1 00:00:01,440 --> 00:00:04,800 [SQUEAKING][RUSTLING][CLICKING] 2 00:00:10,843 --> 00:00:12,260 JONATHAN GRUBER: Today, what we're 3 00:00:12,260 --> 00:00:16,760 going to do is continue our discussion of factor markets 4 00:00:16,760 --> 00:00:22,160 by essentially talking about how capital markets impact 5 00:00:22,160 --> 00:00:23,418 real world decisions. 6 00:00:23,418 --> 00:00:25,460 So last time, we talked about the capital market. 7 00:00:25,460 --> 00:00:27,002 We talked about, essentially, the way 8 00:00:27,002 --> 00:00:29,420 that firms finance their capital is 9 00:00:29,420 --> 00:00:32,330 by going to a pool of savings that individuals 10 00:00:32,330 --> 00:00:33,530 decided how much to make. 11 00:00:33,530 --> 00:00:35,720 Individuals make it into temporal choice 12 00:00:35,720 --> 00:00:37,115 on how much to save. 13 00:00:37,115 --> 00:00:38,990 Actually, technically, they can make a choice 14 00:00:38,990 --> 00:00:40,880 about how much to consume each period. 15 00:00:40,880 --> 00:00:43,040 That then yields an amount of savings. 16 00:00:43,040 --> 00:00:44,930 And then based on that pool of savings, 17 00:00:44,930 --> 00:00:47,870 firms borrow at some interest rate, i, 18 00:00:47,870 --> 00:00:50,480 and they decide how much to invest. 19 00:00:50,480 --> 00:00:52,640 Now, today we're going to talk about a number 20 00:00:52,640 --> 00:00:54,800 of interesting applications that arise 21 00:00:54,800 --> 00:00:57,535 from capital markets that are important in the real world. 22 00:00:57,535 --> 00:00:58,910 And I'm going to start by talking 23 00:00:58,910 --> 00:01:01,310 about the concept of present value. 24 00:01:05,740 --> 00:01:07,340 Present value. 25 00:01:07,340 --> 00:01:10,510 Now, the key insight when we think about capital markets 26 00:01:10,510 --> 00:01:16,110 is that $1 tomorrow is worth less than $1 today. 27 00:01:16,110 --> 00:01:18,085 $1 tomorrow is worth less than $1 today. 28 00:01:18,085 --> 00:01:21,210 That's because if you had the dollar today, 29 00:01:21,210 --> 00:01:25,520 you could productively invest it and have more than $1 tomorrow. 30 00:01:25,520 --> 00:01:27,387 So $1 today is worth more, because you 31 00:01:27,387 --> 00:01:29,720 could do something productive with that $1 if you had it 32 00:01:29,720 --> 00:01:31,550 today. 33 00:01:31,550 --> 00:01:34,820 What that means is that dollars in different periods 34 00:01:34,820 --> 00:01:36,090 are worth different things. 35 00:01:36,090 --> 00:01:37,840 You can't just add them up. 36 00:01:37,840 --> 00:01:40,160 OK, the analogy I like is thinking about-- 37 00:01:40,160 --> 00:01:42,950 imagine you had a pound of apples, a pound of steak, 38 00:01:42,950 --> 00:01:44,630 and a pound of gold. 39 00:01:44,630 --> 00:01:47,270 You wouldn't just add them up and say, I have three pounds. 40 00:01:47,270 --> 00:01:48,347 That'd be useless. 41 00:01:48,347 --> 00:01:49,930 You'd want to know what each is worth, 42 00:01:49,930 --> 00:01:52,790 and you'd want add up the dollar value of them. 43 00:01:52,790 --> 00:01:56,390 It's a similar thing with money received over time. 44 00:01:56,390 --> 00:01:58,910 You can't just say, I'm getting $1 today, $1 next year, 45 00:01:58,910 --> 00:02:00,680 and $1 five years from now. 46 00:02:00,680 --> 00:02:02,200 They aren't the same thing. 47 00:02:02,200 --> 00:02:03,950 Money received at different points of time 48 00:02:03,950 --> 00:02:06,080 are worth different amounts, because money 49 00:02:06,080 --> 00:02:09,300 received in the future forgoes the possibility of investing it 50 00:02:09,300 --> 00:02:09,800 today. 51 00:02:12,780 --> 00:02:14,430 So what do we do to deal with this? 52 00:02:14,430 --> 00:02:16,110 Well, in economics, we deal with this 53 00:02:16,110 --> 00:02:18,830 by the concept of present value. 54 00:02:18,830 --> 00:02:23,840 Present value is the value of every period's payments 55 00:02:23,840 --> 00:02:25,743 in terms of today. 56 00:02:25,743 --> 00:02:28,410 So the way we deal with the fact that money in different periods 57 00:02:28,410 --> 00:02:32,010 is worth different amounts is by what we call discounting it 58 00:02:32,010 --> 00:02:33,660 back to today. 59 00:02:33,660 --> 00:02:35,670 We essentially take future dollars 60 00:02:35,670 --> 00:02:39,330 and discount them back to today to get present value. 61 00:02:39,330 --> 00:02:43,200 We discount them, because future dollars are worth less. 62 00:02:43,200 --> 00:02:45,240 So let's think of it this way. 63 00:02:45,240 --> 00:02:49,247 Suppose that the interest rate is 10%. 64 00:02:49,247 --> 00:02:50,080 Let's do an example. 65 00:02:50,080 --> 00:02:54,000 Imagine the interest rate, i, is 10%. 66 00:02:54,000 --> 00:03:00,650 And let's say that you want to have $100 next year. 67 00:03:00,650 --> 00:03:03,420 Next year, you want to have $100. 68 00:03:03,420 --> 00:03:07,800 Well, how much do you have to put in the bank today? 69 00:03:07,800 --> 00:03:12,540 Well, we can solve the equation, which is that you want 70 00:03:12,540 --> 00:03:16,420 the amount you put in the bank today-- let's call that y-- 71 00:03:16,420 --> 00:03:19,330 times one plus the interest rate, 72 00:03:19,330 --> 00:03:21,580 because that's what you make by having it in the bank, 73 00:03:21,580 --> 00:03:22,990 equal to 100. 74 00:03:22,990 --> 00:03:25,090 That's the equation we want to solve. 75 00:03:25,090 --> 00:03:27,315 The money amount you put in today, y, 76 00:03:27,315 --> 00:03:28,690 times one plus the interest rate. 77 00:03:28,690 --> 00:03:31,010 You want that to be equal to 100. 78 00:03:31,010 --> 00:03:35,740 So what that says is that y equals 90.9. 79 00:03:35,740 --> 00:03:41,350 If you put $90.90 in the bank today at a 10% interest rate, 80 00:03:41,350 --> 00:03:44,460 you will have $100 tomorrow. 81 00:03:44,460 --> 00:03:48,150 More generally, we say that the present value 82 00:03:48,150 --> 00:03:52,530 of any future payment is the future value, 83 00:03:52,530 --> 00:03:55,740 the amount you get in the future, over one 84 00:03:55,740 --> 00:03:58,560 plus i to the power little t, where 85 00:03:58,560 --> 00:04:00,890 t is the periods in the future. 86 00:04:00,890 --> 00:04:05,750 So money received t periods in the future today 87 00:04:05,750 --> 00:04:08,930 is worth the amount you get in the future over one plus i 88 00:04:08,930 --> 00:04:09,440 to the t. 89 00:04:12,660 --> 00:04:15,412 So that is our general formula for how 90 00:04:15,412 --> 00:04:16,620 we think about present value. 91 00:04:16,620 --> 00:04:18,750 Take all the future payments, and you discount them 92 00:04:18,750 --> 00:04:22,540 back to today by dividing by one plus i to the t. 93 00:04:22,540 --> 00:04:25,770 Now, that works well if there's one future payment coming. 94 00:04:25,770 --> 00:04:27,720 But what if, as in many cases, there's 95 00:04:27,720 --> 00:04:30,180 a whole stream of future payments coming? 96 00:04:30,180 --> 00:04:31,880 Well, the logic then is the same. 97 00:04:31,880 --> 00:04:33,850 You just want to take each future payment 98 00:04:33,850 --> 00:04:38,100 and discount it by how far it is in the future. 99 00:04:38,100 --> 00:04:44,400 So suppose that you say that you want me to loan you $30 100 00:04:44,400 --> 00:04:50,020 and that you'll pay me back $10 each of the next three years. 101 00:04:50,020 --> 00:04:52,360 And suppose the interest rate's 10%. 102 00:04:52,360 --> 00:04:54,202 Well, I will say no to that. 103 00:04:54,202 --> 00:04:55,660 Because I will say, if you're going 104 00:04:55,660 --> 00:04:59,470 to pay me back $10 each of the next three years, then 105 00:04:59,470 --> 00:05:01,540 what is the present value of that? 106 00:05:01,540 --> 00:05:06,745 The present value is next year's $10 over 1.1, 107 00:05:06,745 --> 00:05:10,180 because the interest rate is 10%, plus the $10 the year 108 00:05:10,180 --> 00:05:15,360 after that over 1.1 squared, plus the $10 the year 109 00:05:15,360 --> 00:05:27,070 after that over 1.1 cubed, which if I add it up, is 24.87. 110 00:05:27,070 --> 00:05:29,250 So I am losing money. 111 00:05:29,250 --> 00:05:32,370 If I give you $30 today and if you give me 112 00:05:32,370 --> 00:05:36,010 $10 back each of the next three years, I'm losing money. 113 00:05:36,010 --> 00:05:36,540 Why? 114 00:05:36,540 --> 00:05:38,207 Because if I had simply taken that money 115 00:05:38,207 --> 00:05:40,380 and invested it in the bank, I would've 116 00:05:40,380 --> 00:05:42,550 had a lot more than the $30 I'm going 117 00:05:42,550 --> 00:05:44,560 to get from you after three years. 118 00:05:44,560 --> 00:05:47,640 OK, so the money that comes in the future 119 00:05:47,640 --> 00:05:50,790 must be discounted back to today. 120 00:05:50,790 --> 00:05:52,770 That's the key insight of present value. 121 00:05:52,770 --> 00:05:54,120 You can't just add it up. 122 00:05:54,120 --> 00:05:56,160 You've got to put it in today's terms 123 00:05:56,160 --> 00:05:59,083 by discounting it by the interest rate 124 00:05:59,083 --> 00:06:00,250 and how far into the future. 125 00:06:00,250 --> 00:06:00,827 Yeah. 126 00:06:00,827 --> 00:06:02,910 AUDIENCE: So aside from just the change in value 127 00:06:02,910 --> 00:06:05,765 that's caused by interest, how do you take into consideration 128 00:06:05,765 --> 00:06:08,120 the fact that the value of the currency itself 129 00:06:08,120 --> 00:06:09,230 hasn't changed over time? 130 00:06:09,230 --> 00:06:11,200 JONATHAN GRUBER: We're assuming now inflation is zero. 131 00:06:11,200 --> 00:06:12,617 So we're assuming right now, we're 132 00:06:12,617 --> 00:06:13,742 not dealing with inflation. 133 00:06:13,742 --> 00:06:15,960 We're assuming a world where prices don't change. 134 00:06:15,960 --> 00:06:18,050 We'll come back to inflation in a few minutes. 135 00:06:18,050 --> 00:06:21,010 But for now, just assume that prices don't change. 136 00:06:21,010 --> 00:06:25,990 OK, so basically, essentially, the formula 137 00:06:25,990 --> 00:06:30,030 then for the present value, your general formula 138 00:06:30,030 --> 00:06:31,870 for present value you need to know 139 00:06:31,870 --> 00:06:34,195 is that present value equals-- 140 00:06:37,900 --> 00:06:39,550 if you get a flat stream of payment 141 00:06:39,550 --> 00:06:44,860 f for a number of periods, it's f times one over one 142 00:06:44,860 --> 00:06:52,900 plus i to the one plus one over one 143 00:06:52,900 --> 00:06:58,900 plus i squared plus one over one plus i 144 00:06:58,900 --> 00:07:02,980 cubed plus dot dot dot dot dot dot for how many periods 145 00:07:02,980 --> 00:07:03,520 you get it. 146 00:07:03,520 --> 00:07:05,770 So if you're getting a payment f over a certain number 147 00:07:05,770 --> 00:07:07,370 of periods, you've got to discount it 148 00:07:07,370 --> 00:07:09,510 by how many periods you're going to get it. 149 00:07:09,510 --> 00:07:12,640 Or more generally, a common formula 150 00:07:12,640 --> 00:07:14,530 we'll ask you to use in this class 151 00:07:14,530 --> 00:07:17,120 is to think about the formula for perpetuity. 152 00:07:17,120 --> 00:07:20,590 A perpetuity is a flat payment you get forever. 153 00:07:20,590 --> 00:07:24,400 So if we take the infinite sum of this equation, 154 00:07:24,400 --> 00:07:29,080 we can summarize it as present value approximately equals 155 00:07:29,080 --> 00:07:31,430 f over the interest rate. 156 00:07:31,430 --> 00:07:35,720 So if I promise you to pay you forever a certain amount f, 157 00:07:35,720 --> 00:07:37,980 that is worth f over the interest rate. 158 00:07:37,980 --> 00:07:40,280 So in other words, if the interest rate is 10%, 159 00:07:40,280 --> 00:07:44,340 a promise to pay you $10 forever is worth about $100. 160 00:07:44,340 --> 00:07:45,840 That's just the Infinite sum. 161 00:07:45,840 --> 00:07:47,700 If you've read A Beautiful Mind, John Nash 162 00:07:47,700 --> 00:07:49,230 can do that in his head. 163 00:07:49,230 --> 00:07:52,440 But I can't, but that's just the formula. 164 00:07:52,440 --> 00:07:56,190 So basically, that is the general formula for perpetuity. 165 00:07:56,190 --> 00:08:01,380 And that makes life easy. 166 00:08:01,380 --> 00:08:03,588 We'll give you a lot of examples. 167 00:08:03,588 --> 00:08:05,130 Because if I say I want you to pay me 168 00:08:05,130 --> 00:08:06,260 for eight years in the future, I've 169 00:08:06,260 --> 00:08:07,677 got to write out eight terms here. 170 00:08:07,677 --> 00:08:08,730 It's a pain in the ass. 171 00:08:08,730 --> 00:08:10,947 So what we'll say is money forever, 172 00:08:10,947 --> 00:08:12,530 and then you'll just use the shortcut, 173 00:08:12,530 --> 00:08:14,350 which is the present value for perpetuity. 174 00:08:14,350 --> 00:08:15,360 It's just f over i. 175 00:08:18,080 --> 00:08:19,670 Questions about that? 176 00:08:19,670 --> 00:08:20,744 Yeah? 177 00:08:20,744 --> 00:08:23,517 AUDIENCE: Does this also assume the rate of change over time? 178 00:08:23,517 --> 00:08:25,100 JONATHAN GRUBER: That's a great point. 179 00:08:25,100 --> 00:08:27,420 Yes, I'm assuming constant interest right over time. 180 00:08:27,420 --> 00:08:29,930 Now in reality, you'd want to have each period's interest 181 00:08:29,930 --> 00:08:32,929 rate here, and then you can't use this formula, 182 00:08:32,929 --> 00:08:34,820 because the interest rate itself is changing. 183 00:08:34,820 --> 00:08:36,530 Very good point. 184 00:08:36,530 --> 00:08:39,559 OK, now the other way to think about this 185 00:08:39,559 --> 00:08:41,877 is instead of thinking just-- this 186 00:08:41,877 --> 00:08:43,669 will be easy for most of you, but just it's 187 00:08:43,669 --> 00:08:45,110 useful to think it through. 188 00:08:45,110 --> 00:08:47,060 Let's flip it on its head and not think about present value. 189 00:08:47,060 --> 00:08:48,530 Let's think about future value. 190 00:08:48,530 --> 00:08:50,250 This is a useful tool as well. 191 00:08:50,250 --> 00:08:51,620 Let's flip it on its head. 192 00:08:51,620 --> 00:08:54,560 OK, so let's think about the value 193 00:08:54,560 --> 00:08:56,450 of a future stream of payments. 194 00:08:56,450 --> 00:09:00,800 Well, by the same logic we wrote before, future value-- 195 00:09:00,800 --> 00:09:03,600 by the same logic we wrote before, 196 00:09:03,600 --> 00:09:05,120 if you're going to have money that's 197 00:09:05,120 --> 00:09:08,240 tiers in the future, the future value of that money 198 00:09:08,240 --> 00:09:10,430 that you're going to get-- 199 00:09:10,430 --> 00:09:13,502 if you're going to basically take your money and invest it, 200 00:09:13,502 --> 00:09:14,960 you're going to have money that you 201 00:09:14,960 --> 00:09:17,000 are going to invest today and put it 202 00:09:17,000 --> 00:09:18,780 in the bank at some interest rate, 203 00:09:18,780 --> 00:09:22,190 then the future value is the amount you put in times one 204 00:09:22,190 --> 00:09:24,770 plus the interest rate to the t. 205 00:09:24,770 --> 00:09:26,570 So I've simply reversed that formula, 206 00:09:26,570 --> 00:09:28,350 present value, future value. 207 00:09:28,350 --> 00:09:31,312 So basically, future value, if you put money in the bank 208 00:09:31,312 --> 00:09:32,770 at some interest rate, you're going 209 00:09:32,770 --> 00:09:37,540 to get to have over time that money times one 210 00:09:37,540 --> 00:09:39,330 plus i to the t. 211 00:09:39,330 --> 00:09:42,630 Now, the reason we write this formula out and flip it for you 212 00:09:42,630 --> 00:09:45,930 is because I want to highlight the key feature here that I 213 00:09:45,930 --> 00:09:47,430 want to drill into your heads. 214 00:09:47,430 --> 00:09:49,560 One of the, I don't know, I guess 10 things 215 00:09:49,560 --> 00:09:51,840 I most care you leave this course thinking about 216 00:09:51,840 --> 00:09:54,360 if you're not going to major in economics or remembering-- 217 00:09:54,360 --> 00:10:00,120 is the beauty of compounding, which 218 00:10:00,120 --> 00:10:02,820 is that with a formula like this, 219 00:10:02,820 --> 00:10:05,410 you earn interest on your interest. 220 00:10:05,410 --> 00:10:07,093 If you leave money in the bank, you 221 00:10:07,093 --> 00:10:09,510 don't just earn interest on the initial amount you put in. 222 00:10:09,510 --> 00:10:12,460 You earn interest on the interest you earn over time. 223 00:10:12,460 --> 00:10:15,250 OK, and this can be quite large. 224 00:10:15,250 --> 00:10:17,733 So let's do a simple example just 225 00:10:17,733 --> 00:10:19,650 to show you how big this can be and to get you 226 00:10:19,650 --> 00:10:21,858 all thinking about what you should do with your money 227 00:10:21,858 --> 00:10:23,520 when you get a job. 228 00:10:23,520 --> 00:10:27,910 OK, imagine you plan to work full time from age 22 229 00:10:27,910 --> 00:10:29,228 to age 70. 230 00:10:29,228 --> 00:10:30,770 A little daunting to think about now. 231 00:10:30,770 --> 00:10:32,450 Probably, most people will retire after 70 232 00:10:32,450 --> 00:10:34,310 by the time you guys retire, but let's just 233 00:10:34,310 --> 00:10:36,840 think about 22 to 70. 234 00:10:36,840 --> 00:10:41,360 And let's say that you can save at a constant 7% interest rate. 235 00:10:41,360 --> 00:10:42,180 Inflation is zero. 236 00:10:42,180 --> 00:10:43,430 The interest rate is constant. 237 00:10:43,430 --> 00:10:44,060 Make life easy. 238 00:10:44,060 --> 00:10:46,940 7% interest rate. 239 00:10:46,940 --> 00:10:50,870 And let's consider two different plans you have for savings. 240 00:10:50,870 --> 00:10:51,650 Plan one. 241 00:10:54,180 --> 00:10:57,210 Plan one is that you're going to save 242 00:10:57,210 --> 00:11:02,400 $3,000 a year for the first 15 years that you work 243 00:11:02,400 --> 00:11:04,337 and then stop saving. 244 00:11:04,337 --> 00:11:05,920 3,000 a year for 15 years, then you're 245 00:11:05,920 --> 00:11:07,920 going to leave that in the bank, leave it alone, 246 00:11:07,920 --> 00:11:09,020 never save anymore. 247 00:11:09,020 --> 00:11:12,210 Just let that money sit in the bank. 248 00:11:12,210 --> 00:11:14,580 Well in that case, what will you have? 249 00:11:14,580 --> 00:11:19,650 Well, after the first 15 years of putting $3,000 in the bank 250 00:11:19,650 --> 00:11:26,652 every year, if you work out the math, you will have $75,000. 251 00:11:26,652 --> 00:11:31,520 $75,387 after 15 years. 252 00:11:31,520 --> 00:11:34,220 OK, now that's not just 15 years times-- 253 00:11:34,220 --> 00:11:35,960 that's bigger than 15 times 3,000, 254 00:11:35,960 --> 00:11:38,080 because you're earning interest along the way. 255 00:11:38,080 --> 00:11:39,443 OK, that's those 15 years. 256 00:11:39,443 --> 00:11:41,360 Then, you're just going to let that sit there. 257 00:11:41,360 --> 00:11:42,560 And that's going to sit there. 258 00:11:42,560 --> 00:11:44,768 Remember, after 15 years-- you started working at 22. 259 00:11:44,768 --> 00:11:46,250 You're only 37 years old. 260 00:11:46,250 --> 00:11:50,132 That's going to then sit there for the next 33 years. 261 00:11:50,132 --> 00:11:51,340 You're not going to touch it. 262 00:11:51,340 --> 00:11:52,715 You're not going to save anymore. 263 00:11:52,715 --> 00:11:54,710 What that means is after 33 years, 264 00:11:54,710 --> 00:12:02,140 this turns into $75,387 times 1.07 to the 33rd. 265 00:12:02,140 --> 00:12:07,760 OK, after 33 years, or $703,000. 266 00:12:07,760 --> 00:12:10,550 703,010. 267 00:12:10,550 --> 00:12:12,830 OK, so you save $3,000. 268 00:12:12,830 --> 00:12:13,830 It's not a lot of money. 269 00:12:13,830 --> 00:12:15,210 You guys can make a lot of money. 270 00:12:15,210 --> 00:12:19,110 $3,000 for 15 years, and then you never have to save again. 271 00:12:19,110 --> 00:12:21,420 Contrast that with a different approach. 272 00:12:21,420 --> 00:12:22,920 Let's say you say, look. 273 00:12:22,920 --> 00:12:23,530 That's stupid. 274 00:12:23,530 --> 00:12:24,030 I'm young. 275 00:12:24,030 --> 00:12:24,630 I'm going to party. 276 00:12:24,630 --> 00:12:26,120 I'll worry about retirement when retirement is closer. 277 00:12:26,120 --> 00:12:28,290 I'm going to save nothing the first 15 years, 278 00:12:28,290 --> 00:12:30,795 and then I'm going to save $3,000 every year. 279 00:12:30,795 --> 00:12:32,670 The first 15 years I'm going to save nothing, 280 00:12:32,670 --> 00:12:35,160 then I'll save $3,000 every year. 281 00:12:35,160 --> 00:12:38,220 OK, well if you do that and do the math, 282 00:12:38,220 --> 00:12:45,900 you end up with when you retire, $356,800. 283 00:12:45,900 --> 00:12:47,910 Think about this for one second. 284 00:12:47,910 --> 00:12:53,410 In this case, you saved for more than twice as many years. 285 00:12:53,410 --> 00:12:59,230 You saved for 33 years, and you ended up with half as much. 286 00:12:59,230 --> 00:13:01,680 That's the miracle of compounding. 287 00:13:01,680 --> 00:13:04,110 The earlier you save, the more money 288 00:13:04,110 --> 00:13:05,400 you can make along the way. 289 00:13:05,400 --> 00:13:08,540 And that's why you guys need to start saving right away. 290 00:13:08,540 --> 00:13:09,160 Yeah? 291 00:13:09,160 --> 00:13:10,327 AUDIENCE: What was plan two? 292 00:13:10,327 --> 00:13:13,220 JONATHAN GRUBER: Plan two was I do nothing the first 15 years, 293 00:13:13,220 --> 00:13:16,338 then I save $3,000 a year for the remaining 30 294 00:13:16,338 --> 00:13:17,130 years of my career. 295 00:13:21,010 --> 00:13:25,660 So literally, in plan one, I save for 15 years, 296 00:13:25,660 --> 00:13:27,040 and then I stop. 297 00:13:27,040 --> 00:13:28,905 Here, I save for 33 years. 298 00:13:28,905 --> 00:13:30,280 But by starting earlier and using 299 00:13:30,280 --> 00:13:31,780 the miracle of compounding, I end up 300 00:13:31,780 --> 00:13:33,320 with twice as much money. 301 00:13:33,320 --> 00:13:35,088 OK, now this is actually pretty-- 302 00:13:35,088 --> 00:13:36,880 this is one of the few things in this class 303 00:13:36,880 --> 00:13:38,838 my kids could understand when they were little. 304 00:13:38,838 --> 00:13:41,427 Because have any of you been to the Boston Science Museum? 305 00:13:41,427 --> 00:13:42,510 Have any of you guys been? 306 00:13:42,510 --> 00:13:46,150 OK, there's a little kid area, where they've got this ramp. 307 00:13:46,150 --> 00:13:48,360 And you can essentially drop balls down a ramp. 308 00:13:48,360 --> 00:13:50,610 And one ramp is flat and then steep, 309 00:13:50,610 --> 00:13:52,488 and one ramp is steep and then flat. 310 00:13:52,488 --> 00:13:54,780 And of course, the one that's steep and then flat wins. 311 00:13:54,780 --> 00:13:55,710 It's faster. 312 00:13:55,710 --> 00:13:57,335 And that's just because of compounding. 313 00:13:57,335 --> 00:13:59,160 That's because acceleration is compounding. 314 00:13:59,160 --> 00:14:01,785 OK, so basically, the point is that the earlier 315 00:14:01,785 --> 00:14:03,660 you start saving, the more money you'll have. 316 00:14:03,660 --> 00:14:05,070 And that's why you guys should pay attention 317 00:14:05,070 --> 00:14:06,940 when you're offered a job and offered a 401k 318 00:14:06,940 --> 00:14:09,150 and not think, retirement, I'll never retire. 319 00:14:09,150 --> 00:14:12,030 You say, no, I want to save now, because the more I save now, 320 00:14:12,030 --> 00:14:15,270 the more that will compound by the time I retire. 321 00:14:15,270 --> 00:14:18,162 OK, now you can actually see this. 322 00:14:18,162 --> 00:14:19,620 It's not just MIT students who have 323 00:14:19,620 --> 00:14:21,790 to think about this but professional athletes. 324 00:14:21,790 --> 00:14:23,330 So probably, none of you have heard 325 00:14:23,330 --> 00:14:26,670 of Bobby Bonilla Any of you guys heard of Bobby Bonilla? 326 00:14:26,670 --> 00:14:28,693 OK, well if you were 25 years ago in this class, 327 00:14:28,693 --> 00:14:30,110 if you were into sports, you would 328 00:14:30,110 --> 00:14:31,277 have heard of Bobby Bonilla. 329 00:14:31,277 --> 00:14:34,770 He was a pretty good player in his time. 330 00:14:34,770 --> 00:14:38,058 And he retired. 331 00:14:38,058 --> 00:14:40,350 But by the end of his career, he was kind of a slacker. 332 00:14:40,350 --> 00:14:41,517 He wasn't really worth much. 333 00:14:41,517 --> 00:14:43,020 He was playing for the Mets. 334 00:14:43,020 --> 00:14:44,520 And the Mets said, look. 335 00:14:44,520 --> 00:14:46,050 In 1999, they said, look. 336 00:14:46,050 --> 00:14:48,397 We basically want to pay you off to leave the team. 337 00:14:48,397 --> 00:14:49,230 You have a contract. 338 00:14:49,230 --> 00:14:51,690 We're just going to basically pay the remaining 5.9 million 339 00:14:51,690 --> 00:14:54,480 on your contract in 1999, give you the money. 340 00:14:54,480 --> 00:14:57,220 Most athletes would've said great, I'm off to Vegas. 341 00:14:57,220 --> 00:14:58,470 Bobby Bonilla didn't. 342 00:14:58,470 --> 00:14:59,310 He said, well, look. 343 00:14:59,310 --> 00:15:01,590 I've got enough money right now, but I 344 00:15:01,590 --> 00:15:02,920 might need the money later. 345 00:15:02,920 --> 00:15:07,410 So instead, why don't you defer the money at an 8% interest 346 00:15:07,410 --> 00:15:10,680 rate and pay me starting in 2011 when 347 00:15:10,680 --> 00:15:12,840 I'm getting close to retirement and need the money? 348 00:15:12,840 --> 00:15:13,660 They were like, great. 349 00:15:13,660 --> 00:15:14,130 That's really great. 350 00:15:14,130 --> 00:15:14,700 We don't have to pay you now. 351 00:15:14,700 --> 00:15:15,660 That's great. 352 00:15:15,660 --> 00:15:19,830 Well Bobby Bonilla, by the time his payments started in 2011, 353 00:15:19,830 --> 00:15:22,400 they'd grown to $30 million. 354 00:15:22,400 --> 00:15:24,985 And every year on a certain day-- it just passed recently. 355 00:15:24,985 --> 00:15:26,130 They call it Bobby Bonilla. 356 00:15:26,130 --> 00:15:27,990 Bobby Bonilla, who's now like 70 years old, 357 00:15:27,990 --> 00:15:31,740 gets a million dollar check from the Mets every year. 358 00:15:31,740 --> 00:15:34,470 Because he was patient enough to put this off and get 359 00:15:34,470 --> 00:15:36,660 the virtue of compounding. 360 00:15:36,660 --> 00:15:39,450 So this is sort of-- if Bobby Bonilla, a stupid baseball 361 00:15:39,450 --> 00:15:41,380 player, can do it, you guys can do it. 362 00:15:41,380 --> 00:15:43,830 So make sure that you guys are saving 363 00:15:43,830 --> 00:15:45,510 when you start your jobs. 364 00:15:45,510 --> 00:15:48,700 OK, questions about that? 365 00:15:48,700 --> 00:15:52,420 OK, now let's get a little bit realistic, 366 00:15:52,420 --> 00:15:55,510 and let's recognize that in life, prices aren't constant, 367 00:15:55,510 --> 00:15:58,780 but rather we have inflation. 368 00:15:58,780 --> 00:16:02,080 And how does that affect our thinking here? 369 00:16:02,080 --> 00:16:03,460 How does inflation affect the way 370 00:16:03,460 --> 00:16:05,350 we think about this problem? 371 00:16:05,350 --> 00:16:09,310 Well, it turns out, it actually adds one step, 372 00:16:09,310 --> 00:16:11,590 but it's actually a pretty easy step to put in. 373 00:16:11,590 --> 00:16:12,880 It actually turns out that you can add inflation 374 00:16:12,880 --> 00:16:14,437 without doing a whole lot of work. 375 00:16:14,437 --> 00:16:16,270 So let's talk about first what inflation is. 376 00:16:16,270 --> 00:16:20,010 Inflation is the rise in the price level year over year. 377 00:16:20,010 --> 00:16:23,020 Technically, the inflation rate is a percentage concept. 378 00:16:23,020 --> 00:16:26,950 It's the percent rise in the price level year after year. 379 00:16:26,950 --> 00:16:28,810 You might say, the price level of what? 380 00:16:28,810 --> 00:16:29,590 Of a banana? 381 00:16:29,590 --> 00:16:30,550 Of a computer? 382 00:16:30,550 --> 00:16:31,300 Of what? 383 00:16:31,300 --> 00:16:33,550 Well, what the government does is they 384 00:16:33,550 --> 00:16:37,270 form something called the consumer price index, the CPI. 385 00:16:37,270 --> 00:16:39,200 Did I talk about the CPI yet? 386 00:16:39,200 --> 00:16:40,250 OK, I'm sorry. 387 00:16:40,250 --> 00:16:41,740 I just hate repeating myself. 388 00:16:41,740 --> 00:16:44,150 OK, so they form something called the consumer price 389 00:16:44,150 --> 00:16:44,650 index. 390 00:16:44,650 --> 00:16:46,000 What's the consumer price index? 391 00:16:46,000 --> 00:16:48,640 Literally, the government every quarter, I believe-- 392 00:16:48,640 --> 00:16:50,020 it may be every month-- 393 00:16:50,020 --> 00:16:54,250 goes out and gets the prices of a basket of hundreds of goods. 394 00:16:54,250 --> 00:16:59,080 They literally say, what does a banana cost this month compared 395 00:16:59,080 --> 00:17:00,250 to last month? 396 00:17:00,250 --> 00:17:03,040 What does a laptop cost this month compared 397 00:17:03,040 --> 00:17:04,630 to last month, et cetera? 398 00:17:04,630 --> 00:17:07,060 So they go out, and they price this bundle of goods. 399 00:17:07,060 --> 00:17:09,825 And then literally, they just ask, how has the price-- 400 00:17:09,825 --> 00:17:11,200 they then take a weighted average 401 00:17:11,200 --> 00:17:14,236 of that bundle, where the weights are consumer spending. 402 00:17:14,236 --> 00:17:16,569 So consumers spend a lot more of their income on housing 403 00:17:16,569 --> 00:17:17,580 than bananas. 404 00:17:17,580 --> 00:17:19,955 So the price of housing gets a lot more weight in the CPI 405 00:17:19,955 --> 00:17:21,660 than does the price of bananas. 406 00:17:21,660 --> 00:17:24,700 Essentially, a weighted average of prices in society, 407 00:17:24,700 --> 00:17:26,650 and then they create an index. 408 00:17:26,650 --> 00:17:29,440 1982 is normalized to one, and they just 409 00:17:29,440 --> 00:17:31,570 say how much in percentage terms did 410 00:17:31,570 --> 00:17:33,890 that weighted average bundle go up in price? 411 00:17:33,890 --> 00:17:37,090 OK, and you can see that in Figure 17.1. 412 00:17:37,090 --> 00:17:39,600 Here's historical CPI. 413 00:17:39,600 --> 00:17:41,640 So basically, what you see is, this 414 00:17:41,640 --> 00:17:44,345 is the level of the CPI, which is sort of meaningless. 415 00:17:44,345 --> 00:17:45,960 What we care about is inflation, which 416 00:17:45,960 --> 00:17:49,770 is the year to year percentage change in the CPI. 417 00:17:49,770 --> 00:17:52,390 And what you can see is, basically it's going up. 418 00:17:52,390 --> 00:17:53,670 Prices are going up. 419 00:17:53,670 --> 00:17:58,590 It went up very steeply if you look from 1970 to 1980. 420 00:17:58,590 --> 00:18:01,920 The slope there was much higher than the slope before or after. 421 00:18:01,920 --> 00:18:05,360 We had very rapid inflation in the 1970s. 422 00:18:05,360 --> 00:18:07,032 It then has then since flattened, 423 00:18:07,032 --> 00:18:08,490 and inflation has been much slower. 424 00:18:08,490 --> 00:18:11,160 And inflation averages about 3% a year. 425 00:18:11,160 --> 00:18:15,545 OK, so basically, that's how we measure inflation. 426 00:18:15,545 --> 00:18:18,080 Now, the question is, how does that 427 00:18:18,080 --> 00:18:21,230 affect our thinking about present value 428 00:18:21,230 --> 00:18:23,210 if there's actually inflation? 429 00:18:23,210 --> 00:18:27,260 And the bottom line is, we don't care about dollars. 430 00:18:27,260 --> 00:18:30,250 We care about how many goods we can buy. 431 00:18:30,250 --> 00:18:31,900 Therefore, it doesn't matter what's 432 00:18:31,900 --> 00:18:35,820 happening to how much money we have. 433 00:18:35,820 --> 00:18:38,400 It matters what's happening to how many goods we can buy. 434 00:18:38,400 --> 00:18:40,740 Therefore, what we care about is not 435 00:18:40,740 --> 00:18:42,930 what we call the nominal interest rate. 436 00:18:42,930 --> 00:18:46,380 We care about what we call the real interest rate, r, which 437 00:18:46,380 --> 00:18:48,335 we define as the nominal interest rate, which 438 00:18:48,335 --> 00:18:49,710 is what we've been talking about, 439 00:18:49,710 --> 00:18:53,013 we see advertised on a bank, minus the rate of inflation, 440 00:18:53,013 --> 00:18:54,555 which for some reason we use pi, even 441 00:18:54,555 --> 00:18:55,920 though that's also profits. 442 00:18:55,920 --> 00:18:58,580 So sorry about that. 443 00:18:58,580 --> 00:19:01,810 OK, so we define the real interest rate 444 00:19:01,810 --> 00:19:07,280 as the nominal interest rate minus the inflation rate. 445 00:19:07,280 --> 00:19:09,060 The real interest rate is the nominal rate 446 00:19:09,060 --> 00:19:10,320 minus the inflation rate. 447 00:19:10,320 --> 00:19:12,900 And what the real interest rate measures 448 00:19:12,900 --> 00:19:15,600 is how much more I have in terms of goods 449 00:19:15,600 --> 00:19:17,525 I can consume, not how much more I 450 00:19:17,525 --> 00:19:19,650 have in terms of dollars, which actually in the end 451 00:19:19,650 --> 00:19:21,360 doesn't matter. 452 00:19:21,360 --> 00:19:26,550 OK, so suppose that I'm going to save $100 at a 10% interest 453 00:19:26,550 --> 00:19:27,117 rate. 454 00:19:27,117 --> 00:19:28,200 Let's go a simple example. 455 00:19:28,200 --> 00:19:31,120 I save $100 at a 10% interest rate. 456 00:19:31,120 --> 00:19:34,200 OK, then next year, I have $110. 457 00:19:34,200 --> 00:19:35,520 But that's irrelevant. 458 00:19:35,520 --> 00:19:38,170 What I want to know is, how many goods can I buy next year? 459 00:19:38,170 --> 00:19:39,750 So for example, let's say you spend all your money 460 00:19:39,750 --> 00:19:40,500 on Skittles. 461 00:19:40,500 --> 00:19:42,180 That's all you buy. 462 00:19:42,180 --> 00:19:46,050 OK, and let's say Skittles cost $1 this year. 463 00:19:46,050 --> 00:19:49,343 And there's no inflation, so they cost $1 next year. 464 00:19:49,343 --> 00:19:51,260 Then, what that means with a 10% interest rate 465 00:19:51,260 --> 00:19:54,930 is you can buy 10 more bags of Skittles next year. 466 00:19:54,930 --> 00:19:57,960 This year, your $100 could buy you 100 bags of Skittles. 467 00:19:57,960 --> 00:20:00,810 Next year, your $110 can buy 110 bags of Skittles, 468 00:20:00,810 --> 00:20:03,180 so you are 10% richer. 469 00:20:03,180 --> 00:20:07,548 But now, let's say the price of Skittles goes up 10%. 470 00:20:07,548 --> 00:20:09,090 Well, what that means is you can only 471 00:20:09,090 --> 00:20:10,800 buy the same amount of Skittles next year 472 00:20:10,800 --> 00:20:11,925 as you could buy this year. 473 00:20:11,925 --> 00:20:15,360 You could buy 100 bags this year and 100 bags next year. 474 00:20:15,360 --> 00:20:17,550 So it doesn't matter that you have $110 next year. 475 00:20:17,550 --> 00:20:18,600 Who cares? 476 00:20:18,600 --> 00:20:20,715 You only get the same amount of Skittles. 477 00:20:20,715 --> 00:20:22,590 What you care about is the goods you can buy. 478 00:20:22,590 --> 00:20:23,430 We wrote down utility. 479 00:20:23,430 --> 00:20:25,230 We didn't put dollars of utility function. 480 00:20:25,230 --> 00:20:27,282 We put consumption. 481 00:20:27,282 --> 00:20:28,740 So the interest rate you care about 482 00:20:28,740 --> 00:20:30,190 is the real interest rate. 483 00:20:30,190 --> 00:20:33,420 If the nominal interest rate is 10% but inflation is 10%, 484 00:20:33,420 --> 00:20:35,490 then the real interest rate is zero. 485 00:20:35,490 --> 00:20:37,900 You can't buy any more goods next year. 486 00:20:37,900 --> 00:20:39,900 All the money you made by putting it in the bank 487 00:20:39,900 --> 00:20:44,250 got eaten up by how much more expensive things are. 488 00:20:44,250 --> 00:20:46,460 So what that means is, all the math we've done 489 00:20:46,460 --> 00:20:50,133 and everything we'll talk about all goes through. 490 00:20:50,133 --> 00:20:52,550 You just need to be thinking about using the real interest 491 00:20:52,550 --> 00:20:55,330 rate, not the nominal interest rate. 492 00:20:55,330 --> 00:20:58,510 But otherwise, everything we've done goes through. 493 00:20:58,510 --> 00:21:00,070 You just need to essentially think 494 00:21:00,070 --> 00:21:02,140 about this in terms of how many goods 495 00:21:02,140 --> 00:21:05,380 you can buy, not how much money you have. 496 00:21:05,380 --> 00:21:07,090 Now, this isn't quite-- 497 00:21:07,090 --> 00:21:10,060 let me just take two minutes and do a little macroeconomics-- 498 00:21:10,060 --> 00:21:12,970 this isn't quite as simple as it sounds, 499 00:21:12,970 --> 00:21:16,510 because of course, you see in the bank, i, 500 00:21:16,510 --> 00:21:17,740 in the bank window, i. 501 00:21:17,740 --> 00:21:19,240 You don't see pi. 502 00:21:19,240 --> 00:21:20,240 You don't see inflation. 503 00:21:20,240 --> 00:21:21,715 That's what we revealed ex post. 504 00:21:21,715 --> 00:21:23,590 So really, technically-- you don't know this. 505 00:21:23,590 --> 00:21:25,182 It's just for those who care. 506 00:21:25,182 --> 00:21:26,890 You don't have to know this for the test. 507 00:21:26,890 --> 00:21:30,345 Technically, what you really want is expected inflation. 508 00:21:30,345 --> 00:21:32,470 When you think of putting in the money in the bank, 509 00:21:32,470 --> 00:21:34,180 you know you'll learn 3%. 510 00:21:34,180 --> 00:21:35,680 The real interest rate is that minus 511 00:21:35,680 --> 00:21:38,780 what you think inflation is going to be. 512 00:21:38,780 --> 00:21:40,580 So it actually becomes complicated. 513 00:21:40,580 --> 00:21:41,690 It's not as simple. 514 00:21:41,690 --> 00:21:44,120 Ex post, it's easy to find the real interest rate. 515 00:21:44,120 --> 00:21:46,040 Ex ante, it's not so easy, because it 516 00:21:46,040 --> 00:21:48,500 depends on what you think inflation is going to be. 517 00:21:48,500 --> 00:21:49,730 So there's some tricks there. 518 00:21:49,730 --> 00:21:52,105 There's also a bunch of tricks in measuring the inflation 519 00:21:52,105 --> 00:21:53,070 rate. 520 00:21:53,070 --> 00:21:55,760 So for example, like I said, the Bureau of Labor Statistics 521 00:21:55,760 --> 00:21:59,730 goes out and has a bundle of 600 goods and gets their prices. 522 00:21:59,730 --> 00:22:00,620 But what is a good? 523 00:22:00,620 --> 00:22:01,940 I mean, a banana is a banana. 524 00:22:01,940 --> 00:22:04,220 But a laptop, what the hell is a laptop? 525 00:22:04,220 --> 00:22:05,540 How much ram does it have? 526 00:22:05,540 --> 00:22:08,240 What's the graphics card? 527 00:22:08,240 --> 00:22:10,020 How fancy is the display? 528 00:22:10,020 --> 00:22:11,690 Well, the Bureau of Labor Statistics 529 00:22:11,690 --> 00:22:13,982 doesn't go out and price literally hundreds of laptops. 530 00:22:13,982 --> 00:22:16,090 It prices one or two. 531 00:22:16,090 --> 00:22:18,470 And the problem with that is the following. 532 00:22:18,470 --> 00:22:21,860 Let's say you find that today, a laptop is 1,000, 533 00:22:21,860 --> 00:22:23,980 and tomorrow it's 1500. 534 00:22:23,980 --> 00:22:25,120 But it can do-- 535 00:22:25,120 --> 00:22:28,540 let's say today, a laptop is 1,000, and tomorrow, it's 1500. 536 00:22:28,540 --> 00:22:31,280 But it can do a ton more stuff. 537 00:22:31,280 --> 00:22:33,560 Well, we would say inflation's 50%, 538 00:22:33,560 --> 00:22:35,443 but that's not really right. 539 00:22:35,443 --> 00:22:37,610 Because the good you're consuming is not the laptop, 540 00:22:37,610 --> 00:22:39,990 it's the computing ability of the laptop. 541 00:22:39,990 --> 00:22:42,000 And that's gone up. 542 00:22:42,000 --> 00:22:44,270 So to say inflation's 50% is wrong. 543 00:22:44,270 --> 00:22:47,370 Inflation's 50% minus the quality improvement 544 00:22:47,370 --> 00:22:49,290 of the better laptop you got. 545 00:22:49,290 --> 00:22:50,320 Think of it another way. 546 00:22:50,320 --> 00:22:54,750 Imagine laptop prices didn't go up, but ram doubled. 547 00:22:54,750 --> 00:22:56,880 Would you say you're no better off 548 00:22:56,880 --> 00:22:59,640 buying a laptop with twice as much ram at the same price? 549 00:22:59,640 --> 00:23:01,180 No, you're better off. 550 00:23:01,180 --> 00:23:04,530 But our inflation concept would say, no, you're the same off. 551 00:23:04,530 --> 00:23:07,160 So the trick here is, it's simple in practice, 552 00:23:07,160 --> 00:23:10,020 and we'll pretend it's simple just to say r is i minus pi. 553 00:23:10,020 --> 00:23:12,040 But two tricks-- a, it's expected pi, 554 00:23:12,040 --> 00:23:13,860 which is hard to guess. 555 00:23:13,860 --> 00:23:16,613 And b, inflation is really hard to measure, 556 00:23:16,613 --> 00:23:19,030 because there's things like quality bias and other things. 557 00:23:19,030 --> 00:23:20,790 There's a whole field of macroeconomics worrying 558 00:23:20,790 --> 00:23:23,290 about inflation measurement, so we won't spend a lot of time 559 00:23:23,290 --> 00:23:23,800 on it. 560 00:23:23,800 --> 00:23:26,860 But it's just sort of interesting just 561 00:23:26,860 --> 00:23:29,730 to talk about how at high level we go through things here. 562 00:23:29,730 --> 00:23:31,250 Like everything else in this class, 563 00:23:31,250 --> 00:23:32,730 largely, we get it right. 564 00:23:32,730 --> 00:23:35,160 Largely, expected inflation is not too badly modeled 565 00:23:35,160 --> 00:23:36,660 by last year's inflation. 566 00:23:36,660 --> 00:23:38,640 And quality bias, we can model and stuff. 567 00:23:38,640 --> 00:23:40,380 So this isn't a bad model, but it just 568 00:23:40,380 --> 00:23:41,880 points to some of the subtleties you 569 00:23:41,880 --> 00:23:43,255 have to deal with in reality when 570 00:23:43,255 --> 00:23:47,260 you try to implement these basic sort of formulations. 571 00:23:47,260 --> 00:23:51,490 Now, with that in mind, I'm going to now say, 572 00:23:51,490 --> 00:23:54,080 let's assume inflation is zero again. 573 00:23:54,080 --> 00:23:56,800 So we'll go back and use i, and we'll 574 00:23:56,800 --> 00:24:00,670 use i interchangeably with r for the rest of this course 575 00:24:00,670 --> 00:24:02,050 unless asked differently. 576 00:24:02,050 --> 00:24:04,300 Unless told definitely, assume inflation is zero, 577 00:24:04,300 --> 00:24:06,850 so i and r are interchangeable. 578 00:24:06,850 --> 00:24:09,430 With that in mind, let's go to the next topic, which 579 00:24:09,430 --> 00:24:13,780 is taking these tools, how do we model choices over time? 580 00:24:17,490 --> 00:24:19,050 How do people model? 581 00:24:19,050 --> 00:24:22,368 How do people make decisions over time? 582 00:24:22,368 --> 00:24:23,535 And there's a simple answer. 583 00:24:23,535 --> 00:24:26,940 So this is tricky, because if I said to you, hey, 584 00:24:26,940 --> 00:24:27,870 I'm going to give-- 585 00:24:27,870 --> 00:24:30,060 do you want $30 or $50? 586 00:24:30,060 --> 00:24:31,188 You would say, I want $50. 587 00:24:31,188 --> 00:24:32,730 But actually, you shouldn't say that. 588 00:24:32,730 --> 00:24:34,830 You should say, over what period of time am I getting the 30, 589 00:24:34,830 --> 00:24:37,170 and over what period of time am I getting the 50? 590 00:24:37,170 --> 00:24:38,620 If it's today, I want 50. 591 00:24:38,620 --> 00:24:41,280 But if the 50 is 20 years in the future and the 30's today, 592 00:24:41,280 --> 00:24:43,150 I might want the 30. 593 00:24:43,150 --> 00:24:46,240 What that means is, you have to evaluate choices 594 00:24:46,240 --> 00:24:48,670 in present value terms. 595 00:24:48,670 --> 00:24:50,590 You can't just add up the money, you 596 00:24:50,590 --> 00:24:53,710 have to evaluate those choices in present value terms. 597 00:24:53,710 --> 00:24:55,720 And then, you need to pick the option 598 00:24:55,720 --> 00:24:57,578 with the highest present value. 599 00:24:57,578 --> 00:24:59,370 So once again, let's come back to athletes, 600 00:24:59,370 --> 00:25:02,100 because athletic contracts deal with this all the time. 601 00:25:02,100 --> 00:25:03,600 Let's imagine an athlete considering 602 00:25:03,600 --> 00:25:05,810 two different contracts. 603 00:25:05,810 --> 00:25:11,190 Contract one, contract a, pays $1 million today. 604 00:25:14,330 --> 00:25:27,760 Contract b pays 500,000 today and 1.5 million in 10 years. 605 00:25:30,650 --> 00:25:32,790 OK, now when you read it in the newspaper, 606 00:25:32,790 --> 00:25:34,540 you'll see this guy got offered a million, 607 00:25:34,540 --> 00:25:36,602 this guy got offered two million. 608 00:25:36,602 --> 00:25:38,060 That's what the newspaper will say. 609 00:25:38,060 --> 00:25:40,422 But that's wrong, because these are 610 00:25:40,422 --> 00:25:41,880 paid at different periods of times, 611 00:25:41,880 --> 00:25:43,088 so they're different amounts. 612 00:25:43,088 --> 00:25:48,560 Indeed, the present value of the first contract is what? 613 00:25:48,560 --> 00:25:49,310 $1 million. 614 00:25:49,310 --> 00:25:50,050 It's today. 615 00:25:50,050 --> 00:25:52,280 What's the present value of the second contract? 616 00:25:52,280 --> 00:25:54,410 Someone tell me how I'd write that down. 617 00:25:54,410 --> 00:25:57,020 I'd write down the present value of the second contract. 618 00:25:57,020 --> 00:25:57,540 Yeah? 619 00:25:57,540 --> 00:26:02,060 AUDIENCE: 500,000 plus 1.5 million 620 00:26:02,060 --> 00:26:06,912 over one plus whatever the interest is based on the time. 621 00:26:06,912 --> 00:26:08,460 JONATHAN GRUBER: Exactly. 622 00:26:08,460 --> 00:26:11,190 Which is one plus the interest rate to the 10, 623 00:26:11,190 --> 00:26:13,560 because you're getting it in 10 years. 624 00:26:13,560 --> 00:26:17,640 So essentially, that means that whether it's a better deal 625 00:26:17,640 --> 00:26:20,160 or not depends on the interest rate. 626 00:26:20,160 --> 00:26:24,110 Indeed, if the interest rate is 7%, 627 00:26:24,110 --> 00:26:27,470 and the interest rate is 7%, this 628 00:26:27,470 --> 00:26:29,880 has a present value of 1.3 million. 629 00:26:29,880 --> 00:26:31,600 So it's a good deal. 630 00:26:31,600 --> 00:26:36,270 If the interest rate was 14%, then 631 00:26:36,270 --> 00:26:44,530 this deal would have a present value of 0.9 million. 632 00:26:44,530 --> 00:26:46,245 So it's a worse deal. 633 00:26:46,245 --> 00:26:48,120 So whether or not this a better or worse deal 634 00:26:48,120 --> 00:26:50,780 depends on the interest rate. 635 00:26:50,780 --> 00:26:52,130 Why is that? 636 00:26:52,130 --> 00:26:54,980 Why is this a worse deal the higher the interest rate? 637 00:26:57,520 --> 00:27:00,652 AUDIENCE: Because if he'd gotten the money earlier, 638 00:27:00,652 --> 00:27:02,860 he wouldn't have benefited from being able to collect 639 00:27:02,860 --> 00:27:04,110 that interest earlier. 640 00:27:04,110 --> 00:27:06,610 JONATHAN GRUBER: Exactly, he could have invested it earlier, 641 00:27:06,610 --> 00:27:10,250 gotten the compounding, and had way more money in 10 years. 642 00:27:10,250 --> 00:27:13,680 So the higher the interest rate, the more you 643 00:27:13,680 --> 00:27:16,260 want to get your money upfront and save it, 644 00:27:16,260 --> 00:27:19,930 the less valuable is money in the future. 645 00:27:19,930 --> 00:27:21,790 Now, essentially, what this says is 646 00:27:21,790 --> 00:27:23,690 that you have to always use present value to bring things 647 00:27:23,690 --> 00:27:24,565 into current dollars. 648 00:27:24,565 --> 00:27:26,470 Now, this is not an abstract concept. 649 00:27:26,470 --> 00:27:28,970 Let's take Max Scherzer, who's a pitcher with the Washington 650 00:27:28,970 --> 00:27:30,320 Nationals. 651 00:27:30,320 --> 00:27:32,720 Max Scherzer a couple of years ago 652 00:27:32,720 --> 00:27:40,410 signed a seven year $210 million contract, which 653 00:27:40,410 --> 00:27:42,870 he was able to brag was the second highest ever signed 654 00:27:42,870 --> 00:27:45,870 by a pitcher and the 10th highest contract ever signed 655 00:27:45,870 --> 00:27:47,100 by any baseball player. 656 00:27:47,100 --> 00:27:48,510 Seven years, 210. 657 00:27:48,510 --> 00:27:52,320 But in fact, that contract was not-- 658 00:27:52,320 --> 00:27:55,460 we're going to pay you $30 million a year for seven years. 659 00:27:55,460 --> 00:27:57,210 It was, we're going to pay you $15 million 660 00:27:57,210 --> 00:27:59,040 a year for 14 years. 661 00:27:59,040 --> 00:28:00,840 You're going to play for only seven. 662 00:28:00,840 --> 00:28:03,320 We're going to pay you over 14 years. 663 00:28:03,320 --> 00:28:05,060 So in fact, in present value terms, 664 00:28:05,060 --> 00:28:06,500 that was worth somewhat less. 665 00:28:06,500 --> 00:28:08,060 If you use the current interest rate 666 00:28:08,060 --> 00:28:10,850 when he signed it which was about 4.7%, 667 00:28:10,850 --> 00:28:14,030 it was only worth actually 166 million. 668 00:28:14,030 --> 00:28:15,990 Not too shabby, but suddenly it drops 669 00:28:15,990 --> 00:28:17,540 to the 20th most valuable baseball 670 00:28:17,540 --> 00:28:19,970 contract and about fourth among pitchers. 671 00:28:19,970 --> 00:28:22,860 So Max Scherzer was able to feel better about himself that he 672 00:28:22,860 --> 00:28:24,777 signed this valuable contract, but in fact, it 673 00:28:24,777 --> 00:28:26,068 was worth less than he thought. 674 00:28:26,068 --> 00:28:27,830 I mean, shed no tears for Max Scherzer. 675 00:28:27,830 --> 00:28:28,940 He's doing fine. 676 00:28:28,940 --> 00:28:30,838 But it was worth less than he thought. 677 00:28:30,838 --> 00:28:32,630 Or maybe an example that's more in our mind 678 00:28:32,630 --> 00:28:36,080 with the Mega Millions-- think about a lottery winner. 679 00:28:36,080 --> 00:28:41,020 So if a Mega Millions winner gets $290 million, 680 00:28:41,020 --> 00:28:45,110 which sounds like a great deal, that's paid out over 20 years. 681 00:28:45,110 --> 00:28:48,040 So it's not $290 million, it's 14 and and a half million 682 00:28:48,040 --> 00:28:50,400 for each of 20 years. 683 00:28:50,400 --> 00:28:53,990 So in present value terms, if we think about a 7% interest 684 00:28:53,990 --> 00:28:58,470 rate, then that's not 290 million, it's 164 million. 685 00:28:58,470 --> 00:29:00,660 Once again, not too shabby. 686 00:29:00,660 --> 00:29:04,430 OK, but a lot less than the advertised amount. 687 00:29:04,430 --> 00:29:09,520 So we have to take these dollars and put them in present value. 688 00:29:09,520 --> 00:29:11,860 So now, here's an interesting question for that. 689 00:29:11,860 --> 00:29:14,740 If you look at the recent lottery, 690 00:29:14,740 --> 00:29:18,525 you had a choice of one person won 1.6 billion, 691 00:29:18,525 --> 00:29:20,900 one person one that, a person in South Carolina won that. 692 00:29:20,900 --> 00:29:23,870 And they were given a choice of the 1.6 billion, 693 00:29:23,870 --> 00:29:25,870 which is paid actually over 30 years, 694 00:29:25,870 --> 00:29:28,980 or a lump sum they could get right away. 695 00:29:28,980 --> 00:29:32,710 How should they decide which of those options to take? 696 00:29:32,710 --> 00:29:34,960 How should they decide whether to take the 1.6 billion 697 00:29:34,960 --> 00:29:37,240 paid over 30 years, so 1.6 over 30, paid 698 00:29:37,240 --> 00:29:41,050 in equal installments over time versus just getting a lump 699 00:29:41,050 --> 00:29:41,980 sum today. 700 00:29:41,980 --> 00:29:44,260 Not of 1.6 million, but a lower amount. 701 00:29:44,260 --> 00:29:46,120 How should they think about that? 702 00:29:46,120 --> 00:29:48,520 AUDIENCE: They should evaluate the present value. 703 00:29:48,520 --> 00:29:49,420 JONATHAN GRUBER: They should add the present value. 704 00:29:49,420 --> 00:29:50,710 They should say, well, what do I think the interest 705 00:29:50,710 --> 00:29:51,800 rate is going to be? 706 00:29:51,800 --> 00:29:53,970 If I think it's going to be really low-- 707 00:29:53,970 --> 00:29:56,300 let's say the interest rate is going to be zero. 708 00:29:56,300 --> 00:29:59,164 Then which deal should I take? 709 00:29:59,164 --> 00:30:00,627 AUDIENCE: [INAUDIBLE] 710 00:30:00,627 --> 00:30:02,710 JONATHAN GRUBER: I should spread it out over time, 711 00:30:02,710 --> 00:30:04,630 because the money in the future is worth the same as today, 712 00:30:04,630 --> 00:30:06,620 so I might as well take the 1.6 billion. 713 00:30:06,620 --> 00:30:07,330 But if I think the interest rate is 714 00:30:07,330 --> 00:30:09,730 going to be higher, than I should take the money upfront 715 00:30:09,730 --> 00:30:11,770 and invest that money and earn my own interest. 716 00:30:11,770 --> 00:30:13,255 So essentially, it becomes a debate 717 00:30:13,255 --> 00:30:15,130 of what you think the interest rate is versus 718 00:30:15,130 --> 00:30:16,922 what the state thinks the interest rate is. 719 00:30:16,922 --> 00:30:19,870 They're setting those two to be equal under some assumption 720 00:30:19,870 --> 00:30:20,745 of the interest rate. 721 00:30:20,745 --> 00:30:22,245 I don't know what number they chose. 722 00:30:22,245 --> 00:30:23,500 Whatever number they chose. 723 00:30:23,500 --> 00:30:25,720 It was some number they chose, because this is our assumption 724 00:30:25,720 --> 00:30:26,470 of the interest rate. 725 00:30:26,470 --> 00:30:27,520 You've got to decide, do you think the interest rate's 726 00:30:27,520 --> 00:30:28,730 going to be higher or lower? 727 00:30:28,730 --> 00:30:30,250 If you think it's going to be higher than the state thinks 728 00:30:30,250 --> 00:30:32,940 it is, then you want the money upfront, and you'll invest it. 729 00:30:32,940 --> 00:30:34,440 If you think it's going to be lower, 730 00:30:34,440 --> 00:30:36,700 than you should take the money over time, because the state is 731 00:30:36,700 --> 00:30:38,158 giving you basically a better deal. 732 00:30:40,390 --> 00:30:42,440 Do you understand that? 733 00:30:42,440 --> 00:30:45,830 OK, so now armed with this, let's 734 00:30:45,830 --> 00:30:51,260 go and think about how do firms make investment decisions? 735 00:30:53,870 --> 00:30:55,990 How do firms make investment decisions? 736 00:30:59,530 --> 00:31:05,320 Remember, investment is about the delay 737 00:31:05,320 --> 00:31:08,980 of current consumption for future assumptions. 738 00:31:08,980 --> 00:31:10,930 It's about putting some aside today 739 00:31:10,930 --> 00:31:13,360 by spending money on a machine which will deliver 740 00:31:13,360 --> 00:31:15,830 you benefits in the future. 741 00:31:15,830 --> 00:31:18,070 Now, this adds one wrinkle to what we've 742 00:31:18,070 --> 00:31:21,418 done so far, which is that we've only talked about money that's 743 00:31:21,418 --> 00:31:23,710 always positive, some amount you get get in the future. 744 00:31:23,710 --> 00:31:25,020 When you're making an investment decision, 745 00:31:25,020 --> 00:31:26,490 it's a little bit more complicated, 746 00:31:26,490 --> 00:31:29,200 because you're actually spending money today 747 00:31:29,200 --> 00:31:31,005 to make money tomorrow. 748 00:31:31,005 --> 00:31:32,380 So in that case, we talk about we 749 00:31:32,380 --> 00:31:35,200 call net present value, which is the same thing, 750 00:31:35,200 --> 00:31:37,210 it just allows for negative values. 751 00:31:37,210 --> 00:31:39,160 Net present value, which is essentially 752 00:31:39,160 --> 00:31:42,370 saying in every period, you want to account 753 00:31:42,370 --> 00:31:46,690 for the cost of that period and the benefits of that period, 754 00:31:46,690 --> 00:31:49,960 and you want to invest only if the net present value is 755 00:31:49,960 --> 00:31:51,490 greater than zero. 756 00:31:51,490 --> 00:31:54,160 So for example, think about a project 757 00:31:54,160 --> 00:31:58,180 that has a stream of payments in every period of r sub i, 758 00:31:58,180 --> 00:32:01,050 every period it's got a stream of payments of r sub i, 759 00:32:01,050 --> 00:32:03,402 and a set of costs that's c sub i. 760 00:32:03,402 --> 00:32:05,235 The costs are the upfront investments, maybe 761 00:32:05,235 --> 00:32:06,810 the maintenance of the machine. 762 00:32:06,810 --> 00:32:09,360 Whatever it costs to run it. 763 00:32:09,360 --> 00:32:12,130 Then, the net present value of that investment 764 00:32:12,130 --> 00:32:22,330 is r0 minus c0, comma r1 minus c1 over one plus i-- 765 00:32:22,330 --> 00:32:30,740 over one plus i plus r2 minus c2 over one plus i 766 00:32:30,740 --> 00:32:34,550 squared plus dot dot dot for as many periods 767 00:32:34,550 --> 00:32:37,310 as the investment lasts. 768 00:32:37,310 --> 00:32:41,930 That's the net present value of an investment. 769 00:32:41,930 --> 00:32:44,570 So basically, what you want to ask 770 00:32:44,570 --> 00:32:48,350 is, take each period's costs of benefits into account. 771 00:32:48,350 --> 00:32:51,480 On net, is it greater than zero? 772 00:32:51,480 --> 00:32:55,800 OK, so the key point is that basically, sometimes 773 00:32:55,800 --> 00:32:58,950 investments which have upfront costs 774 00:32:58,950 --> 00:33:00,810 can be valuable as long as the long run 775 00:33:00,810 --> 00:33:02,550 benefits are large enough. 776 00:33:02,550 --> 00:33:06,570 So if you think about an investment that's got 100-- 777 00:33:06,570 --> 00:33:10,980 so think about a simple, trivial example of the first period 778 00:33:10,980 --> 00:33:15,600 you buy a machine, and it costs $100. 779 00:33:15,600 --> 00:33:18,520 So c0 is 100. 780 00:33:18,520 --> 00:33:21,590 And let's say for every period thereafter, 781 00:33:21,590 --> 00:33:26,330 that machine will deliver you revenues, revenue i-- 782 00:33:26,330 --> 00:33:28,310 revenues for i greater than zero-- 783 00:33:28,310 --> 00:33:30,170 of 200. 784 00:33:30,170 --> 00:33:32,870 But it will have maintenance costs, costs i 785 00:33:32,870 --> 00:33:34,970 greater than zero, of 50. 786 00:33:37,590 --> 00:33:39,310 So what's the net present value? 787 00:33:39,310 --> 00:33:45,060 Well, the net present value is simply minus 100. 788 00:33:45,060 --> 00:33:47,620 And let's say the machine is going to last forever. 789 00:33:47,620 --> 00:33:52,840 Minus 100 plus 150 over i. 790 00:33:52,840 --> 00:33:54,090 Think about that for a second. 791 00:34:02,570 --> 00:34:05,210 Basically, what we're saying is, you're throwing 100 at it 792 00:34:05,210 --> 00:34:06,936 today, so that's negative. 793 00:34:06,936 --> 00:34:08,519 But every period in the future, you're 794 00:34:08,519 --> 00:34:11,752 going to net $150, because you're going to make $200 795 00:34:11,752 --> 00:34:13,210 and you have $50 maintenance costs. 796 00:34:13,210 --> 00:34:14,668 And we have the formula, so we just 797 00:34:14,668 --> 00:34:16,159 apply the formula for perpetuity. 798 00:34:16,159 --> 00:34:18,770 We have a set of future payments of $150, 799 00:34:18,770 --> 00:34:24,190 so your net present value is minus 100 plus 150 over i. 800 00:34:24,190 --> 00:34:27,100 So let's think about, look at this formula for a second. 801 00:34:27,100 --> 00:34:28,510 What does that say? 802 00:34:28,510 --> 00:34:31,300 What is the relationship between whether the firm's going 803 00:34:31,300 --> 00:34:33,550 to want to invest and the interest rate? 804 00:34:35,833 --> 00:34:37,375 What does this imply the relationship 805 00:34:37,375 --> 00:34:39,920 is between a firm's desire for investment and the interest 806 00:34:39,920 --> 00:34:40,420 rate? 807 00:34:40,420 --> 00:34:42,489 If the interest rate goes up, will firms 808 00:34:42,489 --> 00:34:45,719 want to do more investment, or less investment, and why? 809 00:34:45,719 --> 00:34:47,719 Will firms want to be more eager to buy machines 810 00:34:47,719 --> 00:34:49,460 or less eager to buy machines, and why, as the interest 811 00:34:49,460 --> 00:34:50,150 rate goes up? 812 00:34:50,150 --> 00:34:50,922 Yeah. 813 00:34:50,922 --> 00:34:51,980 AUDIENCE: They'll be less eager. 814 00:34:51,980 --> 00:34:53,147 JONATHAN GRUBER: Less eager. 815 00:34:53,147 --> 00:34:54,719 AUDIENCE: [INAUDIBLE] 816 00:34:54,719 --> 00:34:55,505 JONATHAN GRUBER: They'll be less eager. 817 00:34:55,505 --> 00:34:56,719 Say it again, because why? 818 00:34:56,719 --> 00:34:58,344 AUDIENCE: Because if they're borrowing. 819 00:35:00,562 --> 00:35:02,520 JONATHAN GRUBER: Yeah, or I think an easier way 820 00:35:02,520 --> 00:35:04,392 to think of borrowing, just think about, 821 00:35:04,392 --> 00:35:05,600 they've got a bunch of money. 822 00:35:05,600 --> 00:35:08,000 Apple's got a bunch of money today they're sitting on. 823 00:35:08,000 --> 00:35:10,690 If they buy the machine, they're going to get this return. 824 00:35:10,690 --> 00:35:13,190 If they don't buy the machine, they could put it in the bank 825 00:35:13,190 --> 00:35:16,130 or invest it in Apple stock and get some interest rate, i. 826 00:35:16,130 --> 00:35:19,760 The higher the interest rate, the less they want invest. 827 00:35:19,760 --> 00:35:20,990 Or think of it this way. 828 00:35:20,990 --> 00:35:26,220 The interest rate is the opportunity cost of investment. 829 00:35:26,220 --> 00:35:28,460 The more the firm invests in their machines, 830 00:35:28,460 --> 00:35:32,030 the less they can earn saving through some other mechanism. 831 00:35:32,030 --> 00:35:35,150 And the price that they pay by foregoing 832 00:35:35,150 --> 00:35:38,110 that other savings is i. 833 00:35:38,110 --> 00:35:38,740 Yeah. 834 00:35:38,740 --> 00:35:41,520 AUDIENCE: So does that mean if you're looking at a machine, 835 00:35:41,520 --> 00:35:43,808 it's better to try to then push the cost further 836 00:35:43,808 --> 00:35:46,100 into the future, because then they can't also divide by 837 00:35:46,100 --> 00:35:47,460 the [INAUDIBLE] sign? 838 00:35:47,460 --> 00:35:49,790 JONATHAN GRUBER: Basically, you always want 839 00:35:49,790 --> 00:35:51,700 to try to make as much money early as you can 840 00:35:51,700 --> 00:35:53,242 and make the cost as late as you can. 841 00:35:53,242 --> 00:35:58,480 For any given amount, you'd absolutely like to do that. 842 00:35:58,480 --> 00:36:00,980 That's why we'll talk about this in my public finance class. 843 00:36:00,980 --> 00:36:02,840 We talk about why, when you're paying taxes, 844 00:36:02,840 --> 00:36:05,110 you always want to try to find shenanigans that allow 845 00:36:05,110 --> 00:36:06,985 you to pay your taxes later. 846 00:36:06,985 --> 00:36:08,360 So for any given amount of taxes, 847 00:36:08,360 --> 00:36:09,808 the later you pay it, the less it 848 00:36:09,808 --> 00:36:12,350 costs you, because you get to earn the interest along the way 849 00:36:12,350 --> 00:36:15,500 and then pay it later on. 850 00:36:15,500 --> 00:36:17,840 This is a key macroeconomic concept. 851 00:36:17,840 --> 00:36:20,240 You'll often hear in the news, high interest rates 852 00:36:20,240 --> 00:36:21,843 are bad for business. 853 00:36:21,843 --> 00:36:23,510 And you might have thought, why is that? 854 00:36:23,510 --> 00:36:24,645 This is why. 855 00:36:24,645 --> 00:36:27,020 High interest rates are bad for the economy, you'll hear. 856 00:36:27,020 --> 00:36:29,030 Why are high interest rates bad for the economy? 857 00:36:29,030 --> 00:36:29,730 You might say, wait a second. 858 00:36:29,730 --> 00:36:30,850 That makes no sense. 859 00:36:30,850 --> 00:36:33,067 A high interest rate means I earn more on my savings. 860 00:36:33,067 --> 00:36:34,400 Why is that bad for the economy? 861 00:36:34,400 --> 00:36:35,900 It's bad for the economy, because it 862 00:36:35,900 --> 00:36:38,140 lowers the demand for capital. 863 00:36:38,140 --> 00:36:39,760 Because the higher the interest rate, 864 00:36:39,760 --> 00:36:42,420 the less firms actually want to invest. 865 00:36:42,420 --> 00:36:46,650 The more they just want to stock their money away in the bank. 866 00:36:46,650 --> 00:36:52,450 So that is the key question. 867 00:36:52,450 --> 00:36:55,560 Now, then let me ask another question. 868 00:36:55,560 --> 00:36:59,845 If you're a firm, what's the right i to use? 869 00:36:59,845 --> 00:37:02,220 If you're a firm thinking about this investment decision, 870 00:37:02,220 --> 00:37:05,270 we know the higher i is, the less you want invest. 871 00:37:05,270 --> 00:37:06,230 But what is i? 872 00:37:06,230 --> 00:37:07,438 Once again, forget inflation. 873 00:37:07,438 --> 00:37:08,360 Inflation is zero. 874 00:37:08,360 --> 00:37:12,880 What's the right what we call firm discount rate? 875 00:37:12,880 --> 00:37:15,097 The discount rate is the amount by which 876 00:37:15,097 --> 00:37:17,430 firms are going to discount future dollars to bring them 877 00:37:17,430 --> 00:37:18,180 back to today. 878 00:37:18,180 --> 00:37:21,575 How does the firm think about what i to use? 879 00:37:21,575 --> 00:37:22,700 What i should the firm use? 880 00:37:27,260 --> 00:37:27,860 Your Apple. 881 00:37:27,860 --> 00:37:28,610 Yeah, go ahead. 882 00:37:28,610 --> 00:37:30,943 AUDIENCE: [INAUDIBLE] i that makes that positive, right? 883 00:37:30,943 --> 00:37:32,527 JONATHAN GRUBER: Well, they don't want 884 00:37:32,527 --> 00:37:34,287 to invest unless it's positive. 885 00:37:34,287 --> 00:37:35,120 That's a good point. 886 00:37:35,120 --> 00:37:37,315 But the way that is, they write down the math, 887 00:37:37,315 --> 00:37:38,610 and they plug in an i. 888 00:37:38,610 --> 00:37:41,720 What i do they plug in? 889 00:37:41,720 --> 00:37:42,220 Yeah. 890 00:37:42,220 --> 00:37:44,290 AUDIENCE: Is it published by the government? 891 00:37:44,290 --> 00:37:47,340 JONATHAN GRUBER: Well, i might be. 892 00:37:47,340 --> 00:37:50,870 But there's not one answer. 893 00:37:50,870 --> 00:37:53,420 What's the general answer the firm wants to use? 894 00:37:53,420 --> 00:37:55,082 What's the general answer? 895 00:37:55,082 --> 00:37:56,790 That the firm-- if you're a firm thinking 896 00:37:56,790 --> 00:37:58,290 about making an investment, you want 897 00:37:58,290 --> 00:38:00,380 to discount that investment. 898 00:38:00,380 --> 00:38:02,040 What do you want to discount it by? 899 00:38:02,040 --> 00:38:03,040 Yeah. 900 00:38:03,040 --> 00:38:05,380 AUDIENCE: The opportunity cost of the next best return. 901 00:38:05,380 --> 00:38:07,830 JONATHAN GRUBER: The next best thing you could do. 902 00:38:07,830 --> 00:38:09,892 So if I'm thinking about buying this machine, 903 00:38:09,892 --> 00:38:11,350 when I discount it, I want to think 904 00:38:11,350 --> 00:38:14,290 about what's the next best thing I could do with that money? 905 00:38:14,290 --> 00:38:16,227 That's the discount rate I want to use. 906 00:38:16,227 --> 00:38:18,310 So in a world where firms either can buy a machine 907 00:38:18,310 --> 00:38:19,790 or put it in the bank, it's easy. 908 00:38:19,790 --> 00:38:21,040 It's the bank interest rate. 909 00:38:21,040 --> 00:38:22,390 But life's not that easy. 910 00:38:22,390 --> 00:38:24,995 Firms have dozens of investments. 911 00:38:24,995 --> 00:38:26,370 So for every investment, you want 912 00:38:26,370 --> 00:38:28,167 to discount it by the next best thing 913 00:38:28,167 --> 00:38:29,250 you can do with the money. 914 00:38:29,250 --> 00:38:30,340 It's the concept of opportunity cost. 915 00:38:30,340 --> 00:38:32,940 That's why it's the very first thing we taught in this class. 916 00:38:32,940 --> 00:38:34,857 Opportunity cost is always what drives things. 917 00:38:37,640 --> 00:38:40,190 Questions about that? 918 00:38:40,190 --> 00:38:42,450 Now, this isn't just for firms. 919 00:38:42,450 --> 00:38:45,240 This same math applies to consumers as well. 920 00:38:45,240 --> 00:38:47,070 Let's think about me. 921 00:38:47,070 --> 00:38:49,440 A number of years ago, I had to decide 922 00:38:49,440 --> 00:38:53,190 whether to insulate my ancient house. 923 00:38:53,190 --> 00:38:56,580 Let's write down the numbers to think how this worked. 924 00:38:56,580 --> 00:38:58,110 I had heating bills at that time, 925 00:38:58,110 --> 00:39:01,200 back when gas was cheaper, of about $2,000 926 00:39:01,200 --> 00:39:06,630 a year was my heating bills for the house. 927 00:39:06,630 --> 00:39:09,300 The best estimate I could get was 928 00:39:09,300 --> 00:39:12,090 that if I insulated my house, I would 929 00:39:12,090 --> 00:39:15,180 lower my heating costs by 25%. 930 00:39:15,180 --> 00:39:20,850 So my heating costs would fall by $500 per year 931 00:39:20,850 --> 00:39:23,610 if I escalated my house. 932 00:39:26,430 --> 00:39:29,220 But to insulate my house, I had to pay the guy to insulate it. 933 00:39:29,220 --> 00:39:36,790 And the insulation cost $4,000. 934 00:39:36,790 --> 00:39:40,482 How do I think about whether I should insulate or not? 935 00:39:40,482 --> 00:39:41,940 How do I think about that decision? 936 00:39:41,940 --> 00:39:43,357 What equation should I write down? 937 00:39:45,660 --> 00:39:46,780 Yeah. 938 00:39:46,780 --> 00:39:52,753 AUDIENCE: Minus 4,000 plus 500 over i. 939 00:39:52,753 --> 00:39:53,795 JONATHAN GRUBER: Exactly. 940 00:39:57,310 --> 00:39:58,955 I should say, I'll assume I'm going 941 00:39:58,955 --> 00:40:01,390 to own the house forever, or at least long enough that I 942 00:40:01,390 --> 00:40:03,320 can treat it as forever. 943 00:40:03,320 --> 00:40:04,830 And I write down that formula. 944 00:40:04,830 --> 00:40:06,950 And what that formula says is that if I 945 00:40:06,950 --> 00:40:12,370 think the interest rate is less than 12.5%, I should insulate. 946 00:40:12,370 --> 00:40:14,770 If I think the interest rate is more than 12.5%, 947 00:40:14,770 --> 00:40:17,320 I should just invest the money and use the returns 948 00:40:17,320 --> 00:40:20,222 that I invested to pay my higher heating bills. 949 00:40:20,222 --> 00:40:22,180 So it all depends on what the interest rate is. 950 00:40:25,220 --> 00:40:26,330 So that's why-- I did it. 951 00:40:26,330 --> 00:40:28,580 I insulated. 952 00:40:28,580 --> 00:40:31,400 So the same logic we can think of 953 00:40:31,400 --> 00:40:37,473 is basically, essentially the same idea as firms. 954 00:40:37,473 --> 00:40:39,890 You want to think about the upfront costs and the long run 955 00:40:39,890 --> 00:40:41,620 returns. 956 00:40:41,620 --> 00:40:44,030 And here's a fun economics question. 957 00:40:44,030 --> 00:40:47,790 What if I don't intend to hold the house forever? 958 00:40:47,790 --> 00:40:50,250 I would argue I should still use this formula. 959 00:40:50,250 --> 00:40:51,860 Why? 960 00:40:51,860 --> 00:40:52,850 Yeah? 961 00:40:52,850 --> 00:40:55,472 AUDIENCE: Because whenever you decide to sell the house, 962 00:40:55,472 --> 00:40:56,430 you increase the value. 963 00:40:56,430 --> 00:40:57,972 JONATHAN GRUBER: Exactly, because I'm 964 00:40:57,972 --> 00:41:00,183 increasing the value of an asset that I'll then sell. 965 00:41:00,183 --> 00:41:01,600 So presumably, by insulating, I've 966 00:41:01,600 --> 00:41:03,470 raised the price of my house. 967 00:41:03,470 --> 00:41:04,780 How much have I raised it by? 968 00:41:04,780 --> 00:41:08,403 Exactly 500 over i, so I'm going to insulate and sell next year. 969 00:41:08,403 --> 00:41:09,820 I should still insulate, because I 970 00:41:09,820 --> 00:41:13,430 should get 500 over i more dollars for my house. 971 00:41:13,430 --> 00:41:14,680 So in fact, it doesn't matter. 972 00:41:14,680 --> 00:41:16,870 If you can sell an asset, then actually 973 00:41:16,870 --> 00:41:18,822 your horizon is always infinite. 974 00:41:18,822 --> 00:41:20,530 It's not just the short horizon, which is 975 00:41:20,530 --> 00:41:23,360 kind of an interesting insight. 976 00:41:23,360 --> 00:41:25,490 So the last thing I want to talk about 977 00:41:25,490 --> 00:41:28,400 is the fact that these decisions are not 978 00:41:28,400 --> 00:41:30,740 just relevant-- you guys are like retirement, 979 00:41:30,740 --> 00:41:33,560 business machines, insulation-- god, you're old, John. 980 00:41:33,560 --> 00:41:35,220 I don't care about any of this stuff. 981 00:41:35,220 --> 00:41:37,220 Well, let's talk about something you care about, 982 00:41:37,220 --> 00:41:39,210 which is going to college. 983 00:41:39,210 --> 00:41:40,680 Let's talk about your decision. 984 00:41:40,680 --> 00:41:43,263 You've already made it, but you've got a little sibling, 985 00:41:43,263 --> 00:41:45,180 and they're deciding whether to go to college. 986 00:41:47,955 --> 00:41:49,560 And they're not going to go to MIT. 987 00:41:49,560 --> 00:41:51,750 They're going to go to a more typical school. 988 00:41:51,750 --> 00:41:54,780 And they've got to decide whether to go to college. 989 00:41:54,780 --> 00:41:59,070 Well in fact, their decision is an investment decision, 990 00:41:59,070 --> 00:42:01,115 just like any other investment decision. 991 00:42:01,115 --> 00:42:02,490 What they're investing in is what 992 00:42:02,490 --> 00:42:06,240 we call their human capital. 993 00:42:06,240 --> 00:42:10,590 When you get education, you're investing in yourself, just 994 00:42:10,590 --> 00:42:12,660 like you invest in a machine. 995 00:42:12,660 --> 00:42:15,030 Because you are, you hope, raising 996 00:42:15,030 --> 00:42:18,960 the value of what you can do, of what you can earn, 997 00:42:18,960 --> 00:42:21,510 by investing in learning stuff. 998 00:42:21,510 --> 00:42:24,530 Well, that human capital investment 999 00:42:24,530 --> 00:42:27,800 has the same features of any other investment. 1000 00:42:27,800 --> 00:42:31,380 There's an opportunity cost, which is what? 1001 00:42:31,380 --> 00:42:34,020 What's the opportunity cost of investing your time 1002 00:42:34,020 --> 00:42:35,853 in going to college-- what's the opportunity 1003 00:42:35,853 --> 00:42:37,720 cost of going to college? 1004 00:42:37,720 --> 00:42:39,250 AUDIENCE: You could get a job. 1005 00:42:39,250 --> 00:42:39,550 JONATHAN GRUBER: You could-- 1006 00:42:39,550 --> 00:42:40,270 there's two. 1007 00:42:40,270 --> 00:42:41,995 One is, you can get a job. 1008 00:42:41,995 --> 00:42:43,870 AUDIENCE: You could also invest your tuition. 1009 00:42:43,870 --> 00:42:45,950 JONATHAN GRUBER: You could not pay tuition. 1010 00:42:45,950 --> 00:42:47,575 So if you think about going to college, 1011 00:42:47,575 --> 00:42:49,410 you're sacrificing two things. 1012 00:42:49,410 --> 00:42:52,090 All that money you're paying, you 1013 00:42:52,090 --> 00:42:55,013 could basically invest instead of giving it to some college. 1014 00:42:55,013 --> 00:42:57,430 And you could be out earning money instead of sitting here 1015 00:42:57,430 --> 00:42:59,190 listening to me. 1016 00:42:59,190 --> 00:43:03,492 OK, so if you think about that, it actually 1017 00:43:03,492 --> 00:43:05,450 becomes a harder decision than you might think. 1018 00:43:05,450 --> 00:43:07,610 So let's think about a simple example. 1019 00:43:07,610 --> 00:43:10,420 Let's imagine that if you don't go to college, 1020 00:43:10,420 --> 00:43:13,240 you work from age 18 to 70. 1021 00:43:13,240 --> 00:43:16,260 And if you do go to college, you work from age 22 to 70. 1022 00:43:16,260 --> 00:43:17,960 So we're going to ignore grad school. 1023 00:43:17,960 --> 00:43:20,210 Four years of college, you either start working at 18, 1024 00:43:20,210 --> 00:43:22,410 or you start working at 22. 1025 00:43:22,410 --> 00:43:25,100 And let's say college costs $35,000 a year. 1026 00:43:25,100 --> 00:43:27,910 Obviously, not MIT. 1027 00:43:27,910 --> 00:43:33,170 OK, let's say college costs $35,000 a year. 1028 00:43:33,170 --> 00:43:45,070 And let's say that if you worked starting in high school, 1029 00:43:45,070 --> 00:43:55,650 you could have earned $20,000. 1030 00:43:57,580 --> 00:43:58,955 You could have started at $20,000 1031 00:43:58,955 --> 00:44:02,690 if you'd gone to work at age 18. 1032 00:44:02,690 --> 00:44:04,760 Well, we can actually graph what this 1033 00:44:04,760 --> 00:44:10,520 looks like in figure 17.2 17.2. 1034 00:44:10,520 --> 00:44:16,080 If you think about age 18, from age 18 to age 22, 1035 00:44:16,080 --> 00:44:18,270 that's the green area. 1036 00:44:18,270 --> 00:44:20,310 If you go to college, you give up 1037 00:44:20,310 --> 00:44:25,810 the $35,000 in tuition and the 20,000 you could have earned. 1038 00:44:25,810 --> 00:44:29,740 The bottom line is basically-- the red line 1039 00:44:29,740 --> 00:44:32,050 is your lifetime earnings if you go to high school, 1040 00:44:32,050 --> 00:44:34,210 if you don't go to college. 1041 00:44:34,210 --> 00:44:38,920 The blue line is your lifetime earnings 1042 00:44:38,920 --> 00:44:40,630 if you do go to college. 1043 00:44:40,630 --> 00:44:43,840 Empirical estimates suggest that at age 22, 1044 00:44:43,840 --> 00:44:47,170 the typical college graduate earns $45,000. 1045 00:44:47,170 --> 00:44:49,240 Yes, you're not the typical college graduate. 1046 00:44:49,240 --> 00:44:51,520 The typical college graduate earns $45,000. 1047 00:44:51,520 --> 00:44:54,935 And the typical high school non-college education person 1048 00:44:54,935 --> 00:44:57,100 earns $28,000. 1049 00:44:57,100 --> 00:45:00,450 So at age 22, you come out of college earning 45, 1050 00:45:00,450 --> 00:45:02,920 and if you'd not gone to college, you earn 28. 1051 00:45:02,920 --> 00:45:06,760 Not you, but a normal person. 1052 00:45:06,760 --> 00:45:09,730 But moreover, knowledge you earn more when you leave college, 1053 00:45:09,730 --> 00:45:12,150 your earnings grows faster. 1054 00:45:12,150 --> 00:45:13,900 So if you're college educated, it not only 1055 00:45:13,900 --> 00:45:16,960 means you earn 17,000 more at 22, 1056 00:45:16,960 --> 00:45:19,270 it also means your earnings grows faster. 1057 00:45:19,270 --> 00:45:24,230 So that by age 51, the average college educated person 1058 00:45:24,230 --> 00:45:27,020 earns $80,000, while the average high school 1059 00:45:27,020 --> 00:45:29,820 person earns $45,000. 1060 00:45:29,820 --> 00:45:32,120 So what you see here is, the blue line 1061 00:45:32,120 --> 00:45:34,730 starts above the red line and the gap widens over time. 1062 00:45:37,640 --> 00:45:39,530 And maybe, I would have learned to clip this 1063 00:45:39,530 --> 00:45:40,910 on if I hadn't gone to college. 1064 00:45:40,910 --> 00:45:43,800 OK, so the gap widens over time. 1065 00:45:43,800 --> 00:45:45,440 So how do we think about this decision? 1066 00:45:45,440 --> 00:45:47,960 Well, the cost is the green area. 1067 00:45:47,960 --> 00:45:51,410 The cost is over four years, you could have earned money 1068 00:45:51,410 --> 00:45:53,480 and you wouldn't have had to pay tuition. 1069 00:45:53,480 --> 00:45:55,820 The benefit is the yellow area. 1070 00:45:55,820 --> 00:45:57,800 Over that entire time after graduation, 1071 00:45:57,800 --> 00:45:59,630 you're making more money. 1072 00:45:59,630 --> 00:46:01,720 Now obviously, in terms of size, the yellow area 1073 00:46:01,720 --> 00:46:04,220 is much, much bigger than the green area. 1074 00:46:04,220 --> 00:46:07,370 But the yellow area comes later. 1075 00:46:07,370 --> 00:46:08,290 That's the key thing. 1076 00:46:08,290 --> 00:46:10,040 So if I look and say, look, it's obvious-- 1077 00:46:10,040 --> 00:46:11,967 before this lecture, you might say, well, 1078 00:46:11,967 --> 00:46:13,550 it's obvious you should go to college. 1079 00:46:13,550 --> 00:46:15,320 Look, the yellow is way bigger than the green. 1080 00:46:15,320 --> 00:46:17,960 But that's not necessarily true, because the green comes now, 1081 00:46:17,960 --> 00:46:19,430 and the yellow comes later. 1082 00:46:19,430 --> 00:46:22,160 Indeed, if you look at the table, 1083 00:46:22,160 --> 00:46:24,440 this actually shows the net present value 1084 00:46:24,440 --> 00:46:26,450 of going to college and high school. 1085 00:46:26,450 --> 00:46:28,763 And what this shows is at low interest rates, 1086 00:46:28,763 --> 00:46:30,430 you're much better off going to college. 1087 00:46:30,430 --> 00:46:33,790 So if there's interest rate, then college 1088 00:46:33,790 --> 00:46:34,990 is a much, much better deal. 1089 00:46:34,990 --> 00:46:37,430 Your net present value of earnings 1090 00:46:37,430 --> 00:46:39,960 if if you go to college is 2.6 million, 1091 00:46:39,960 --> 00:46:43,510 while it's only 1.6 million if you don't go to college. 1092 00:46:43,510 --> 00:46:47,830 But once the interest rate gets above 8%, 1093 00:46:47,830 --> 00:46:51,160 it suddenly becomes a worse deal to go to college. 1094 00:46:51,160 --> 00:46:54,160 That is at only a 9% interest rate, which existed not that 1095 00:46:54,160 --> 00:46:56,960 long ago in our history. 1096 00:46:56,960 --> 00:47:00,100 It was actually a worse deal for the average person 1097 00:47:00,100 --> 00:47:01,840 to go to college. 1098 00:47:01,840 --> 00:47:02,340 Yeah. 1099 00:47:02,340 --> 00:47:03,820 AUDIENCE: Isn't that not accounting for financial aid, 1100 00:47:03,820 --> 00:47:04,320 though? 1101 00:47:04,320 --> 00:47:06,278 Because if you didn't have the 35,000 to spend, 1102 00:47:06,278 --> 00:47:08,200 you wouldn't have been able to invest it? 1103 00:47:08,200 --> 00:47:09,220 JONATHAN GRUBER: Well, actually, it's interesting. 1104 00:47:09,220 --> 00:47:10,780 It depends on the form of financial aid. 1105 00:47:10,780 --> 00:47:10,990 Why? 1106 00:47:10,990 --> 00:47:12,370 Someone tell me why it's dependent on the form 1107 00:47:12,370 --> 00:47:13,540 of financial aid? 1108 00:47:13,540 --> 00:47:15,500 Financial aid comes in different forms. 1109 00:47:15,500 --> 00:47:18,760 So why does it depend on how you get the financial aid? 1110 00:47:18,760 --> 00:47:19,515 Yeah. 1111 00:47:19,515 --> 00:47:21,390 AUDIENCE: Because if you have to pay it back. 1112 00:47:21,390 --> 00:47:23,405 JONATHAN GRUBER: If it's a grant, then yeah, 1113 00:47:23,405 --> 00:47:25,360 you should just take that out of the cost. 1114 00:47:25,360 --> 00:47:27,450 But if it's a loan, it depends what interest 1115 00:47:27,450 --> 00:47:28,878 rate you get the loan at. 1116 00:47:28,878 --> 00:47:30,670 If the loan is at the market interest rate, 1117 00:47:30,670 --> 00:47:33,370 then it's no different. 1118 00:47:33,370 --> 00:47:36,190 But that's a great point, which is why college financial aid 1119 00:47:36,190 --> 00:47:37,570 comes in two forms. 1120 00:47:37,570 --> 00:47:40,990 Grants for very low income people, and low interest loans 1121 00:47:40,990 --> 00:47:42,373 for other people. 1122 00:47:42,373 --> 00:47:44,290 Why do we give low interest loans for college? 1123 00:47:44,290 --> 00:47:46,180 Because of this graph. 1124 00:47:46,180 --> 00:47:49,030 Because we're saying, we think people need 1125 00:47:49,030 --> 00:47:51,010 to invest in their education. 1126 00:47:51,010 --> 00:47:53,343 We're afraid that if they faced a regular interest rate, 1127 00:47:53,343 --> 00:47:55,635 they won't be willing to do it, because the green would 1128 00:47:55,635 --> 00:47:56,890 be bigger than the yellow. 1129 00:47:56,890 --> 00:47:59,873 So we're actually going to subsidize their interest rate. 1130 00:47:59,873 --> 00:48:02,290 So you might have thought to yourself, sort of a weird way 1131 00:48:02,290 --> 00:48:04,873 to get people to go to college is to have a lower student loan 1132 00:48:04,873 --> 00:48:05,780 interest rate. 1133 00:48:05,780 --> 00:48:07,545 But in fact, it makes perfect sense. 1134 00:48:07,545 --> 00:48:08,920 By having a student loan interest 1135 00:48:08,920 --> 00:48:11,140 rate that's lower than the market rate, 1136 00:48:11,140 --> 00:48:12,790 you encourage people to go to college, 1137 00:48:12,790 --> 00:48:15,595 because essentially you lower this discount rate, 1138 00:48:15,595 --> 00:48:17,470 at least on the part that's tuition payments. 1139 00:48:19,380 --> 00:48:23,160 So that's actually very exciting way to think about 1140 00:48:23,160 --> 00:48:25,800 and a very important part of public policy 1141 00:48:25,800 --> 00:48:28,560 is how we set the interest rate on student loans. 1142 00:48:28,560 --> 00:48:31,270 For any of you-- how many of you guys have a student loan? 1143 00:48:31,270 --> 00:48:31,950 Do you know? 1144 00:48:31,950 --> 00:48:32,960 Any of you guys have a student loan? 1145 00:48:32,960 --> 00:48:33,752 You might not know. 1146 00:48:33,752 --> 00:48:36,030 Anyway, I set the interest rate on that student loan. 1147 00:48:36,030 --> 00:48:36,895 So thank you. 1148 00:48:36,895 --> 00:48:38,520 Actually, when I was in the government, 1149 00:48:38,520 --> 00:48:39,937 I was in the government 14 months, 1150 00:48:39,937 --> 00:48:41,190 the Clinton Administration. 1151 00:48:41,190 --> 00:48:42,510 It was super fun. 1152 00:48:42,510 --> 00:48:44,580 But looking back, I only got one thing done, 1153 00:48:44,580 --> 00:48:46,872 which I got to set the interest rate for student loans. 1154 00:48:46,872 --> 00:48:48,400 So that was kind of fun. 1155 00:48:48,400 --> 00:48:52,320 But otherwise, it was just a lot of fun being there. 1156 00:48:52,320 --> 00:48:58,680 So anyway, let's stop there, and we will continue. 1157 00:48:58,680 --> 00:48:59,680 What's today, Wednesday? 1158 00:48:59,680 --> 00:49:00,750 So no class on Monday. 1159 00:49:00,750 --> 00:49:04,550 That's Veterans Day, so we'll meet in a week, next Wednesday.