to solve this whole model, you could get two equations. You could, you just have to solve these two simultaneous equations, which I did. Okay, now.


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[Assistant] And then you can find the effect. So all these old economists, the economist critiquers would say, well P big should equal, okay, what will be the price of land by the way? So what's the price of land going to be in the end?


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[Assistant] What's going to be the price of land, according to Fisher, at time one? At time one, let's say.


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[Assistant] Right here, what's the price of land? Remember it's the price after the dividend is paid. So what's the price of land?


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[Assistant] Remember the dividends are just 1 plus 1, you know, 1 plus, so there's gonna be 1 plus 1 plus 1 plus 1.


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[Assistant] P small, incidentally, equals, I could always write that as 1 over 1 plus r small.


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[Assistant] So it's the price of land starting here just after the dividend is paid.


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[Assistant] Well, start telling me the formula. So if I wanna multiply, if I wanna do the first terms, what is this first term?


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[Assistant] So you would put 1 plus r small here. Okay, and now what would you put over here?


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[Assistant] Okay, very good. So now you guys really know what's going on. What would you put over here?


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[Assistant] Okay, exactly. 1 plus r small times 1 plus r big times 1 plus r small. Okay, that's that one. I'm going to stop with that too much.


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[Assistant] Okay, plus dot dot dot. Okay, so you have the idea now. What's the idea? Discounting between, you're taking the present value of all the dividends.


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[Assistant] So this, this dividend, you have to discount it by 1 plus r small. This one, you have to discount it twice. First to bring it back here, that's 1 plus r big. Then to bring it back here, that's another 1 plus r small. So 1 plus r big, 1 plus r small. The third dividend, you discount first at the small.


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[Assistant] It's not the same formula because at time two you're starting here and the first discount is P big.


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[Assistant] 1 plus r small times 1 plus r big plus dot dot dot. So this isn't the same as that.


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[Assistant] Okay, it would only be the same as that if r big was equal to r small. If p small was equal to p big. So, which one, which one do you think is, uh,


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[Assistant] That's the answer to the critics' puzzle. So you see, you've taken something that appeared in the newspapers. It sounds like common sense. If there are all these young, if there are all these middle-aged people like me, bidding up the, you know, there were so many of us who want to hold stocks. We're at the peak of our earning power, we've got tremendous amounts of money, uhm,


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[Assistant] We want to, we want to, you know, what are we going to do with it except put it into stocks? You'd think common sense that the price of stocks would have to go up. When we get old and we're selling all our stocks, you'd think the price of stocks would have to go down.


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[Assistant] Okay, so that would tell you that the interest rate was going to be, uhm,


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[Assistant] So that would, okay, so that would, so that would suggest that the price


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[Assistant] If this interest rate was low and this interest rate was high.


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[Assistant] Okay, but does that happen or does that happen? You can't know until you solve it in the model. You know, the critique, the critic said, oh that can't be right because somehow, you know, the price should even out and everybody will be looking ahead and buying or selling at the right time. You can't buy and sell at the right time because you're gonna be dead.


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[Assistant] So you don't have much choice except when you're young here to save and when you're old here to dis-save. So, you know, they seem not to have overlooked that small problem. So anyway, uhm, okay.


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[Assistant] The point is that to know the answer, you can't just reason it out verbally. You have to write down a model, solve for the model, and see what happens. And sure enough, it happens like... Okay, so we'll go back to the paper now. Well, okay, are there any questions about this?


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[Assistant] Okay, so all I did in this spreadsheet is I wrote down those two equations. So you see that I've got the, uhm,


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[Assistant] Young and the old are the same half-half log utilities. The small generation is three-one, the big generation is six-two. Land is always producing one every period, and we get two different prices.


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[Assistant] The P.A., the price is called P.A., that's the A generation.


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[Assistant] In the money making peak of the big generation, the real interest rate is small. And so that means you're not discounting very much.


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[Assistant] And so the prices are high of land. And so sure enough.


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[Assistant] The price, when the small generation is young, is 1.29, and when the big generation is young, it's 2.08. Vastly higher.


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[Assistant] So it really is the case that as the generations rise and fall, the interest rates rise and fall, and the price of land rises and falls, and everybody's rational and anticipating everything.


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[Assistant] Okay, so, so there really is, you know, it really could be, I'm not saying it's true, you know, because it could be a coincidence that these things all matched up, but the fact is,


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[Assistant] Demography can have a big effect on economic equilibrium in the stock market and you can be an economist and believe in demography. You don't have to be a Marxist or something to think demography and fertility and all that stuff is going to affect the economy. For a long time, economics tried to wall itself off from other social sciences and say,


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[Assistant] Those fertility people and, you know, all those touchy-feely people, it's got nothing to do with the real markets. Well, it has a lot to do with the real markets.


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[Assistant] Okay, so one last thing. Would you rather be in the small generation or the big generation?


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[Assistant] Yep. Okay, that's correct. So I'm screwed. And so why is that?


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[Assistant] Well, it turned out to be the utility of the, uhm,


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[Assistant] This is, uh, the utility of the big generation per person. You know, of course, adding the two people together is bigger. So per person was this, a lot less than the generation of the, the utility of the small. So why did that happen? Why exactly is that happening?


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[Assistant] So remember, I'm distinguishing sort of your peak, I'm calling young your peak earning years, and old I'm calling the stuff when you're retired and not earning very much. So why is it that a high interest rate is good?


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[Assistant] And you've got a high interest rate, that means a high return.


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[Assistant] So you, you can make a big return through your life, whereas my generation had a very low return. You know, the money, the return I'm getting now, terrible.


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[Assistant] Negative. You know, the return I'm giving you now is just hideous. But when, you know, when my parents were young, they were making an astronomical return. Incredible rates of return.


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[Assistant] And that's why it's not so good to be part of a big generation.


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[Assistant] So other people had said the same thing, they said big generations have to squeeze into the same houses, so there's less housing stock, you know, or we build more houses, the next generation comes along, there are all these houses built for them, and there are less of them to, you know, so they get better houses, and you know, everything's better when you're the small generation, and you're screwed as the big generation, and here's an example of it.


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[Assistant] Okay, so that's it for Social Security, all the things I wanted to say about Social Security.


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[Assistant] The exam, as I say, will end with uh, you know, you won't have to do the two generations and all that stuff on the exam.


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[Assistant] But the first part about solving for the .55, that one you might have to do something like that.


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[Assistant] You know, you can have a controversy in the newspapers with arguments on both sides. You never can figure out the right answer until you write down a model.


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[Assistant] And I think the course gets a lot more interesting, okay? But we needed all this background basics to have the logic of finance.


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[Assistant] But finance is really nothing without uncertainty. You know, if you don't know what's going to happen tomorrow,


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[Assistant] That's when the thing gets interesting. That's when you have to think harder. That's when people make mistakes.


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[Assistant] That's when a hedge fund can make a profit. That's when, you know, everything gets more exciting when there's uncertainty, and we have to start adding uncertainty.


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[Assistant] So since I only have a few minutes, I'm gonna spend the last few minutes just reminding you of what you're supposed to know about uncertainty.


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[Assistant] Uhm, which is this slide. Okay, so it's not


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[Assistant] So there are two kinds of uncertainty, one of which we're never going to get to. So the uncertainty that we're going to work with in this course is everybody understands what could possibly happen.


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[Assistant] So if there's something about the world that we don't know tomorrow, I'm not going to assume that it's just vague in our minds and, you know, we can't quite make it out. I'm going to assume you actually can make it out. It's just you don't know which of the possibilities are going to happen. So it's many states of the world.


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[Assistant] So a, uh, example of that of course is spinning a dice, or spinning two dice.


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[Assistant] Okay, so we can, uhm, you know, so those are all the possible sums.


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[Assistant] So, there are more states of the world than there are outcomes, notice. You can get 2 through 12 as the sum of the dice, but there's still 36 possible states of the world, and so that


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[Assistant] Random variable, the sum of the two dice, is expressed as a function. It says in every state of the world, what is the random variable's value?


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[Assistant] So that's how I'm going to be thinking of uncertainty that we're here today and a bunch of different things could happen tomorrow.


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[Assistant] And this is an exhaustive list of everything that can happen tomorrow. We're gonna have to come back and criticize this assumption, but it...


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[Assistant] You know, introduces uncertainty in a way which is still quantifiable and not vague.


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[Assistant] Okay, so you can talk about the histogram of outcomes of the dice, you know, how many ways, what chances of the chances of getting a 7, you know, 6 out of 36, etc. So this is stuff I'm sure you all know.


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[Assistant] Okay, uhm, the most famous histogram.


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[Assistant] In, uh, in all of mathematics, is the normal distribution


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[Assistant] You know, you had enough dice and you kept averaging their outcome that would be normally distributed. So lots of things turn out to be normal. One of the properties of normal is that the tail gets small very quickly.


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[Assistant] Okay, and so uhm, you're not going to get very many outliers.


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[Assistant] The normal distribution, uh, is a very common distribution. There are lots of reasons why it should occur all the time. And so, and it's also mathematically very easy to work with.


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[Assistant] An implication, as I say, of normal distribution is that it's very unlikely something extreme is going to happen because this thing goes down exponentially fast to zero. So you're almost never going to see something way out here. Yet we get these crashes


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[Assistant] Fairly frequently. You know, 10, 20, or 30 years or something, there's some gigantic outlier.


[User] Please transcribe this text

[Assistant] So clearly things can't be normally distributed, and that's called fat tail. Okay, and I'm sure you've heard about that in the newspaper. We're gonna come back to that. Okay, now there are a couple things that you need to, uh,


[User] Please transcribe this text

[Assistant] No, so you can, you can represent the payoff of any random variable as a picture, you know, in every state what it's payoff.


[User] Please transcribe this text

[Assistant] Okay, so a riskless random variable, riskless investment will pay the same amount in every state. So I still have a few minutes here. Okay, uhm.


[User] Please transcribe this text

[Assistant] Okay, so now two incredibly important concepts, which I'm sure you know, or at least the mean you know. Just the average, what's the expected payoff? So the expected payoff is you multiply the outcome in every state by the probability of the state and you add it up.


[User] Please transcribe this text

[Assistant] Okay, so there, how many different ways, uh, so if you have one dice,


[User] Please transcribe this text

[Assistant] Okay, you can figure out the expectation of one dice. It's equally likely to get one, two, three, four, five, or six, and so if you add all those up,


[User] Please transcribe this text

[Assistant] Multiplied by a six, you get three and a half. So the expectation of one dice is three and a half. The expectation of two dice is therefore, okay, so, so that's, okay, that's one dice. Okay, now,


[User] Please transcribe this text

[Assistant] The expectation of adding two dice together is of course going to be seven because the expectation of one dice is three and a half and the other dice is three and a half and they're in


[User] Please transcribe this text

[Assistant] And so the expectation of the sum is the sum of the expectation. So it's seven. Okay, so you know that. Now one more thing that you have to know is the variance.


[User] Please transcribe this text

[Assistant] So, how do you measure how uncertain you are about what's going to happen? Well the simplest number to do, like with a dice, is to say, okay, the expectation is three and a half.


[User] Please transcribe this text

[Assistant] When we don't get three and a half, it means there was some error. Our expectation wasn't confirmed. So you could just measure the error as the distance between three and a half and what you actually got. So if you got a four, you could say you were off by a half.


[User] Please transcribe this text

[Assistant] Okay, so it would be, if you got four, when you're expecting three and a half, the error is a half squared.


[User] Please transcribe this text

[Assistant] So it's, uh, you take a six times a half squared plus a six times one and a half squared plus a six times two and a half squared, that's for the high mistakes, and the low mistakes you take a half times


[User] Please transcribe this text

[Assistant] A half squared plus a half times one and a half squared plus a half times two and a half squared.


[User] Please transcribe this text

[Assistant] The expected squared error instead of just the expected error, well, for this simple reason, which you may not have thought of, if you had to guess


[User] Please transcribe this text

[Assistant] If you, if you looked at the error as the penalty for making a wrong guess, and you were forced at the beginning to say, what guess would you like to make for how the dice is going to turn out, how the die is going to turn out, and if you're wrong, we'll, we'll penalize you by the measure of error. Well, if you were just taking the absolute error,


[User] Please transcribe this text

[Assistant] Your best guess would be any number between 3 and 4.