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[Assistant] I was convinced that it was an invitation which he would not refuse, since he could never imagine that it could come from anyone but the lady.


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[Assistant] And so, my dear Watson, we have ended by turning the dancing men to good when they have so often been the agents of evil.


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[Assistant] And I think that I have fulfilled my promise of giving you something unusual for your notebook.


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[Assistant] 3.40 is our train, and I fancy we should be back in Baker Street for dinner.


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[Assistant] Only one word of epilogue. The American Abe Slaney was condemned to death at the winter assizes at Norwich, but his penalty was changed to penal servitude in consideration of mitigating circumstances and the certainty that Hilton Cubitt had fired the first shot.


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[Assistant] Of Mrs. Hilton-Cubitt I only know that I have heard she recovered entirely, and that she still remains a widow, devoting her whole life to the care of the poor and to the administration of her husband's estate. End of The Adventure of the Dancing Men


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[Assistant] I'm not with the demons. I'm not with Sable. I'm a reporter.


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[Assistant] And I wanna see Lee stopped. Just like you.


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[Assistant] To get what, Charles? What do the demons need to get at Grand Central?


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[Assistant] Hi, Miles. I just wanted to see how you're doing with the news about Lee. Look, if you didn't want to work there anymore, May and I would understand.


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[Assistant] That's true. Assuming he's doing the right thing. I got you that job. I'd hate for you to keep doing it if you think it's wrong.


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[Assistant] I know we would. And Miles, I'm proud of you too. Anytime you wanna talk, just call.


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[Assistant] MJ's right. I built the neural interface. That means I can destroy it. There must be something at the lab I can use.


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[Assistant] But now I have to destroy it. With a little creation of my own.


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[Assistant] Let's hope. Okay, closing in on you. Be there soon.


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[Assistant] I'm doing everything in my considerable power to find that canister. However, right now, it would help me for you to go back to your lab. And do your damn job.


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[Assistant] I know I messed up. I'll let you down.


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[Assistant] Doesn't have to be like this. You, me, hating each other? That's how it happened between me and your dad.


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[Assistant] Today what we're gonna do is continue our discussion of factor markets by essentially talking about uhm, how capital markets impact real world decisions.


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[Assistant] So last time we talked about the capital market, we talked about essentially the way that firms finance their capital.


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[Assistant] It's by going to a pool of savings that individuals decide on how much to make. Individuals make an inter-temporal choice on how much to save. Actually, technically make an inter-temporal choice about how much to consume each period. That then yields an amount of savings and then based on that pool of savings firms borrow at some interest rate high and they decide how much to invest. Now, today we're going to talk about another interesting applications that arise from capital markets that are important in the real world.


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[Assistant] Now, the key insight when we think about capital markets is that a dollar tomorrow is worth less than a dollar today.


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[Assistant] A dollar tomorrow is worth less than a dollar today. That's because if you had the dollar today, you could productively invest it and have more than a dollar tomorrow. So a dollar today is worth more because you could do something productive with that dollar if you had it today. Okay?


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[Assistant] What that means is that dollars in different periods are worth different things. You can't just add them up.


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[Assistant] Okay, the analogy I like is thinking about, imagine you had a pound of apples, a pound of steak, and a pound of gold. You wouldn't just add them up and say I have three pounds. That'd be useless. You'd want to know what each is worth, and you'd want to add up the dollar value of them.


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[Assistant] Okay, it's a similar thing with money received over time.


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[Assistant] You can't just say I'm getting a dollar today, a dollar next year, and a dollar five years from now. They aren't the same thing. Money received at different points of time are worth different amounts.


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[Assistant] Because money received in the future forgoes the possibility of investing it today. Okay.


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[Assistant] So what do we do to deal with this? Well, in economics, we deal with this by the concept of present value. Present value is


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[Assistant] The value of every period's payments in terms of today.


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[Assistant] So the way we deal with the fact that money in different periods worth different amounts is by what we call discounting it back to today.


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[Assistant] We said to take future dollars and discount them back to today to get present value. We discount them because future dollars are worth less. Okay. So let's think of it this way.


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[Assistant] Suppose that, uhm, the interest rate, uh, is 10%. Let's do an example. Imagine the interest rate, I, is 10%.


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[Assistant] And let's say that you want to have $100 next year. You want your, you want next year you want to have $100. Well how much do you have to put in the bank today? Okay?


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[Assistant] Well, we can solve the equation, which is that you want the amount you put in the bank today, let's call that y.


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[Assistant] Times 1 plus the interest rate, because that's what you make by having the bank, equal to 100. That's the equation you want to solve. Right? The money amount you put in today, y, times 1 plus the interest rate, you want that to be equal to 100.


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[Assistant] If you put $90.90 in the bank today at a 10% interest rate, you will have $100 tomorrow.


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[Assistant] More generally, we say that the present value of any future payment


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[Assistant] Is the future value, the amount you get in the future, over 1 plus i to the power little t, where t is the periods in the future.


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[Assistant] So money received T. periods in the future today.


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[Assistant] That is our general formula for how we think about present value. You take all the future payments and you discount them back to today by dividing by one plus i to the t.


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[Assistant] Now that works well if there's a future payment and one future payment coming, but what if, as in many cases, there's a whole stream of future payments coming? Well the logic then is the same.


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[Assistant] You just wanna take each future payment and discount it by how far it is in the future. Okay?


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[Assistant] So suppose that, uh, you say, uhm, that you want me to loan you thirty dollars, and that you'll pay me back ten dollars each of the next three years. Okay? And suppose the industry is ten percent. Well, I will say no to that.


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[Assistant] Because I will say, if you're going to pay me back $10 each of the next three years, then what's the present value of that? The present value is next year's $10 over 1.1, because the interest rate is 10%.


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[Assistant] Plus the ten dollars the year after that, over 1.1 cubed.


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[Assistant] If I, if I give you $30 today, and you give me $10 back each of the next three years,


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[Assistant] I'm losing money. Why? Because if I'd simply taken that money and invested it in the bank.


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[Assistant] I would have had a lot more than the $30 I'm going to get for you after 3 years. Okay?


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[Assistant] So the money that comes in the future must be discounted back to today. That's the key insight of present value. You can't just add it up. You've got to put it in today's terms by discounting it by the interest rate and how far it will future. Yeah.


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[Assistant] So we're assuming right now, we're not dealing with inflation, we're assuming a world where prices don't change. We'll come back to inflation in a few minutes. But for now, just assume that prices don't change. Okay? So basically,


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[Assistant] Plus, dot, dot, dot, dot, dot, dot, for how many periods you get it. So if you're getting a payment F over a certain number of periods, you've gotta discount it by how many periods you're gonna get it. Okay? Or more generally,


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[Assistant] A common formula we'll ask you to use in this class is to think about the formula for a perpetuity. A perpetuity is a flat payment you get forever. So if we take the infinite sum of this equation, we can summarize it as present value approximately equals f over the interest rate. So if I promise you to pay you forever a certain amount f,


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[Assistant] That is worth F over the interest rate. So in other words, if the interest rate is 10%, a promise to pay you $10 forever is worth about $100.


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[Assistant] That's a rough, that's just the infinite sum. If you read A Beautiful Mind, John Nash drew that in his head. But, I can't, but that's just the formula. Okay?


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[Assistant] So basically, that is the general formula for perpetuity.


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[Assistant] And that makes, uhm, and that makes, uh,


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[Assistant] Life easy. We'll give you a lot of examples where we, you know, cause if I say I want you to pay him for eight years in the future, you got to write out eight terms here. It's a pain in the ass. So it will say is money forever. And then you can just use the shortcut, which is the present value for a perpetuity. It's just F over I. Okay. Questions about that. Yeah.


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[Assistant] That's a great point. Yes, I'm assuming constant interest rate over time. Now in reality, you'd want to have each period's interest rate here, and then you can't use this formula. Because the interest rate itself is changing. Very good point. Okay? Now, the other way to think about this,


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[Assistant] Is, instead of thinking just, this will be easy for most of you, but just it's useful to think it through. Let's flip on his head and not think about present value, let's think about future value.


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[Assistant] This is a useful tool as well, it's slipping on its head. Okay? So let's think about the value of a future stream of payments. Well, by the same logic we wrote before, future value, by the same logic we wrote before,


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[Assistant] If you're gonna have money that's tears in the future, the future value of that money that you're gonna get,


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[Assistant] Okay, if you're gonna basically take your money and invest it, you're gonna have money that you can invest today and put it in the bank at some interest rate, then the future value


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[Assistant] Is the amount you put in times one plus the interest rate.


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[Assistant] So I've simply reversed that formula, present value, future value.


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[Assistant] So basically, future value, if you put money in the bank at some interest rate, you're going to get to have, uhm, uh, over time, uh, that money times one plus i to the t.


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[Assistant] Now, the reason we write this formula out and sort of flip it for you is because I want to highlight the key feature here that I want to drill into your heads.


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[Assistant] I don't know, I guess 10 things I most care you leave this course thinking about if you're not going to major in economics for remembering is the beauty of compounding.


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[Assistant] With a formula like this, you earn interest on your interest. If you leave money in the bank, you don't just earn interest on the initial amount you put in. You earn interest on the interest you earn over time. Okay? And this can be quite large. So let's do a simple example. Okay?


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[Assistant] Just to show you how big this can be and to get you all thinking about what you should do with your money when you get a job. Okay, imagine you plan to work full time from age 22 to age 70.


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[Assistant] We're daunting to think about now. Probably most people retire after 70 by the time you guys retire, but let's just think about 22 to 70. Okay.


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[Assistant] And let's say that you can save at a constant 7% interest rate. Inflation is zero, the interest rate is constant. Make life easy. 7% interest rate. Okay?


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[Assistant] And let's consider two different plans you have for savings. Plan one.


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[Assistant] For the first 15 years that you work and then stop saving.


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[Assistant] After the first 15 years of putting $3,000 in the bank.


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[Assistant] Okay, that's, now that's not just 15 years times, that's bigger than 15 times 3000, cause you're earning interest along the way. Okay, that's not 15 years. Then you're just gonna let that sit there.


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[Assistant] And that's gonna sit there. Remember, after 15 years, you started working at 22, you're only 37 years old.


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[Assistant] That's gonna then sit there for the next 33 years.


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[Assistant] You're not gonna touch it, you're not gonna save anymore. What that means is after 33 years, this turns into 75387 times 1.07 to the 33rd. Okay, after 33 years,


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[Assistant] Okay. So you say $3,000. That's not a lot of money. You guys can make a lot of money, $3,000 for 15 years. And then you never had to save again. Contrast that with different approach.


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[Assistant] Let's say you say, look, that's stupid, I'm young, I'm in a party, I'll worry about retirement when retirement is closed, so I'm going to save nothing the first 15 years. And then I'm going to save $3,000 every year.


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[Assistant] For 15 years, I'm going to save nothing. Then I'll save $3,000 every year. Okay?


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[Assistant] Well, if you do that and do the math, you end up with, when you retire, 356,800.


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[Assistant] In this case, you saved for more than twice as many years. You saved for 33 years. And you ended up with half as much. That's the miracle of compounding. The earlier you save,


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[Assistant] The more money you can make it along the way. And that's why you guys need to start saving right away. Yeah.


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[Assistant] Then I save for the remaining 30, I save $3000 for the remaining 30 years of my career.


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[Assistant] Okay, so literally in plan one, I stayed for 15 years and then I stopped. Here I stayed for 33 years.


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[Assistant] Okay, now, this is actually pretty, I can act, this is one of the few things in this class my kids couldn't understand when they were little. Because, haven't you been to the Boston Science Museum? And you guys been, okay, there's a little kid area where they've got this ramp. And you can essentially drop balls down a ramp.


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[Assistant] And one ramp is flat and then steep, and one ramp is steep and then flat. And of course the one that's steep and then flat wins. It's faster. And that's just because of compounding. That's because acceleration is compounding.


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[Assistant] Okay, so basically the point is that the earlier you start saving, the more money you'll have. And that's why you guys should pay attention when you're offered a job and offered a 401k and not think retirement, I'll never retire.


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[Assistant] You say, no, I want to save now, because the more I save now, the more that'll compound by the time I retire. Okay?


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[Assistant] Now, you can actually see this. It's not just MIT students have to think about this, but professional athletes. So, probably none of you have heard of Bobby Bonilla. Any of you guys heard of Bobby Bonilla?


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[Assistant] No? Okay, well, if you were 25 years ago in this class, if you weren't just Fortune Warner or Bobby Bonilla, he was a pretty good player, uhm, uh, in his time. And, uhm, he retired, uhm,


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[Assistant] Uh, he, but by the end of his career, he was kind of a slacker. He wasn't really worth much. He was playing for the Mets. And the Mets said, look,


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[Assistant] You have a contract, we're just going to basically buy, pay the remaining 5.9 million on your contract in 1999, give you the money. Most athletes would have said, great, I'm off to Vegas. Bobby Bonilla didn't. He said, well, look, I've got enough money right now, but I might need the money later. So instead, why don't you defer the money at an 8% interest rate and pay me starting in 2011, when I'm getting close to retirement and need the money. They were like, great, that's really great. We don't have to pay you now. That's great. Well, Bobby Bonilla,


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[Assistant] By the time his payments started in 2011, they had grown to 30 million dollars.


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[Assistant] And every year on a certain day, it just passed the reason they call it Bobby Bonilla Day.


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[Assistant] Bobbie, who's now like 70 years old, gets a one, gets a million dollar check from the Mets every year. Okay? Because he's patient enough to put this off and get the virtue of compounding.


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[Assistant] Okay, so this is sort of, if Bobby Bonita, you know, stupid baseball player can do it, you guys can do it.


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[Assistant] So, make sure that you guys are saving when you start your jobs. Okay, questions about that?


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[Assistant] Okay, now let's get a little bit realistic and let's recognize that in life prices aren't constant, but rather we have inflation. And how does that affect our thinking here? How does inflation affect the way we think about this problem? Well it turns out it actually adds


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[Assistant] One step, but it's actually a pretty easy step to put in. It actually turns out you can add inflation without doing a whole lot of work.


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[Assistant] So let's talk about first what inflation is. Inflation is the rise in the price level year over year. Technically the inflation rate is a percentage concept. It's the percent rise in the price level year after year. You might say the price level of what?


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[Assistant] Of a banana, of a computer, of what? Well, what the government does is they form something called the Consumer Price Index. The CPI, did I talk about the CPI yet?


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[Assistant] Okay, I'm sorry, I just, I hate repeating myself. Okay, so they formed something called the Consumer Price Index. What's the Consumer Price Index? Literally the government every quarter, I believe it is, and maybe every month.


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[Assistant] Goes out and gets the prices of a basket of hundreds of goods. They literally say what does a banana cost this month compared to last month?


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[Assistant] What does a laptop cost this month compared to last month, et cetera?


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[Assistant] So they go out and they price this bundle of goods and then literally they just ask, how has the price, they then take a weighted average of that bundle where the weights are consumer spending. So consumers spend a lot more of their income on housing than bananas.


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[Assistant] Essentially a weighted average of prices in society, and then they create an index. 1982 is normalized to 1.


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[Assistant] And they just say how much in percentage terms did that weighted average bundle go up in price? Okay? And you can see that in figure 17-1. Here's the historical CPI.


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[Assistant] So basically what you see is this is the level of the CPI, which is sort of meaningless.


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[Assistant] We care about is inflation, which is the year to year, uh, percentage change in the CPI. And what you can see is basically it's going up. Prices are going up.


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[Assistant] It went up very steeply. If you look from 1970 to 1980, the slope there is much higher than the slope before or after. We had very rapid inflation in the 1970s.


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[Assistant] It then, it then sits flattened, and inflation has been much slower, and inflation averages about 3% a year. Okay? So basically, that's how we measure inflation. Now, the question is, how does that affect our thinking about present value, if there's actually inflation? And the bottom line is, we don't care about dollars. We care about how many goods we can buy.


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[Assistant] Therefore, it doesn't matter what's happening to how much money we have. It matters what's happening to how many goods we can buy.


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[Assistant] Therefore, what we care about is not what we call the nominal interest rate. We care about what we call the real interest rate, R.


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[Assistant] Minus the rate of inflation, which for some reason we use pi even though it's also profits. So sorry about that. Okay.


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[Assistant] Is how much more I have in terms of goods I consume.


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[Assistant] Not how much more I have in terms of dollars, which actually in the end doesn't matter. Okay.


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[Assistant] So, suppose that I'm gonna save $100 at a 10% interest rate. Let's go simple example. I'll save $100 at a 10% interest rate. Okay? What I, then next year I'll have $110. But that's irrelevant. What I want to know is how many goods can I buy next year?


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[Assistant] Okay, and let's say skittles cost a dollar this year, and there's no inflation, so those cost a dollar next year.


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[Assistant] Then what that means with a 10% interest rate is you can buy 10 more bags of Skittles next year. This year your $100 could buy you 100 bags of Skittles.


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[Assistant] Next year $110 to my 110 bags of Skittles. So you are 10% richer. But now let's say the price of Skittles goes up 10%.


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[Assistant] Well what that means is you can only buy the same amount of Skittles next year as you could buy this year. You could buy 100 bags this year and 100 bags next year.


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[Assistant] So it doesn't matter that you have $110 next year, who cares? You can only get the same amount of Skittles.


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[Assistant] What you care about is the goods you can buy. When we worked on utility, we didn't put dollars in utility function, we put consumption.


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[Assistant] So the interest rate you care about is the real interest rate. If the nominal interest rate is 10%, but inflation is 10%, then the real interest rate is zero. You can't buy any more goods next year.


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[Assistant] All the money you made by putting in the bank got eaten up by how much more expensive things are.


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[Assistant] So what that means is all the math we've done and everything we'll talk about can all goes through.


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[Assistant] You just need to be thinking about using the real interest rate, not the nominal interest rate. Okay? But otherwise, everything we've done goes through.


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[Assistant] You just need to essentially think about this in terms of how many goods you can buy, not how much money you have. Now, this isn't quite, let me just take two minutes and do a little macroeconomics. This isn't quite as simple as it sounds.


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[Assistant] Because of course, you see in the bank eye, in the bank window eye, you don't see pie. You don't see inflation. That's what we'll reveal next post.


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[Assistant] So really, technically, you don't have to know this, it's just for those who care. Uh, you don't have to test. Technically, what you really want is expected inflation.


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[Assistant] Right? When you think of putting in the money in the bank, you know you'll earn 3%. The realest rate is that minus what you think inflation is going to be. Right?


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[Assistant] So it actually becomes complicated. It's not as simple. X post, it's easy to find the real interest rate. X ante, it's not so easy. Because it depends on what you think inflation is going to be. There's some tricks there. There's also a bunch of tricks in measuring the inflation rate. So for example, like I said,


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[Assistant] The Bureau of Labor Statistics goes out and has a bundle of 600 goods and it gets their prices.


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[Assistant] But what is a good? I mean, a banana is a banana. But a laptop, what the hell is a laptop? How much RAM does it have? What's the graphics card? Uhm, you know, uh, how fancy is the display? Well, the Bureau of Labor Statistics doesn't go out and price literally hundreds of laptops. It prices one or two. And the problem with that is the following.


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[Assistant] Let's say you find that today a laptop is a thousand, and tomorrow it's fifteen hundred.


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[Assistant] But it can do, let's say today a laptop's a thousand, and tomorrow it's fifteen hundred, but it can do a ton more stuff.


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[Assistant] Well, we would say inflation's 50%, but that's not really right.


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[Assistant] Cause the good you're consuming is not the laptop, it's the computing ability of the laptop. And that's gone up.


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[Assistant] So to say inflation's 50% is wrong. Inflation's 50% minus the quality improvement of the better laptop you got.


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[Assistant] Think of it another way. Imagine laptop prices didn't go up, but RAM doubled. Okay? Would you say you're no better off buying a laptop with twice as much RAM at the same price? No, you're better off. But our inflation concept would say no, you're the same off.


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[Assistant] So, the trick here is it's simple in practice, and we'll pretend it's simple to say R is I minus pi. But two tricks, A, it's expected pi, which is hard to guess. And B, inflation is really hard to measure.


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[Assistant] Because there's things like quality bias and other things. There's a whole field of macroeconomics worrying about inflation measurement. So we'll spend a lot of time on it, but it's just sort of the kind of interesting


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[Assistant] We, we, just to sort of talk about how sort of at high level we go things here, like everything else in this class, largely we get it right.


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[Assistant] Largely expected inflation is not too badly modeled by last year's inflation. And quality bias we can model and stuff. So this isn't a bad model.


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[Assistant] But it just sort of points to some of the subtleties you have to deal with in reality when you try to implement these basic sort of formulations. Okay? Now, with that in mind, I'm gonna now say, let's assume inflation's zero again. Okay? So we'll go back and use i, and we'll use i interchangeably with r for the rest of this course.


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[Assistant] Okay, unless asked differently. Unless told differently, assume inflation zero. So i and r are interchangeable. With that in mind, let's go to the next topic.


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[Assistant] How do people model? How do people make decisions over time?


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[Assistant] And there's a simple answer. So this is tricky because if I said to you, Hey, I'm going to give you what you want, $30 or $50.


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[Assistant] You'd say, I want $50. But actually, you shouldn't say that. You should say, over what period of time am I getting the 30? And over what period of time am I getting the 50? If it's today, I want 50.


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[Assistant] But in the 50s, 20 years in the future, in the 30s today, I might want the 30.


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[Assistant] What that means is you have to evaluate choices in present value terms.


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[Assistant] You can't just add up the money. You have to evaluate those choices in present value terms. And then you need to pick the option with the highest present value.


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[Assistant] So once again, let's come back to athletes because athletic contracts deal with this all the time. Let's imagine an athlete considering two different contracts. Okay. Contract one pays, contract A pays a million dollars today.


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[Assistant] Okay, now when you read in the newspaper, you'll see this guy got offered a million, this guy got offered two million. That's what the newspaper will say, but that's wrong.


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[Assistant] Because these are paid at different periods of time that are different amounts. Indeed, the present value of the first contract is what?


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[Assistant] One million dollars, it's today. What's the present value of the second contract? Someone tell me how to write that down. How to write down the present value of the second contract. Yeaah.


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[Assistant] One plus the interest rate to the ten. Right? Because you're getting it in ten years. Okay? So essentially,


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[Assistant] Uhm, that means that whether it's a better deal or not depends on the interest rate. Indeed, if the interest rate is 7%, and the interest rate is 7%, this has a present value of 1.3 million. So it's a good deal. If the interest rate was 14%,


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[Assistant] So whether or not this is a better or worse deal depends on the interest rate. Why is that? Why is this a worse deal the higher the interest rate? Yeaah.


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[Assistant] Exactly. He could have invested it earlier, gotten the compounding, and had way more money in 10 years. So, the higher the interest rate, the more you want to get your money up front and save it, the less valuable is money in the future. Okay?


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[Assistant] Now, so essentially what this says, you have to always use present value to bring things into current dollars. Now this is not an abstract concept. Let's take Max Scherzer, who's a pitcher with the Washington Nationals.


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[Assistant] Max Schurzer, uhm, a couple years ago signed a seven year


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[Assistant] Two hundred, uh, seven year, two hundred and ten million dollar contract.


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[Assistant] Which he was able to brag was the second highest ever signed by a pitcher.


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[Assistant] And the tenth highest contract ever signed by any baseball player. Seven years to ten. But in fact,


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[Assistant] Uhm, that contract was not, we're gonna pay you thirty million dollars a year for seven years. It was, we're gonna pay you fifteen million dollars a year for fourteen years.


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[Assistant] You're gonna play for only 7. We're gonna pay you over 14 years.


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[Assistant] So in fact, in present value terms, it was worth somewhat less. If you use the current interest rate when you signed it, which is about 4.7%, it was only worth actually $166 million. They're not too shabby.


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[Assistant] But suddenly drops the 20th most viable baseball contract and about fourth among pitchers.


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[Assistant] So Max Scherzer was able to feel better about himself that he signed to, you know, this valuable contract. But in fact, it was worth less than he thought. I mean, shed no tears for Max Scherzer. He's doing fine. But it was worth less than he thought.


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[Assistant] Or maybe an example that's more in our mind with the Mega Millions, think about a lottery winner. So if a Mega Millions winner gets 290 million dollars, which sounds like a great deal, that's paid out over 20 years.


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[Assistant] So it's not 290 million dollars, it's 14 and a half million for each of 20 years. So in present value terms, if we think about a 7% interest rate, then that's not 290 million, it's 164 million. Once again, not too shabby. Okay. But a lot less than the advertised amount. So we have to take these dollars and put them in present value. Okay.


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[Assistant] So now, now here's an interesting question for that. If you look at the recent lottery,


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[Assistant] Okay, you had a choice of the person, one person won 1.6 billion. One person won that. One person in South Carolina won that. And they were given a choice.


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[Assistant] How should I decide whether to take the 1.6 billion, paid over 30 years, so 1.6 over 30, paid in equal installments, you know, uh, over time.


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[Assistant] Versus just getting a lump sum today. Not of 1.6 million, but a less lower amount. How should they think about that?


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[Assistant] They should have a present value. They should say, well, what do I think the interest rate's gonna be? If I think it's gonna be really low. Let's say that the interest rate's going to be zero. Then which deal should I take?


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[Assistant] So essentially it becomes a debate of what you think the interest rate is versus what the state thinks the interest rate is.


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[Assistant] They're setting those two to be equal under some assumption of the interest rate. I don't know what number they chose, whatever number they chose. It was some number they chose because this is our assumption of the interest rate. You've got to decide, do you think this rate is going to be higher or lower? If you think it's going to be higher than the state thinks it is, then you want the money up front.


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[Assistant] Let's go and think about how do firms make investment decisions?


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[Assistant] Of current consumption for future consumption. It's about putting some aside today by spending money on a machine which will deliver you benefits in the future.


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[Assistant] Now this adds one wrinkle to what we've done so far.


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[Assistant] Which is that, we've only talked about money that's always positive, some money you get in the future.


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[Assistant] When you're making an investment decision, it's a little bit more complicated because you're actually spending money today to make money tomorrow. So in that case, we talk about what we call net present value, which is the same thing, it's just the last four negative values.


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[Assistant] Net present value, which is essentially saying in every period you want to count for the cost of that period and the benefits of that period.


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[Assistant] And you want to invest only if the net present value is greater than zero.


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[Assistant] So for example, think about a project that has a stream of payments in every period of R sub i. Every period has got a stream of payments of R sub i. And a set of costs of C sub i.


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[Assistant] The cost of the upfront investment, maybe the maintenance of the machine, whatever it costs to run it. Okay. Then the net present value of that investment is R0 minus C0.


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[Assistant] So basically what you want to ask is,


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[Assistant] Taking each period's cost of benefits into account on net, is it greater than zero? Okay.


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[Assistant] So the key point is that basically sometimes investments which have upfront costs can be valuable as long as the long run benefits are large enough.


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[Assistant] So if you think about an investment that's got a hundred, so imagine, think about a simple, trivial example of, uhm, the first period you buy a machine.


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[Assistant] And it costs, uhm, and it costs $100. So C0 is 100. And let's say for every period they're actor, that machine will deliver you revenues, revenue I, revenues for I greater than 0, of 200.


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[Assistant] But it will have maintenance costs, costs i greater than zero, of 50.


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[Assistant] So what's the net present value? Well, the net present value is simply minus 100. And let's say the machine is going to last forever. Minus 100 plus 150 over i. Think about that for a second.


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[Assistant] Basically what we're saying is, you're throwing 100 out of today, so that's negative, but every period in the future you're gonna net $150. Because you're gonna make $250 maintenance costs.


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[Assistant] And we have the formula, so we just apply the formula for perpetuity. We have a set of future payments of $150. So your net present value is minus 100 plus 150 over i. So let's think about, look at this formula for a second. What does that say? What is the relationship?


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[Assistant] Between what the firm's going to want to invest and the interest rate.


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[Assistant] What does this imply? The relationship is between a firm's desire for investment and the interest rate. As the interest rate goes up, will firms want to do more investment or less investment and why?


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[Assistant] Will firms want to be more eager to buy machines or less eager to buy machines, and why? As the industry goes up. Yeaah.


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[Assistant] I think an easier way to think is borrowing. Just think about, they got a bunch of money. Apple's got a bunch of money today they're sitting on. If they buy the machine, they're going to get this return.


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[Assistant] If they don't buy the machine, they can put it in the bank or invest in Apple stock and get some interest rate high.


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[Assistant] The higher the alternative, the higher the interest rate, the less they want to invest or think of it this way. The interest rate is the opportunity cost of investment.


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[Assistant] Okay, the more the firm invests in their machines, the less they can earn saving through some other mechanism. And the price that they pay by forgoing that other savings is I. Okay, yeah.


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[Assistant] Basically, you always want to try to make as much money early as you can and make the cost as late as you can. For any given amount, you'd absolutely like to shift your, you'd absolutely like to do that.


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[Assistant] That's why we'll talk about this in my public finance class. We talk about why when you're paying taxes, you always want to try to find shenanigans that allow you to pay your taxes later.


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[Assistant] So for any given amount of taxes, the later you pay it, the more it costs, the less it costs you.


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[Assistant] This is a key macroeconomic concept. You'll often hear in the news, high interest rates are bad for business. And you might have thought, why is that? This is why. High interest rates are bad for the economy, you'll hear.


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[Assistant] Why are high interest rates bad for the economy? You might say wait a second, that makes no sense. High interest rate means I earn more in my savings. Why is that bad for the economy? It's bad for the economy because it lowers the demand for capital.


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[Assistant] Because the higher the interest rate, the less firms actually want to invest, the more they just want to stock their money away in the bank. Okay?


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[Assistant] So that is kind of, uhm, that's the key, uhm, that's the key question. Now, then let me ask another question. If you're a firm, what's the right eye to use?


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[Assistant] If you're a firm thinking about this investment decision, we know the higher I is.


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[Assistant] The less you want to invest, but what is I? Once again, forget inflation, inflation zero. What's the right, what we call firm discount rate?


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[Assistant] The discount rate is the amount by which firms are going to discount future dollars to bring them back to today. How does the firm think about what eye to use? What eye should the firm use?


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[Assistant] That's a good point, but, but, but, but the way they do is they write down the math and they plug in an i. What i do they plug in?


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[Assistant] Yeaah. Well, it might be, but it's not, there's not one answer. What's the general answer the firm wants to use? What's the general answer?


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[Assistant] That the firm, if you're a firm thinking about making an investment and you want to discount that investment, what do you want to discount it by? Yeaah.


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[Assistant] So if I'm thinking about building this machine, when I discount it, I want to think about what's the next best thing I could do with that money. That's the discount rate I want to use.


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[Assistant] So in a world where firms either can buy a machine or put it in the bank, it's easy. It's the bank interest rate.


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[Assistant] But life's not that easy. Firms have dozens of investments.


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[Assistant] So where every investment you want to discount it by the next best thing you can do with the money. The concept of opportunity cost, that's why it's the very first thing we taught in this class. Opportunity cost is always what drives things. Okay? Questions about that. Now, this isn't just for firms. This same math applies to consumers as well. Let's think about me.


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[Assistant] A number of years ago, I had to decide whether to insulate my ancient house. Okay? Let's write down the numbers to sort of think how this worked. I had heating bills at that time, back when gas was cheaper, of about $2,000 a year, was my heating bills for the house. Okay? The best estimate I could get


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[Assistant] Was that if I insulated my house, I would lower my heating costs by 25%.


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[Assistant] So my heating costs would fall by $500 per year.


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[Assistant] But to insulate my house, I had to pay the guy to insulate it. And that cost, the insulation, cost $4,000. How do I think about whether I should insulate or not?


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[Assistant] I should say, I'll assume I'm gonna own the house forever, or at least long enough that I can treat it as forever.


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[Assistant] And I write down that formula. And what that formula says is that if I think the insurance is less than 12.5%, I should insulate.


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[Assistant] If I think the interest rate is more than 12.5%, I should just invest the money.


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[Assistant] And use the returns of that investment to pay my higher heating bills. So it all depends on what the interest rate is. Okay? Now, so that's why, and I did it, I insulated. But that's exact, so the same logic we could think of,


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[Assistant] Is, uhm, uh, is basically, uhm, essentially the same idea as firms. You wanna think about the upfront costs and the long run returns. Okay, now here's a fun economics question. What if I don't intend to hold the house forever? I would argue I should still use this formula. Why? Yeah.


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[Assistant] How much are we raised it by? Exactly 500 of our eyes. So I'm going to insulate and sell next year.


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[Assistant] The last thing I want to talk about is the fact that these decisions are not just relevant. You guys are like retirement, business machines, insulation. God, you're old, John. I don't care about any of this stuff. Well, let's talk about something you care about, which is going to college. Let's talk about your decision. You've already made it, but you've got a little sibling and they're deciding whether to go to college.


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[Assistant] Okay, well let's, and, and, and they're not gonna go to MIT. They're gonna go to a more typical school. And they've gotta decide whether to go to college.


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[Assistant] Well, in fact, their decision is an investment decision, just like any other investment decision.


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[Assistant] What they're investing in is what we call their human capital.


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[Assistant] When you get education, you're investing in yourself, just like you invest in a machine.


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[Assistant] Because you are, you hope, raising the value of what you can do, of what you can earn, by investing in learning stuff. Well that human capital investment has the same features of any other investment. There's an opportunity cost, which is what?


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[Assistant] Uhm, you actually, uh, it actually becomes a harder decision than you might think. So let's think about a simple example.


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[Assistant] Let's imagine that if you don't go to college, you work from age 18 to 70. And if you do go to college, you work from age 22 to 70.


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[Assistant] So ignore grad school, okay? Four years of college, either start working at 18 or start working at 22.


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[Assistant] And let's say college costs $35,000 a year, obviously not MIT. Okay, let's say college costs $35,000 a year. Okay.


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[Assistant] Uhm, you could've, let's say that if you worked, while you were, if you worked starting in high school, you could've earned, uhm, actually, Patricia, we don't have the, uh, yeaah, you could've earned $20,000. You could've earned $20,000.


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[Assistant] If you'd, uh, if you'd, you could have started at $20,000 if you'd gone to work at age 18. Okay? Well we can actually graph what this looks like in figure 17-2. 17-2, if you think about age 18, from age 18 to age 22, that's the green area.


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[Assistant] If you go to college you give up the $35,000 in tuition and the $20,000 you could have earned. The bottom line


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[Assistant] Is basically, the red line is your lifetime earnings if you go to high school. If you don't go to college.


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[Assistant] The green, the green line is your lifetime earnings, the blue line, I'm sorry, is your lifetime earnings if you do go to college. Empirical estimates suggest at age 22,


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[Assistant] The typical college graduate earns $45,000.


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[Assistant] Yes, you are not the typical college graduate. The typical college graduate is $45,000, and the typical high school, non-college educated person is $28,000. So at age 22,


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[Assistant] You come out of college earning 45 and if you've not gone to college, you're earning 28. Not you, but a normal person. Okay?


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[Assistant] But moreover, knowledge you earn more when you leave college, your earnings grows faster.


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[Assistant] So if you're college educated, it not only means you earn 17k more at 22, it also means your earnings grows faster. So that by age 51,


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[Assistant] The average college educated person earns $80,000, while the average high school person earns $45,000.


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[Assistant] So how do we think about this decision? Well, the cost is the green area.


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[Assistant] The cost is over four years, you could have earned money, and you wouldn't have to pay tuition. The benefit is the yellow area. Over that entire time after graduation, you're making more money.


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[Assistant] Now obviously in terms of size, the yellow area is much, much bigger than the green area, but the yellow area comes later.


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[Assistant] But that's not necessarily true, because the green comes now, and the yellow comes later. Indeed, if you look at the table,


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[Assistant] This actually shows the net present value of going to college and high school.


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[Assistant] And what this shows is at low interest rates, you're much better off going to college. So if there's no interest rate,


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[Assistant] Okay, then college is a much, much better deal. You're net present value.


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[Assistant] Of earnings, if you go to, your net presently go to college is 2.6 million, which is only 1.6 million if you don't go to college. But once the interest rate gets above 8%, it suddenly becomes a worse deal to go to college.


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[Assistant] That is at only a 9% interest rate, which existed not that long ago. Okay, in our history. It was actually a worse deal for an average person to go to college. Yeah.


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[Assistant] If it's a, if it's a grant, then yea, you should just take that out of the cost. But if it's a loan, depends what interest rate you get the loan at. If the loan is at the market interest rate, then it's no different. Right?


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[Assistant] But that's a great point, which is why college financial aid comes in two forms. Grants for very low income people, and low interest loans for other people. Why do we have low interest loans for college? Because of this graph.


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[Assistant] Because we're saying we want to, we think people need to invest in their education.


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[Assistant] We're afraid that if they face a regular interest rate, they won't be willing to do it, because the green would be bigger than the yellow. So we're actually going to subsidize their interest rate.


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[Assistant] So as you might have thought to yourself, sort of a weird way to get people to go to college is to have a lower student loan interest rate. But in fact, it makes perfect sense. By having a student loan interest rate that's lower than the market rate.


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[Assistant] You encourage people to go to college because essentially you lower this discount rate. For at least, at least on the part that's tuition payments. Okay? So that's actually a very exciting, uhm,


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[Assistant] We need to think about, and a very important part of public policy is how we set the interest rate on student loans. Uh, for any of you, how many of you guys have a student loan?


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[Assistant] Do you know? You guys have a student loan? You might not know. Anyway, I set the interest rate in that student loan.


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[Assistant] So, thank you. Uh, actually when I was in the government, I was in the government for 14 months, the Clinton administration.


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[Assistant] It was super fun, but looking back I only got one thing done, which I got to set the interest rate in student loans. So that was kind of fun. Uh, uh, but otherwise it was just a lot of fun being there. Uhm, so uhm,


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[Assistant] So anyway, uh, let's, uh, stop there, and we will, uhm, we will continue, uh, let's say Wednesday. So no class on Monday, that's Veterans Day, so we'll meet in a week, next Wednesday.


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[Assistant] Prepare for the transfer tomorrow. And do not fail again.


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[Assistant] Marco, it's gonna be okay. I haven't been okay for a long time.


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[Assistant] You're the ones who are gonna need help when they come for you.


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[Assistant] Alright, uh, let's get started, uh, today with our lecture on factor markets.


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[Assistant] So when we talked about producer theory, we talked about input prices. That firms had prices for their wages and their capital.


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[Assistant] And we just sort of pose those as given. I just sort of gave you values for the wage and the rental rate of capital. But we never really talked about where those prices come from. Given that they may be the most important prices in our whole economy, it's probably worth spending a little time on talking about where do W and R actually come from. And that's what we'll do for the next three lectures, is talk about factor markets.


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[Assistant] Talk about the markets that give us the price of labor and capital.


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[Assistant] We're gonna start, uhm, by talking about factor demand, uh, the general demand for labor and capital.


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[Assistant] And then we'll move on to talk about factor supply. Where does supply come from?


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[Assistant] We'll then develop the equilibrium and that will tell us where wages and, uh, the interest rate come from.


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[Assistant] So that's sort of the map of where we're going is we're basically going to develop the markets that give us the wage rate and the interest rate. So let's start with factor demand.


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[Assistant] We're going to start with the cleanest case. We're going to assume that factor markets are perfectly competitive. So unless I say otherwise, we're assuming the market for workers


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[Assistant] Or the market for machines or capital is perfectly competitive. Okay, we'll come back and bend that a little bit later.


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[Assistant] So what that means is that there's basically many sellers and buyers, okay? So any worker, okay, is basically competing with lots of workers.


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[Assistant] That is lots of firms and workers competing to match with each other. We're also going to assume a perfectly competitive output market.


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[Assistant] That is, we're gonna examine this for the case not of a monopoly firm, but of a perfectly competitive firm. So just so you can see, a perfectly competitive firm competing with lots of other firms to hire workers. Okay? So let's start by talking about short-run labor demand.


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[Assistant] In this context, let's talk about short run labor demand. Now in the short run, capital's fixed.


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[Assistant] So our decision is just, do we add another worker or not?


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[Assistant] As with everything else in this course, we want to consider the marginal benefits and the marginal costs of that decision. The marginal benefit of, uhm, of an extra worker is that one extra unit of labor


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[Assistant] Because we don't actually care as a firm about units of output. We care about revenues. So the benefit of a worker is not just the


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[Assistant] How many units it produces, but the value of those units.


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[Assistant] And what is the value of the next unit produced? It's the marginal revenue. So the value of the next unit of labor


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[Assistant] Is what we call the marginal revenue product. MRP.


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[Assistant] Sub L. The marginal revenue product is the marginal product of labor times marginal revenue. That's the benefit of another unit of labor. It's not just what they make, but what it's worth. Okay, it's not just what they make, but what it's worth. Okay? So that's the marginal benefit.


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[Assistant] That's the marginal benefit. What's the marginal cost of another unit of labor? This is the marginal benefit of another unit of labor. What's the marginal cost? Well the marginal cost of labor is just the wage. So we simply set this equal to the wage. We set the marginal revenue product of labor equal to the wage. And that gives us our optimization condition. For the awful amount of labor that firms want to demand. Is to set the marginal revenue product of labor equal to the wage.


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[Assistant] Now, to go further, remember, I said this is a perfectly competitive output market. So what is the marginal revenue in a perfectly competitive output market? What's the marginal revenue of a firm producing?


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[Assistant] Price. So you can write this more to say that one is that the marginal product of labor times the price equal to the wage.


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[Assistant] So basically, what we're saying here, think about it, is higher workers until the cost of the next unit of labor is the same as what that unit will actually produce for you. Okay? The next unit of labor costs you W. It produces for you MPL times P. So you want to hire workers until that condition is met. Okay? So think about that. Figure 15-1 sort of shows this. Okay?


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[Assistant] We have a, uhm, we have a supply of labor in 51 that's horizontal. Because we're assuming a competitive market for workers.


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[Assistant] Okay, we're seeing a competitive market for workers. That is, a perfectly competitive market. So if I try to pay workers one penny more than other firms, every worker in the world will want to work for me.


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[Assistant] If I pay workers one penny less than other firms, no workers will want to work for me. That's what a perfectly competitive labor market means.


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[Assistant] So just like a perfectly competitive firm doesn't get to set the price of their product, it's given to them by the competitive market.


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[Assistant] A perfectly competitive firm in the input market doesn't get to set the wage they pay.


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[Assistant] It's given them through the kind of process that delivered us, uh, our prices on the output side.


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[Assistant] Okay, so we get a horizontal labor supply curve, and then we have this downward sloping labor demand curve. Why is it downward sloping? Someone raise their hand and tell me. Why is the labor demand curve downward sloping?


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[Assistant] Exactly. The diminishing marginal product of labor means you have a downward sloping marginal benefit of labor.


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[Assistant] Each additional, remember holding capital fix is only one shovel. So each additional worker adds less and less to digging that hole. Okay, so marginal product is diminishing. Since p is a constant, that doesn't really affect the slope. I mean it affects the slope, it doesn't really affect the sign. It doesn't affect the sign. It's diminishing because the marginal product of labor is diminishing. So the equilibrium is where they intersect. So the bottom line, this is complicated and new.


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[Assistant] The bottom line intuition is to think about as I decide whether to hire.


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[Assistant] That, uhm, so in other words, the reason it's not just a marginal product is imagine if two workers are equally productive. With one more hour of work, they each make three more units.


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[Assistant] Okay? We clearly would not want to pay the same wage to someone who uses three more computer chips as someone who uses three more potato chips.


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[Assistant] Not because computers are inherently valuable. In fact, potato chips are much more delicious than computer chips. Because they sell, they sell for a higher price.


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[Assistant] So therefore, you'd want to pay more to the worker who produces more units of a more valuable good. So, let's, uh, let's think about a sports example. Okay, and I realize we're all about baseball today, as we should be. Go Red Sox. But, uh, let's focus on basketball for a minute. Okay?


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[Assistant] Uh, now imagine you're owner of a team in the NBA, the National Basketball Association.


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[Assistant] So basically, in that case, your goal is to, what your goal is wins. That's the goal. That's the profit you're trying to maximize is your wins. Let's say, you're probably trying to maximize your...


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[Assistant] So your labor demand, the marginal product you care about, is the contribution of the next player to your win total.


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[Assistant] That's what we care about. The marginal product of labor is how much does that next player add to my win total?


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[Assistant] Okay, so for example, LeBron James, the best player in basketball.


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[Assistant] Arguably that's playing history. We could have that, we could have the LeBron versus Michael debate some other time.


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[Assistant] Okay, LeBron James, uh, makes 31 million dollars. And that's because his marginal product is enormous. He adds a huge amount of wins to any team.


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[Assistant] Okay, we'll see us with the, we'll run the experiment today to watch how the Cleveland Cavaliers tank this year once LeBron is left. Okay? Now other players don't make as much. Let's compare LeBron James to Nate Robinson.


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[Assistant] You guys might not know who Nate Robinson is. He's one of the shortest players in the history of the NBA at a paltry 5-9.


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[Assistant] He was a very exciting player. It was kind of fun watching this little guy run among these giants. Okay? Uhm, but, uh, but he was just okay.


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[Assistant] He wasn't a great player, he was a fine player, and he made about $2 million a year by the end of his career. Okay? So basically you had LeBron making $31 million.


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[Assistant] And Nate Robinson make it 2 million and that's sort of related to their marginal products. LeBron adds a lot more to your wits.


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[Assistant] In Israel, they love basketball, they have a league, and he went to Israel and he was dominant.


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[Assistant] He was the best player in Israel because they don't, they're not, it's not as good as the U.S. Okay. So his marginal product went way up.


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[Assistant] Okay, and what we care about is the wage is equal to the market product times the price. So you have a situation where a player got better, but got paid less, because they got better, he moved from making computer chips to making potato chips.


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[Assistant] Okay. He moved from a market where he was earning a valuable commodity to when he was earning one that was much less. So, uh, so basically it's a situation that example shows why I have to care about both the quantity of the additional worker and the value of what they're producing. Okay. Any questions about that? Yeah.


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[Assistant] The firms sell the goods into a market where people have perfect information and can shop across all firms easily.


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[Assistant] A perfectly competitive input market is where firms hire workers in a situation where workers have perfect information and compare across all firms equally.


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[Assistant] So basically the point is, think about a perfectly, think about a perfectly competitive output market. Think about a market where lots of people are shopping and all the options are in front of them. A very competitive labor market is where you as a worker,


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[Assistant] Have lots of firms you can work for and they're all clearly in front of you. And they all offer a wage and you can see it.


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[Assistant] What we're saying is, we're not saying the firms have information about the laborers. The firms essentially, uh, I think that's the best way to describe this.


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[Assistant] So once again, the firms are from the firms perspective.


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[Assistant] They do have perfect information. No, the wages aren't, yes, right, the workers aren't the same, they have different marginal products. The firms know you're better than you or vice versa. But from the firm's perspective, from the worker's perspective,


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[Assistant] Very competitive output market. The consumers can easily shop across all the firms they might buy from.


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[Assistant] Think for a second about long-run labor demand. Well, what's different?


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[Assistant] The only thing that's different is in the long run capital can adjust as well.


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[Assistant] The only thing that's different about the long run, all the intuition, everything's the same, it's just that capital can adjust as well.


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[Assistant] So the figure shows two different short run labor demand curves at two different levels of capital.


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[Assistant] Okay, so the short run labor demand, when k, when k bar equals 32 is that lower one, the short run labor demand when k bar equals 108 is the higher one. And what this says is, in the short run,


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[Assistant] You've got these two labor demand curves. In the long run, you can optimize capital. You can pick a point on either curve depending on which level of capital you choose.


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[Assistant] You're more flexible because you can optimize not just over workers, but over machines as well. It's the same intuition we developed before talking about short run and long run costs.


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[Assistant] Because I basically am more flexible. I can, I not only can choose along a curve, I can choose which curve I use. And by definition that means that the long one is more elastic. Okay, that's a small sort of side point there. Now, last thing I want to talk about here is capital demand.


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[Assistant] We talked about short run and long run labor demand. Let's talk about capital demand. It basically is the same thing.


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[Assistant] So we want to hire workers so the marginal product of labor times the price of our good equals the wage rate. We want to invest in more machines until the marginal product of capital of the next machine times the price for our good is equal to the interest rate.


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[Assistant] Do you want to rent it? Well it depends. What will it produce? And what can you sell that stuff for? So you rent the next machine, if the, if the marginal product of capital, the goods it produces, times what you sell those goods for,


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[Assistant] You want to do that until that equals the interest rate. Okay? Questions about that? Yeah.


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[Assistant] Right now, I think, I just put this down here, we'll come back to it, but I'm gonna focus on labor for this lecture. Okay? So let's focus on labor.


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[Assistant] And let's, so I just put that down and we'll come back to capital, but focus on labor for a minute and make sure you understand where labor demand comes from. Now let's talk about where does labor supply come from?


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[Assistant] We talked about firm, at the firm level, labor supply is perfectly elastic. So go back to figure 15-1. That was a firm level curve. Okay? That was a firm level curve. That's a perfectly elastic labor supply to a firm. But that doesn't mean labor supply to the market is perfectly elastic. So now we want to derive market labor supply. So I'll call this deriving market labor supply.


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[Assistant] This is basically the question of, how do we model how hard people want to work? This is, once again, getting into what make economics exciting. Okay?


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[Assistant] You sort of knew that economics was involved in how much Ford cars charge for a car.


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[Assistant] But you might not have thought so much about how economics was involved in deciding how hard you work. But it is. And we're going to use the same tools of consumer choice. Indeed, I used to teach this right as an application of consumer choice. But now I teach it here. Because it's the same tools of consumer choice. But now consumers, instead of choosing good A versus good B, are going to choose how hard they're going to work. Okay? So basically, like any choice, there's a trade-off.


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[Assistant] There's a trade-off. On the one hand, if you work harder, you get more stuff. So you bring home more income, you can buy more pizzas and cookies.


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[Assistant] Okay, remember, we talked about income as a fixed thing your parents gave you, but in reality, sorry kids, you're gonna have to make your own money someday.


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[Assistant] Okay, in reality you're going to make a Y. It's not going to be given to you. So if you want to buy more pizza and cookies, you're going to have to raise your Y. It's not going to be given.


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[Assistant] Okay, so the reason you want to work harder is to buy more pizza and cookies.


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[Assistant] The reason you don't want to work harder is because you're not an MIT student. Okay, that is normal people actually don't like work. Newsflash. Okay. Normal people actually like leisure. There's a thing called leisure, it turns out. Okay, normal people like it. Okay.


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[Assistant] So the trade off for regular people, it's always a hard thing to teach at MIT, okay, is that basically,


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[Assistant] Pete, the trade-off is if you work harder, you get more stuff, but you spend more time doing something you don't want to do. Now, this is weird. We talked about trade-offs before. We talked about the trade-offs between goods. Pizza and cookies. Now we're talking about the trade-off between a good and a bad. The good is more stuff to eat. The bad is working harder. And we don't really know how to model that. So the trick we're gonna use here is we're gonna flip the bad into a good. Instead of modeling labor, we're gonna model leisure.


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[Assistant] So to get labor supply, we're gonna model leisure supply, and then just flip it around to get labor supply. Okay? So that is, we're gonna say, your ultimate labor supply,


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[Assistant] The amount of hours you work, the amount you work, the amount of hours you work, call them h, okay, is equal to 24.


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[Assistant] Minus, uh, is equal to 24, uhm, minus leisure. Call it that. Let's call it leisure. Let's call it little l. Leisure's little l.


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[Assistant] Don't model your hours, model your work, model how many hours of leisure.


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[Assistant] Okay, so this is a general modeling trick. So what we want to ask is, now, not how do we derive the supply of labor, how do we derive the demand for leisure? How do we derive how much leisure people want? Well, once I say it that way, you know what to do. Which as I just said, they're two goods. Consumption and leisure.


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[Assistant] I don't know how much of one good you choose, of each good you choose, well that's a consumer, consumer choice problem. You know how to do that. Okay? So basically take figure 15-3. Okay?


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[Assistant] In figure 15-3, now, instead of doing pizza versus cookies,


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[Assistant] Now our decision is all consumption. So think about consumption as a bundle. Okay. Versus leisure.


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[Assistant] So on the y-axis is how, the goods you choose. On the x-axis is how much leisure you take. Okay, it says n, but actually it should be little l. Okay, should be little l. So let's call that little l. Okay? So basically, as you go more positive on the x-axis, that's more leisure.


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[Assistant] But because this equation, that implies as you go to the left on the axis, that's more work. Okay, yeaah. H is hours of work.


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[Assistant] H's hours of work. So as you go to the left, you work more. As you go to the right, you take more leisure. But we're modeling the good, which is leisure. And then we just go to our standard


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[Assistant] Uhm, we go to our standard consumer choice equation. We have a budget constraint and preferences. The indifference curve comes from your utility function. It comes from your indifference between how much you consume and how much leisure you take. And the indifference curve comes from, like, any consumer choice decision. But instead of assuming it would be pizza and cookies, now it's how much stuff you want versus how much leisure you want to take. So it's the same sort of indifference curve. The budget constraint


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[Assistant] What the market tells you is the cost of leisure. What is the price of leisure?


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[Assistant] Which is that basically, this is why, once again, they call economics a dismal science. Instead of having fun sitting around, we're telling you, you know, by the way, you could be working and making a wage. So you're actually spending money by taking leisure. By taking leisure, you are spending money. What are you spending? You're spending the money you could be earning. So the opportunity, so leisure has a price, and the price of leisure is the wage. It's what you could be earning if you were working.


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[Assistant] So the budget constraint has the slope of minus w. So if you look at the budget constraint, you could take 24 hours of leisure and have zero consumption. Okay, that's the x-axis intercept. Or you take no leisure and have 24w worth of consumption. Okay?


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[Assistant] So basically that is the trade off you face.


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[Assistant] One other modeling trick, couple of, so couple of modeling tricks here. Modeling trick one is a model of the good, not the bad.


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[Assistant] Okay. Modeling trick two is I wrote on the x-axis goods, but we don't think of quantities, we think of dollars.


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[Assistant] Okay, which allows you to think in terms of dollars of goods rather than quantity of goods. That's another modeling trick we'll do. We call it making a numeraire good.


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[Assistant] Okay, you don't remember that term. But the point is, the trick we'll do is we want to model dollars, not quantities.


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[Assistant] We just make the quantities cost a dollar, and then we can model quantities basically as dollars. So that's the other trick we're doing. So the y-axis is dollars, but it's also quantities because you make the price of everything be a dollar. Okay.


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[Assistant] It's just another trick that makes life easier. Okay, so two modeling tricks here. The numeraire trick, which is making the price of dollars so quantities become dollars, and the good is, and the bad is good trick, which is model the good and then reverse that to get the bad.


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[Assistant] Having done that, we know what to do. We get an optimum, which is the tangency between, uh, the indifference curve and the budget constraint, and we're done.


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[Assistant] And so what do you do? You choose, we're gonna call this L, we'll call it little L. You choose little L star hours of leisure.


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[Assistant] Which means you choose 24 minus little L star hours of work. Okay. So basically you sat down, you made the decision. How much do I want to eat versus how much do I want to watch TV? You make that trade off and that determines how hard you work. Okay. Now, yeah.


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[Assistant] So basically, now, what's really interesting about this...


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[Assistant] Because when we're doing a substitution effects for a good, they work together. As long as the good was normal, they work together. When the price went up, you substituted away from the good and you were poor. So you can substitute it down for two reasons. Now, a normal leisure effect is an inferior labor effect. What I mean by that is that when your wage goes up, you work more through the substitution effect, but now you're richer.


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[Assistant] And when you're richer, you buy more of everything, including leisure. So if you take more leisure, you do less labor.


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[Assistant] So the income effect naturally goes against the substitution effect. I've said this a couple of times, don't worry. The income effect naturally goes against the substitution effect here.


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[Assistant] For consumption goods, the income effect naturally work together.


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[Assistant] Okay, and we're, we, we almost never saw sort of a given good type phenomenon. We think of effect could sort of switch the overall effect. For labor, that's much more likely. And it's much more likely, not because


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[Assistant] Leisure, not because of any inferior good, it's because leisure is a normal good, and labor is the opposite of leisure. So once again, let me say it again. The wage goes up. The substitution effect, when the wa- think of leisure as a good. When the wage goes up, that's the price of leisure going up. When the price of a good goes up, the substitution effect says you want less of it. Okay? So, when the wage goes up, the substitution effect


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[Assistant] Because you want to substitute a weight. Leisure just got more expensive. You now feel worse sitting around watching TV because you could be out there making more money. Yeaah.


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[Assistant] Says that you are richer. Right? Your wage went up. You're richer. When you're richer, you want more of all normal goods. Leisure for non-MIT students is a normal good. So you want more of it.


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[Assistant] Work, take less leisure means work harder. Work more hours. But the ego effect says take more leisure, which means work less hours. So you don't know what the net effect is.


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[Assistant] Okay. When normal people win lotteries, they don't go work harder. They don't work. Okay. So that's the point. You are now richer because your wage went up. So you work less and that offsets it. So let's show this in a graph. Let's go back to our income and substitution effect graphs like we did before. Figure 15-4. Okay. Now we're back to, once again, this is just applied consumer theory. Okay. Let's go back to the income and substitution effects. We start with budget constraint one at wage one.


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[Assistant] And we have our initial tangency at A. Okay, with, with leisure of N1 or little l1. Now our wage goes up. Our wage goes up, therefore the budget constraint pivots up. Think about what that means.


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[Assistant] You can still only have 24 hours of leisure. That's a fixed point.


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[Assistant] But as you take less leisure, you make more money. So budgetary now pivots up. Well, that has two effects. The first is the substitution effect.


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[Assistant] Remember how we get that? We draw an imaginary budget constraint at the new price ratio. The price ratio is just W because I've assumed the price of goods is one. The new price ratio tangent to the old indifference curve. That is point B. So the substitution effect says take less leisure. Okay, you're, the price of leisure has gone up. So holding utility costs, you want to take less leisure.


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[Assistant] The income effect, however, says you are now richer, so take more leisure.


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[Assistant] So the negative effect goes the opposite way of substitution effect, naturally.


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[Assistant] Not, you don't need a weird thing for that to happen like with pizza and cookies. It comes naturally. So for normal goods,


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[Assistant] The angle effect goes the opposite way. Now in this case, we end up with leisure still going down. We end up with the wage goes up, leisure goes down, and therefore labor supply goes up.


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[Assistant] So we end up with our standard intuition, which is I tell you, if I'm gonna pay you more, you're gonna work harder or less hard. The standard intuition is I'll work more hard. Okay? But, as figure 15-5 shows, it would not be super odd to get a Giffengood effect here. Which is, the wage goes up, the substitution effect shifts you to the left, but the Ingham effect shifts you even more to the right, and you actually end up with more leisure.


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[Assistant] Once again, my intuition, if I say to you the price of pizza went up, what happens to your demand for pizza? You think of a standard, you say, well, I'm going to demand less pizza. If I say to you the wage went up, what happened to how hard you work? It's not clear. Think of a simple example.


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[Assistant] Think of yourself, actually, back before you were an MIT student, when you were a kid, saving for something. You were saving to buy a bike. And the bike was 150 bucks. Okay, bike was 200 bucks, and you're earning 10 bucks an hour. Okay? So you had to work 20 hours to get the bike. Now I gave you a race to 15 hours. To 15 dollars an hour. Or to 20 dollars an hour. Would you work harder or less hard? Well, if all you want is the bike, you'd work less hard.


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[Assistant] So in fact, a higher wage caused you to work less hard. That's not that bizarre a case, right? That makes sense. The point is, it's actually quite sensible that you couldn't end up with labor supply being a given good with a higher wage causing you to work less. It's not a crazy outcome. Given goods and consumer goods are crazy. It's not at all crazy to think that in cases like having a target, a purchase target, a higher wage would cause people to work less. Yeah.


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[Assistant] Absolutely applies. There's no violation here. We haven't violated any of the laws. All we've done is just said income effects are bigger. It didn't apply with given goods too. It's all just saying income effects dominate substitution effects.


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[Assistant] This is pretty wild. What this says is that basically you've got a situation where even in the normal world you can get the paying workers more and makes them work less. Which is kind of bizarre. Okay? Questions about that?


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[Assistant] What I want to do here to make the intuition easy, I want to go back to that literature circa, probably 40 years ago.


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[Assistant] So, the literature looked at men and women, and married women, and asked, what was their elasticity of labor supply? Well, let's think for a second about what we'd expect. And to do that, let's think about the substitution effect, and the income effect. Let's start with men. The male substitution effect. Let's start with the substitution effect. Men versus married women. Who has a bigger substitution effect and why? That is when the wage goes up.


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[Assistant] Who, who has a bigger substitution response to that and why? Men are married women.


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[Assistant] You know, circa 40 years ago, you gotta see enough TV and stuff to know how life was a little bit. Okay? So who's gonna respond? Who's the bigger guy?


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[Assistant] Okay, uhm, let's, that's one option, yeaah.


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[Assistant] Right, so it's actually married women, because men are already working 40 hours. They can't, there's no, so think about a married man in 1975.


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[Assistant] Okay, men didn't raise their kids. Men, quite frankly, didn't give much of a shit about their kids. Okay? Men just worked. That's what men did in 1975. Okay? They worked and they worked their 40 hours and then went home.


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[Assistant] In the era women were entering the labor force, the real opportunities for work, but it was also fine to hang out at home.


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[Assistant] A lot of your friends are hanging out at home, you can take care of your kids, there are a lot of things to do. So women had a much larger substitution effect than men. Okay, because men, what


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[Assistant] Remember, what's the substitution effect? It's about the next best alternative. For men, there was no next best alternative. It was just work. You know, basically between nine to five on a weekday, there was nothing else to do. Okay? For women, there was other things to do, which is you could hang out with friends who weren't working, or you could take care of the kids. Yeah.


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[Assistant] Okay, well, let's, but once again, if I'm a man, you might think that I could then, but then once again,


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[Assistant] Okay, now let's go to the other side. Let's go to the income effect. So let's not say this is zero, let's say it's small. This is big, and this is small.


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[Assistant] Uh, so it could be some men were willing to spend time with their kids, etc. Okay, now let's go to the income effect.


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[Assistant] Exactly. There's actually two reasons it's meant. One, you're more likely to target income. Two is you can't have an income effect if you don't work.


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[Assistant] Okay, the income effect is proportional to how hard you were working. If you weren't working, then there's no income effect.


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[Assistant] Right, income effect is essentially, the income effect for labor is essentially the hours


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[Assistant] What Manny said was a reason why DHGY might be bigger for men than women, because they have these targets. More relevantly, if women weren't working, they didn't have the H. This is zero, so the income affects zero. So for men, this was big. And for women, this was small. Okay. Put this together.


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[Assistant] And what does it suggest about the relative shapes of labor supply for men and women? Someone raise their hand and tell me. What does it suggest about the labor supply curve would look like for men and women in this era?


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[Assistant] By the income effect, the wage goes up at least to less labor supply. So for men,


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[Assistant] For women, with a big substitution effect and a small income effect, this suggests a standard, steep, upwards, standard, upward sloping supply curve. Think of the income effect being zero. Then we get the standard substitution effect. We know the sign effect. So for women, this suggests an upward sloping supply curve, just like a substitution effect suggests a downward sloping demand curve. For men, it's not clear. You could very much get a Giffen effect here.


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[Assistant] There's not much opportunity for substitution, but they might work a lot less if they get rich. Okay?


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[Assistant] So that is sort of the, what I like about this example, it's hard, what I like about this example is it illustrates how substationing effects can come together to deliver a bottom line answer. What do we know?


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[Assistant] What we know is that actually the evidence is that female labor supply was very elastic. That circa this era, female labor supply is an elasticity of between .5 and 1. That if you raised women's wage by 10%, there was a 5 to 10% increase in their labor supply. Which is pretty, not elastic elastic, but reasonably elastic. Okay? Whereas for men, it was pretty much zero. It wasn't negative, it wasn't positive, it was basically zero. Basically men just worked 40 hours and then went home.


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[Assistant] Okay, so basically in an era where for women,


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[Assistant] The layer slide was very elastic and of the standard direction.


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[Assistant] Higher wage leads you to work harder, an upward sloping supply curve.


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[Assistant] Right, well first of all, this is gonna come down. Because in fact, it's now more standard just to work. Right? In fact, now, for a woman today,


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[Assistant] In many communities, it's like being in Valentine's 70s, which is if you don't go to work, there's no one to hang out with. Okay?


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[Assistant] And there's more sort of activities going on during the day. But in fact, it hasn't. In fact, male layers fly still is pretty inelastic. What's happened is kids are now in child care.


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[Assistant] So basically we've gone from a world where as wages went up, women went, men worked,


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[Assistant] Women either worked or didn't work depending on the wage and if they worked the kids went in child care. Now men work and women work and kids are in child care.


[User] Please transcribe this text

[Assistant] And that's basically the change, the evolution of the labor, roughly speaking, obviously. Still, female labor force participation is only about 70%.


[User] Please transcribe this text

[Assistant] What this has done is allowed the average shoe family household to tread water. So it's the average shoe family household today.


[User] Please transcribe this text

[Assistant] And that's facts about inequality we'll come to. That basically average family in America, despite having, going from the wife not working to the wife working, is no better off than they were 40 years ago. And that has lots of implications we'll talk about. Okay? So, any other questions about that? So let me end with one final example. Okay, an application. Okay, which is to the problem, to the problem we have in the world of child labor.


[User] Please transcribe this text

[Assistant] It's a huge problem around the world as kids being forced to work was a huge problem in the US till the 20th century. It's a huge problem around the world because A, work can often be dangerous and bad for their health, but B, they can't be going to school and having an opportunity to better themselves. If a kid is spending all day working,


[User] Please transcribe this text

[Assistant] When we, we will talk in the next few lectures, in a few lectures about international trade.


[User] Please transcribe this text

[Assistant] And one criticism of international trade is people say, well, if you allow these developing countries to sell more stuff to develop world, that will, they'll put the kids to work more.


[User] Please transcribe this text

[Assistant] So if we have free trade and Vietnam can suddenly sell a bunch of stuff to America, that's more kids they're gonna put to work making that stuff.


[User] Please transcribe this text

[Assistant] So one common argument you hear against free trade is it's bad for kids. But in fact, that argument is not necessarily right because it ignores an important point. Manny?


[User] Please transcribe this text

[Assistant] No, no, that's a different issue. The point, that's right, but the point it ignores is free trade makes families richer. And if families are richer, they may want to buy more education for their kids. So on the one hand, it's true free trade,


[User] Please transcribe this text

[Assistant] Makes kids more valuable than the labor force. On the other hand, it makes family richer. And they want more education for their kids. So to look at that, two Dartmouth professors did a study


[User] Please transcribe this text

[Assistant] We looked at Vietnam and looked at what happened when Vietnam liberalized trade and rights. So let's go to figure 15-6.


[User] Please transcribe this text

[Assistant] And the amount of rice sold was Q sub V. And kids worked in the rice paddies.


[User] Please transcribe this text

[Assistant] When they liberalized trade, suddenly Vietnam could sell to a much larger market. They could sell to the world market. D sub W. That's a bigger market. So they were able to shift up their supply curve and sell more rice.