1 00:00:00,040 --> 00:00:02,460 The following content is provided under a Creative 2 00:00:02,460 --> 00:00:04,150 Commons license. 3 00:00:04,150 --> 00:00:06,910 Your support will help MIT OpenCourseWare continue to 4 00:00:06,910 --> 00:00:10,560 offer high-quality educational resources for free. 5 00:00:10,560 --> 00:00:13,460 To make a donation or view additional materials from 6 00:00:13,460 --> 00:00:17,740 hundreds of MIT courses, visit MIT OpenCourseWare at 7 00:00:17,740 --> 00:00:18,990 ocw.mit.edu. 8 00:00:23,400 --> 00:00:27,730 PROFESSOR: Our topics part of the course by revisiting 9 00:00:27,730 --> 00:00:33,430 another important topic that-- 10 00:00:33,430 --> 00:00:36,750 one of the most important topics in economics which is 11 00:00:36,750 --> 00:00:39,460 where does capital come from. 12 00:00:39,460 --> 00:00:41,950 This is a topic that is essential in economics. 13 00:00:41,950 --> 00:00:45,120 It's also really central, the basis, for what is in finance. 14 00:00:45,120 --> 00:00:47,860 So a lot of what we'll do today is really-- 15 00:00:47,860 --> 00:00:49,100 if you want to learn more about it you take more in 16 00:00:49,100 --> 00:00:51,960 economics but also more courses in Course 15. 17 00:00:51,960 --> 00:00:56,900 So, basically, we spent a lot of time this semester talking 18 00:00:56,900 --> 00:00:58,350 about one input to the production 19 00:00:58,350 --> 00:01:00,780 function which is labor. 20 00:01:00,780 --> 00:01:04,560 We talked about labor supply, labor demand, monopsony 21 00:01:04,560 --> 00:01:06,680 models, et cetera. 22 00:01:06,680 --> 00:01:09,280 We haven't talked much about the other input into the 23 00:01:09,280 --> 00:01:11,410 production function which is capital. 24 00:01:11,410 --> 00:01:13,820 Now, partly, that's because that's a more awkward concept. 25 00:01:13,820 --> 00:01:15,640 It's clear what labor is. 26 00:01:15,640 --> 00:01:18,900 Labor is the workers working in the production process. 27 00:01:18,900 --> 00:01:20,820 Capital's a little bit harder because capital's sort of 28 00:01:20,820 --> 00:01:26,600 everything else-- the machine, the land, the buildings, other 29 00:01:26,600 --> 00:01:28,480 physical inputs. 30 00:01:28,480 --> 00:01:29,870 And we know where labor comes from. 31 00:01:29,870 --> 00:01:31,780 Labor comes from our working. 32 00:01:31,780 --> 00:01:34,190 But it's less clear where capital comes from in some 33 00:01:34,190 --> 00:01:36,330 aggregate concept. 34 00:01:36,330 --> 00:01:40,900 So, basically, the key thing is that all forms of capital 35 00:01:40,900 --> 00:01:42,880 have a common feature. 36 00:01:42,880 --> 00:01:45,430 All forms of capital have a common feature which is what 37 00:01:45,430 --> 00:01:48,760 capital represents is a diversion of current 38 00:01:48,760 --> 00:01:53,870 consumption towards future production and consumption. 39 00:01:53,870 --> 00:01:57,560 So capital's about diverting current consumption towards 40 00:01:57,560 --> 00:02:00,370 future production and consumption. 41 00:02:00,370 --> 00:02:03,580 So the original concept of capital came from farming 42 00:02:03,580 --> 00:02:05,820 where the notion was that farmers every year would take 43 00:02:05,820 --> 00:02:09,300 some of their grain, and, rather than eating it, they'd 44 00:02:09,300 --> 00:02:13,190 put it aside to become seed to plant for the next year. 45 00:02:13,190 --> 00:02:14,530 That was their capital. 46 00:02:14,530 --> 00:02:16,620 And so they diverted their consumption this year which 47 00:02:16,620 --> 00:02:21,900 was eating the grain they grew to produce future consumption 48 00:02:21,900 --> 00:02:23,730 through planting those seeds and creating 49 00:02:23,730 --> 00:02:26,070 consumption for next year. 50 00:02:26,070 --> 00:02:30,390 So, basically, in a modern economy the idea is the same. 51 00:02:30,390 --> 00:02:33,040 And so when we think about capital, what I want you to 52 00:02:33,040 --> 00:02:38,710 think about is I want you to think about, basically, the 53 00:02:38,710 --> 00:02:40,530 capital as money. 54 00:02:40,530 --> 00:02:43,160 Think of the capital in the production function as the 55 00:02:43,160 --> 00:02:46,470 money that we invest in all these other things that aren't 56 00:02:46,470 --> 00:02:48,650 labor-- that we invest in machines, and we invest in 57 00:02:48,650 --> 00:02:51,020 buildings, and we invest in land. 58 00:02:51,020 --> 00:02:54,120 So we want to think about capital not as physical 59 00:02:54,120 --> 00:02:56,360 capital but as financial capital. 60 00:02:56,360 --> 00:02:58,820 That's the way to be thinking about that one aggregate 61 00:02:58,820 --> 00:03:01,160 letter k is this financial capital. 62 00:03:01,160 --> 00:03:04,720 It's the money that's invested in producing goods, in 63 00:03:04,720 --> 00:03:06,940 building machines, and building buildings, 64 00:03:06,940 --> 00:03:08,510 and stuff like that. 65 00:03:08,510 --> 00:03:09,550 OK? 66 00:03:09,550 --> 00:03:13,550 Now, basically, where do firms get that money? 67 00:03:13,550 --> 00:03:14,410 So you're a firm. 68 00:03:14,410 --> 00:03:17,960 You want to build a building or new machine or 69 00:03:17,960 --> 00:03:18,620 something like that. 70 00:03:18,620 --> 00:03:20,440 Where do firms get that money? 71 00:03:20,440 --> 00:03:23,500 They get that money in capital markets. 72 00:03:23,500 --> 00:03:27,585 Capital markets are basically pools of money that firms draw 73 00:03:27,585 --> 00:03:31,300 on to invest and create capital. 74 00:03:31,300 --> 00:03:32,900 So a capital market-- 75 00:03:32,900 --> 00:03:35,410 literally think of it as a pool of money that's out there 76 00:03:35,410 --> 00:03:38,930 that firms can tap into if they want to build a building 77 00:03:38,930 --> 00:03:41,930 or build a machine or buy some land. 78 00:03:41,930 --> 00:03:45,890 They tap into capital markets to make those investments. 79 00:03:45,890 --> 00:03:49,870 So while capital physically represents lots of different 80 00:03:49,870 --> 00:03:53,660 things, financially it represents one thing which is 81 00:03:53,660 --> 00:03:58,790 the pool of money that firms tap into to invest, to divert 82 00:03:58,790 --> 00:04:02,930 current consumption to future consumption. 83 00:04:02,930 --> 00:04:03,560 OK? 84 00:04:03,560 --> 00:04:05,690 It's the pool of money firms tap into to invest. That's 85 00:04:05,690 --> 00:04:07,060 what we mean by capital. 86 00:04:07,060 --> 00:04:10,170 By capital market we represent that pool of money. 87 00:04:10,170 --> 00:04:13,370 So think of capital as financial capital, and think 88 00:04:13,370 --> 00:04:16,740 of where you get financial capital in a capital market as 89 00:04:16,740 --> 00:04:20,079 being that pool of money that firms tap into to make 90 00:04:20,079 --> 00:04:23,730 investments to divert towards the future. 91 00:04:23,730 --> 00:04:27,420 Now, where does that supply of money come from? 92 00:04:27,420 --> 00:04:28,800 Where does that supply of money come from? 93 00:04:28,800 --> 00:04:31,380 Well it comes from households' decisions on how 94 00:04:31,380 --> 00:04:34,070 much to save. OK? 95 00:04:34,070 --> 00:04:37,340 So the pool of money in capital markets, the pool of 96 00:04:37,340 --> 00:04:41,520 money that firms draw on to build capital, comes from 97 00:04:41,520 --> 00:04:45,410 households' decisions on how much to save. 98 00:04:45,410 --> 00:04:48,545 So now we see the tie to labor, the other input in the 99 00:04:48,545 --> 00:04:49,690 production function. 100 00:04:49,690 --> 00:04:53,940 Just as households' decisions on how hard to work determines 101 00:04:53,940 --> 00:04:56,750 the labor input into the production function, 102 00:04:56,750 --> 00:05:00,170 households' decisions on how much to save determines the 103 00:05:00,170 --> 00:05:04,045 capital input into the production function. 104 00:05:04,045 --> 00:05:07,150 So just as my decision how much to work determines how 105 00:05:07,150 --> 00:05:10,450 much labor is available to firms, my decision on how much 106 00:05:10,450 --> 00:05:13,370 to save that's what fills up this pool. 107 00:05:13,370 --> 00:05:13,860 OK? 108 00:05:13,860 --> 00:05:17,970 So this pool of financial capital is filled up by 109 00:05:17,970 --> 00:05:21,550 household savings and then drawn down by firms' demand 110 00:05:21,550 --> 00:05:23,410 for investment. 111 00:05:23,410 --> 00:05:24,970 And that's the way a capital market works. 112 00:05:28,050 --> 00:05:30,060 So, basically, if we think about capital market 113 00:05:30,060 --> 00:05:31,300 equilibrium-- 114 00:05:31,300 --> 00:05:35,750 if you go to Figure 21-1-- 115 00:05:35,750 --> 00:05:37,600 we have equilibrium in capital markets. 116 00:05:37,600 --> 00:05:40,000 Now this is just like we talked about-- this is the 117 00:05:40,000 --> 00:05:40,860 other factor markets. 118 00:05:40,860 --> 00:05:44,320 Just like we talked about labor markets and determining 119 00:05:44,320 --> 00:05:46,430 what determines the wage rate and the optimum amount of 120 00:05:46,430 --> 00:05:48,530 labor hired, it's same with capital markets. 121 00:05:48,530 --> 00:05:50,950 You have some demand for capital. 122 00:05:50,950 --> 00:05:53,550 That comes from firms' demand for investment. 123 00:05:53,550 --> 00:05:54,740 Firms want new machines. 124 00:05:54,740 --> 00:05:56,530 They want new buildings. 125 00:05:56,530 --> 00:06:00,430 That's downward sloping because, initially, there's 126 00:06:00,430 --> 00:06:02,750 very high demand for capital. 127 00:06:02,750 --> 00:06:07,220 But there's a marginal diminishing product. 128 00:06:07,220 --> 00:06:09,460 The more capital I have the less valuable it is on the 129 00:06:09,460 --> 00:06:12,060 margin, the less you are willing to pay for it. 130 00:06:12,060 --> 00:06:15,215 So there's a downward sloping demand curve for capital and 131 00:06:15,215 --> 00:06:17,810 an upward sloping supply curve. 132 00:06:17,810 --> 00:06:22,120 And the price, in this market, is the interest rate. 133 00:06:22,120 --> 00:06:23,460 What is the interest rate? 134 00:06:23,460 --> 00:06:26,720 The interest rate is the rate you have to pay households to 135 00:06:26,720 --> 00:06:29,050 get them to lend you money. 136 00:06:29,050 --> 00:06:31,950 So the interest rate, i, is the rate you have to pay 137 00:06:31,950 --> 00:06:35,590 households to get them to lend you money. 138 00:06:35,590 --> 00:06:43,060 So if that interest rate is very high, firms will not 139 00:06:43,060 --> 00:06:45,610 demand much investment because they'll have to pay a lot of 140 00:06:45,610 --> 00:06:47,910 money to get the financial capital to finance that 141 00:06:47,910 --> 00:06:49,510 investment. 142 00:06:49,510 --> 00:06:52,000 But households will be delighted to supply lots of 143 00:06:52,000 --> 00:06:53,830 savings because they're getting paid a 144 00:06:53,830 --> 00:06:55,080 high price for it. 145 00:06:57,470 --> 00:07:01,980 So, basically, the interest rate serves as the 146 00:07:01,980 --> 00:07:03,290 equilibrating price in this market. 147 00:07:03,290 --> 00:07:06,020 Just as the wage serves as the equilibrating price in the 148 00:07:06,020 --> 00:07:09,270 labor market, the interest rate serves as the 149 00:07:09,270 --> 00:07:11,650 equilibrating price in the capital market. 150 00:07:11,650 --> 00:07:16,060 As the interest rate rises, folks want to save more, 151 00:07:16,060 --> 00:07:18,730 filling more money into that pool of capital. 152 00:07:18,730 --> 00:07:21,870 And firms want to borrow less, taking less money out of that 153 00:07:21,870 --> 00:07:23,260 pool of capital. 154 00:07:23,260 --> 00:07:26,900 And when that supply and demand is equilibrated, at 155 00:07:26,900 --> 00:07:31,400 point e, is going to be where the firm's drawing on the pool 156 00:07:31,400 --> 00:07:34,660 at exactly the rate people are putting money into the pool. 157 00:07:34,660 --> 00:07:37,320 And that's going to be the equilibrium. 158 00:07:37,320 --> 00:07:39,910 OK, so we want to focus on-- 159 00:07:39,910 --> 00:07:42,440 for today's lecture and next lecture as well-- 160 00:07:42,440 --> 00:07:46,180 is what determines the money that goes into that pool. 161 00:07:46,180 --> 00:07:47,610 We know what determines the rate at which firms want to 162 00:07:47,610 --> 00:07:49,920 draw out of that pool. 163 00:07:49,920 --> 00:07:51,750 That's basically going to be determined by the production 164 00:07:51,750 --> 00:07:53,900 function and all the stuff we learned in lectures on 165 00:07:53,900 --> 00:07:55,430 production theory. 166 00:07:55,430 --> 00:07:58,310 You can get your optimal demand for capital. 167 00:07:58,310 --> 00:08:01,060 It's going to be determined by isocosts and isoquants. 168 00:08:01,060 --> 00:08:03,310 And you get some k star. 169 00:08:03,310 --> 00:08:06,730 But what's going to determine what goes into that pool? 170 00:08:06,730 --> 00:08:09,620 That's going to be households' decisions to save. And 171 00:08:09,620 --> 00:08:13,415 households' decisions to save, we say, are determined by a 172 00:08:13,415 --> 00:08:15,950 process we call intertemporal choice. 173 00:08:22,850 --> 00:08:27,110 Added some extra letters there-- intertemporal choice. 174 00:08:27,110 --> 00:08:29,110 Intertemporal choice-- 175 00:08:29,110 --> 00:08:32,960 which is basically, instead of thinking about someone 176 00:08:32,960 --> 00:08:36,690 choosing between apples and bananas, we think of them 177 00:08:36,690 --> 00:08:38,890 choosing between consumption today 178 00:08:38,890 --> 00:08:41,150 and consumption tomorrow. 179 00:08:41,150 --> 00:08:45,040 So think of different periods like different goods. 180 00:08:45,040 --> 00:08:47,920 And I'm choosing between consumption today and 181 00:08:47,920 --> 00:08:49,680 consumption tomorrow. 182 00:08:49,680 --> 00:08:51,720 That's my intertemporal choice-- 183 00:08:51,720 --> 00:08:56,800 the rate at which I choose to trade off consumption in 184 00:08:56,800 --> 00:08:59,240 different periods. 185 00:08:59,240 --> 00:09:01,710 So for example, I'll illustrate how this works. 186 00:09:01,710 --> 00:09:05,760 Let's say that I'm deciding whether to just tell MIT, 187 00:09:05,760 --> 00:09:08,410 "Look, I don't want to work next year. 188 00:09:08,410 --> 00:09:09,600 I want to stay home and take care of my kids. 189 00:09:09,600 --> 00:09:10,730 You're not going to pay me. 190 00:09:10,730 --> 00:09:15,150 I'm taking an unpaid leave for a year." Something professors 191 00:09:15,150 --> 00:09:17,590 can do with enough advance warning to their 192 00:09:17,590 --> 00:09:18,750 chairman and such. 193 00:09:18,750 --> 00:09:20,300 So I'm going to take an unpaid leave next year. 194 00:09:20,300 --> 00:09:21,550 I'm thinking about doing that. 195 00:09:24,660 --> 00:09:26,650 And now I have to say, OK, fine. 196 00:09:26,650 --> 00:09:28,800 Next year I'm going to take this unpaid leave so I have to 197 00:09:28,800 --> 00:09:30,850 decide how to allocate my-- and then I'm going to come 198 00:09:30,850 --> 00:09:32,840 back and life will be the same thereafter. 199 00:09:32,840 --> 00:09:34,720 So it's just about next year I'm going to take this unpaid 200 00:09:34,720 --> 00:09:38,880 leave. I have to decide how to allocate my consumption across 201 00:09:38,880 --> 00:09:41,530 this year while I'm working and next year while I'm taking 202 00:09:41,530 --> 00:09:43,360 an unpaid leave. 203 00:09:43,360 --> 00:09:47,930 And let's say my salary is $80,000 a year. 204 00:09:47,930 --> 00:09:52,520 So one thing I could do is I can consume all $80,000 this 205 00:09:52,520 --> 00:09:56,870 year and consume nothing next year. 206 00:09:56,870 --> 00:10:01,340 That would not be a very satisfactory outcome as I die. 207 00:10:01,340 --> 00:10:05,550 That's obviously not going to be a satisfactory outcome. 208 00:10:05,550 --> 00:10:07,640 But what's the alternative? 209 00:10:07,640 --> 00:10:10,260 MIT's paying me this year, and they're not 210 00:10:10,260 --> 00:10:11,480 paying me next year. 211 00:10:11,480 --> 00:10:12,750 What's the alternative? 212 00:10:12,750 --> 00:10:17,380 Well, the alternative is I can save. And by saving, what we 213 00:10:17,380 --> 00:10:22,870 mean is I can loan some of the money that I make out to firms 214 00:10:22,870 --> 00:10:26,140 to invest in their physical capital in return for which 215 00:10:26,140 --> 00:10:31,320 they'll give me interest. And next year I can live on the 216 00:10:31,320 --> 00:10:35,460 interest I've earned from making that loan. 217 00:10:35,460 --> 00:10:40,800 Now, I don't literally go to Genzyme and Microsoft and 218 00:10:40,800 --> 00:10:42,480 Apple and say I want to loan you money and 219 00:10:42,480 --> 00:10:43,720 negotiate with them. 220 00:10:43,720 --> 00:10:45,350 That obviously would be impossible. 221 00:10:45,350 --> 00:10:49,720 What I do is I implicitly loan to firms through drawing on 222 00:10:49,720 --> 00:10:53,870 various aspects of the capital market. 223 00:10:53,870 --> 00:10:57,510 So does anyone know, how can I implicitly loan to a firm? 224 00:10:57,510 --> 00:10:58,190 Let's say I want to-- 225 00:10:58,190 --> 00:10:58,460 Yeah? 226 00:10:58,460 --> 00:10:59,560 AUDIENCE: Banks. 227 00:10:59,560 --> 00:10:59,960 PROFESSOR: Banks. 228 00:10:59,960 --> 00:11:00,940 So explain what you mean. 229 00:11:00,940 --> 00:11:03,640 AUDIENCE: You deposit money in a savings 230 00:11:03,640 --> 00:11:04,820 account for the bank. 231 00:11:04,820 --> 00:11:08,170 The bank pays you some interest rate so that it can 232 00:11:08,170 --> 00:11:12,054 use your money to loan to bigger companies that want to 233 00:11:12,054 --> 00:11:13,010 take money out of the bank. 234 00:11:13,010 --> 00:11:16,910 And they, in return, get money from the other companies by 235 00:11:16,910 --> 00:11:18,417 the companies paying some interest on 236 00:11:18,417 --> 00:11:20,080 what they took out. 237 00:11:20,080 --> 00:11:20,620 PROFESSOR: Exactly. 238 00:11:20,620 --> 00:11:23,260 We call banks financial intermediaries. 239 00:11:23,260 --> 00:11:26,140 What that means is they basically are the folks who 240 00:11:26,140 --> 00:11:29,060 can get a hold of firms and make those loans. 241 00:11:29,060 --> 00:11:32,640 So, in other words, I don't loan directly to Genzyme. 242 00:11:32,640 --> 00:11:34,920 I loan to the bank-- 243 00:11:34,920 --> 00:11:36,850 Citizens Bank, my bank, and Citizens 244 00:11:36,850 --> 00:11:38,650 Bank loans to Genzyme. 245 00:11:38,650 --> 00:11:43,240 Citizens Bank pays me an interest rate on my savings-- 246 00:11:43,240 --> 00:11:45,615 now close to zero, we'll come to that-- but basically pays 247 00:11:45,615 --> 00:11:48,110 me some interest rate. 248 00:11:48,110 --> 00:11:52,500 Genzyme pays them an interest rate to borrow money, higher 249 00:11:52,500 --> 00:11:54,240 than what they're paying me, and the 250 00:11:54,240 --> 00:11:57,210 difference is bank profit. 251 00:11:57,210 --> 00:12:01,970 So, basically, one way I can loan money is I can put in the 252 00:12:01,970 --> 00:12:04,080 bank and get paid interest. we don't think about putting in 253 00:12:04,080 --> 00:12:06,010 the bank as a loan, but that's basically what you're doing. 254 00:12:06,010 --> 00:12:08,640 You're loaning it to the bank. 255 00:12:08,640 --> 00:12:09,600 And they're paying you interest 256 00:12:09,600 --> 00:12:11,490 rate, i for that loan. 257 00:12:11,490 --> 00:12:12,850 What else can you do? 258 00:12:12,850 --> 00:12:13,580 How else can you-- 259 00:12:13,580 --> 00:12:13,915 Yeah? 260 00:12:13,915 --> 00:12:15,730 AUDIENCE: You can purchase stocks. 261 00:12:15,730 --> 00:12:17,200 PROFESSOR: You could purchase stocks. 262 00:12:17,200 --> 00:12:18,970 So, in other words, what I could do is I could directly 263 00:12:18,970 --> 00:12:23,990 go to a public company, and I could take some of my $80,000 264 00:12:23,990 --> 00:12:25,730 and buy stock in that company. 265 00:12:25,730 --> 00:12:28,690 There I'm essentially directly loaning to them. 266 00:12:28,690 --> 00:12:29,590 I'm directly giving them money. 267 00:12:29,590 --> 00:12:33,620 Now, it's not a loan that's paid back like a bank loan. 268 00:12:33,620 --> 00:12:36,280 It's loan that's paid back hopefully with my stock 269 00:12:36,280 --> 00:12:38,775 becoming more valuable or with a dividend. 270 00:12:41,430 --> 00:12:42,770 So how can I loan? 271 00:12:42,770 --> 00:12:43,940 One is I can invest-- 272 00:12:43,940 --> 00:12:46,480 I could put it in the bank. 273 00:12:46,480 --> 00:12:48,100 The other is I can buy stock. 274 00:12:48,100 --> 00:12:52,610 I can put it in the bank, and the bank pays me interest. I 275 00:12:52,610 --> 00:12:56,150 could buy stock, and that stock pays off in two ways. 276 00:12:56,150 --> 00:13:00,500 One is many companies pay what we call a dividend, what is 277 00:13:00,500 --> 00:13:03,570 called the dividend, which is a quarterly payment that 278 00:13:03,570 --> 00:13:07,570 companies make to their shareholders. 279 00:13:07,570 --> 00:13:09,790 So if I invest in a company that pays a dividend, then 280 00:13:09,790 --> 00:13:12,200 I'll be getting a quarterly check from that company that's 281 00:13:12,200 --> 00:13:14,020 a portion of my investment. 282 00:13:14,020 --> 00:13:18,450 The other is what we call a capital gain which is the 283 00:13:18,450 --> 00:13:20,790 stock could go up in value. 284 00:13:20,790 --> 00:13:23,600 So next year, if the stock goes up, if the stock market 285 00:13:23,600 --> 00:13:25,420 moves steadily-- it doesn't, it jumps up and down, we'll 286 00:13:25,420 --> 00:13:26,270 come to that-- 287 00:13:26,270 --> 00:13:28,480 but if it went steadily up I could just sell some of that 288 00:13:28,480 --> 00:13:30,050 stock next year and have extra money. 289 00:13:32,590 --> 00:13:35,070 So that's the other thing I could do with my $80,000. 290 00:13:35,070 --> 00:13:37,670 I could loan to a company by buying their stock. 291 00:13:37,670 --> 00:13:38,890 How else can I loan to a company? 292 00:13:38,890 --> 00:13:39,645 Yeah? 293 00:13:39,645 --> 00:13:42,615 AUDIENCE: I don't know exactly what the difference is, but 294 00:13:42,615 --> 00:13:44,595 couldn't you also invest your money in a 295 00:13:44,595 --> 00:13:45,100 mutual fund or something? 296 00:13:45,100 --> 00:13:47,100 PROFESSOR: A mutual fund-- that's a good point. 297 00:13:47,100 --> 00:13:49,120 That would be loaning-- 298 00:13:49,120 --> 00:13:53,640 a mutual fund is essentially loaning money to an aggregate 299 00:13:53,640 --> 00:13:56,190 collection of companies. 300 00:13:56,190 --> 00:13:58,500 So there are very different ways I can do stock. 301 00:13:58,500 --> 00:14:01,190 I can do a mutual fund, I can buy individual stocks. 302 00:14:01,190 --> 00:14:02,560 There's lots of different ways, but those are all 303 00:14:02,560 --> 00:14:03,830 different ways to buy stock. 304 00:14:03,830 --> 00:14:04,150 Yeah? 305 00:14:04,150 --> 00:14:04,470 AUDIENCE: You could buy bonds. 306 00:14:04,470 --> 00:14:05,640 PROFESSOR: You could buy bonds. 307 00:14:05,640 --> 00:14:08,070 You could buy company bonds which is I literally loan 308 00:14:08,070 --> 00:14:09,200 directly to the company. 309 00:14:09,200 --> 00:14:10,090 Stocks aren't really a loan. 310 00:14:10,090 --> 00:14:11,530 I'm literally buying an ownership share in the 311 00:14:11,530 --> 00:14:12,900 company, and they're paying me back. 312 00:14:12,900 --> 00:14:14,722 I could buy corporate bonds. 313 00:14:19,220 --> 00:14:22,630 I could buy corporate bonds, and the way those work is it's 314 00:14:22,630 --> 00:14:25,310 literally cutting out the middleman. 315 00:14:25,310 --> 00:14:28,310 I don't loan to Citizens Bank, and they loan to the company. 316 00:14:28,310 --> 00:14:30,950 I just loan to the company, and they pay me back. 317 00:14:30,950 --> 00:14:32,050 That's a corporate bond. 318 00:14:32,050 --> 00:14:34,610 I can also buy, by the way, I can also buy 319 00:14:34,610 --> 00:14:37,360 a government bond. 320 00:14:37,360 --> 00:14:39,360 You may know the government's running more than a trillion 321 00:14:39,360 --> 00:14:40,620 dollar deficit right now. 322 00:14:40,620 --> 00:14:42,230 Somebody's got to finance that. 323 00:14:42,230 --> 00:14:44,050 So you can loan to the government and get paid back 324 00:14:44,050 --> 00:14:45,500 by the government. 325 00:14:45,500 --> 00:14:46,880 OK, let's put the government aside for a minute. 326 00:14:46,880 --> 00:14:48,940 Let's focus where we just-- 327 00:14:48,940 --> 00:14:49,710 we haven't really had a government 328 00:14:49,710 --> 00:14:50,490 sector in our models. 329 00:14:50,490 --> 00:14:52,550 We're where it's just you and the companies. 330 00:14:52,550 --> 00:14:54,220 So let's leave the government channel aside. 331 00:14:54,220 --> 00:14:56,640 But the other thing I can do with my money is I can loan it 332 00:14:56,640 --> 00:14:58,760 through bonds. 333 00:14:58,760 --> 00:15:00,780 The point is that $80,000-- 334 00:15:00,780 --> 00:15:01,800 yeah, I'm sorry. 335 00:15:01,800 --> 00:15:04,167 AUDIENCE: With stocks, if I were to buy a stock from a 336 00:15:04,167 --> 00:15:06,937 company, wouldn't it be primarily and usually through 337 00:15:06,937 --> 00:15:09,000 the secondary market? 338 00:15:09,000 --> 00:15:10,880 I wouldn't be giving any money to the company. 339 00:15:10,880 --> 00:15:14,480 I'd just be giving money to the previous stockholder. 340 00:15:14,480 --> 00:15:15,320 PROFESSOR: That's true. 341 00:15:15,320 --> 00:15:17,560 It basically depends on whether the marginal stock 342 00:15:17,560 --> 00:15:20,120 comes from a new issuance as stock by the company or 343 00:15:20,120 --> 00:15:21,730 through stock that's already floating around 344 00:15:21,730 --> 00:15:23,010 the secondary market. 345 00:15:23,010 --> 00:15:23,880 That's a good point. 346 00:15:23,880 --> 00:15:26,540 So in some sense the-- 347 00:15:26,540 --> 00:15:27,650 likewise with bonds. 348 00:15:27,650 --> 00:15:29,370 A lot of bonds are traded in a secondary market. 349 00:15:29,370 --> 00:15:31,270 So I'm thinking about a simple model where basically new 350 00:15:31,270 --> 00:15:33,270 stock gets issued by the company, I buy it. 351 00:15:33,270 --> 00:15:34,470 More technically you're right. 352 00:15:34,470 --> 00:15:38,010 It's just trading among people, but that sort of makes 353 00:15:38,010 --> 00:15:38,670 things complicated. 354 00:15:38,670 --> 00:15:41,630 Let's put that aside for now. 355 00:15:41,630 --> 00:15:44,480 So, basically, the point is is my $80,000-- 356 00:15:44,480 --> 00:15:47,720 there's lots of things I can do with it. 357 00:15:47,720 --> 00:15:50,520 All of them yield me some rate-- 358 00:15:50,520 --> 00:15:54,240 the key point is all of them have the feature that I'm 359 00:15:54,240 --> 00:15:58,890 diverting today's consumption for tomorrow's consumption. 360 00:15:58,890 --> 00:16:00,980 I'm taking some of my money and, rather than eating it 361 00:16:00,980 --> 00:16:05,020 this year when I'm working, I'm loaning it out in some 362 00:16:05,020 --> 00:16:08,550 way, shape, or form and getting payback in next year 363 00:16:08,550 --> 00:16:09,800 when I'm not working. 364 00:16:12,150 --> 00:16:14,090 And we can summarize. 365 00:16:14,090 --> 00:16:16,610 Now this is a very complicated set of mechanisms, not to 366 00:16:16,610 --> 00:16:18,190 mention the secondary market issues. 367 00:16:18,190 --> 00:16:23,060 And this is basically a semester of 15.401. 368 00:16:23,060 --> 00:16:25,280 This is basically a semester of finance theory. 369 00:16:25,280 --> 00:16:27,260 But basically what we're going to do is compress this all 370 00:16:27,260 --> 00:16:31,250 down and say that I get some interest rate on my money. 371 00:16:31,250 --> 00:16:35,270 However I do it, let's just say that somehow I divert my 372 00:16:35,270 --> 00:16:37,790 money through one of these mechanisms, and it yields some 373 00:16:37,790 --> 00:16:40,450 effective interest rate, i. 374 00:16:40,450 --> 00:16:42,530 And you can know behind that there's lots of ways I can get 375 00:16:42,530 --> 00:16:45,140 that interest. But for now just simplify it down and say 376 00:16:45,140 --> 00:16:48,540 the main thing is I'm diverting my consumption now, 377 00:16:48,540 --> 00:16:51,800 and it's yielding some interest earnings on that 378 00:16:51,800 --> 00:16:54,230 diverted consumption, i. 379 00:16:54,230 --> 00:16:59,340 So what that means is that for every dollar I divert, I get 1 380 00:16:59,340 --> 00:17:02,350 plus i dollars the next year. 381 00:17:02,350 --> 00:17:05,109 So for every dollar of consumption I divert, in one 382 00:17:05,109 --> 00:17:08,030 of these forms, I get 1 plus i dollars next year. 383 00:17:11,920 --> 00:17:14,319 So, basically, I could literally-- 384 00:17:14,319 --> 00:17:17,040 if I wanted to-- let's say the interest rate was 10%, just 385 00:17:17,040 --> 00:17:18,589 for example. 386 00:17:18,589 --> 00:17:21,990 Now what that means is instead of consuming $80,000 this year 387 00:17:21,990 --> 00:17:24,740 and nothing next year, I could consume nothing this year and 388 00:17:24,740 --> 00:17:28,550 $88,000 next year. 389 00:17:28,550 --> 00:17:31,570 Obviously, that's not very satisfactory either. 390 00:17:31,570 --> 00:17:33,520 So how do we think about that? 391 00:17:33,520 --> 00:17:37,510 We think about that in Figure 21-2 shows-- 392 00:17:37,510 --> 00:17:39,060 now this is a complicated diagram we gotta 393 00:17:39,060 --> 00:17:40,540 use to figure 21-2-- 394 00:17:40,540 --> 00:17:44,280 this shows the intertemporal choice model, intertemporal 395 00:17:44,280 --> 00:17:46,520 substitution we also call it. 396 00:17:46,520 --> 00:17:49,430 So the deal is that now instead of the x-axis being 397 00:17:49,430 --> 00:17:51,630 pizza and the y-axis being movies or all the other wacky 398 00:17:51,630 --> 00:17:54,930 things we've done, now the x-axis is first period 399 00:17:54,930 --> 00:17:55,940 consumption. 400 00:17:55,940 --> 00:17:57,610 The y-axis is second period consumption. 401 00:17:57,610 --> 00:17:58,620 You might say what's a period? 402 00:17:58,620 --> 00:18:00,550 Well a period's whatever I want it to be-- a day, a year, 403 00:18:00,550 --> 00:18:02,050 10 years, whatever. 404 00:18:02,050 --> 00:18:02,890 Sometimes I'll say a year. 405 00:18:02,890 --> 00:18:03,930 Sometimes I'll say a period, but the point 406 00:18:03,930 --> 00:18:04,880 is it doesn't matter. 407 00:18:04,880 --> 00:18:07,150 It's about the trade-off. 408 00:18:07,150 --> 00:18:10,400 So in my example, c1 is consumption this year. 409 00:18:10,400 --> 00:18:13,620 c2's consumption next year. 410 00:18:13,620 --> 00:18:18,290 And my trade-off is I can consume $80,000 this year, or, 411 00:18:18,290 --> 00:18:25,810 given the interest rate, I can consume $88,000 next year. 412 00:18:25,810 --> 00:18:28,150 Now the trade-off-- that's a typo, by the way. 413 00:18:28,150 --> 00:18:30,350 That should be minus 1.1. 414 00:18:30,350 --> 00:18:30,530 OK? 415 00:18:30,530 --> 00:18:33,230 This is a 10% interest rate. 416 00:18:33,230 --> 00:18:38,900 The key point is the trade-off is that, basically, I can 417 00:18:38,900 --> 00:18:42,230 trade off for every dollar I don't consume this year, I 418 00:18:42,230 --> 00:18:43,820 consume 1 plus i-- 419 00:18:43,820 --> 00:18:46,830 1 plus r there, should be 1 plus i dollars-- 420 00:18:46,830 --> 00:18:49,460 next year. 421 00:18:49,460 --> 00:18:53,940 We use r and i interchangeably for the interest rate, so 1 422 00:18:53,940 --> 00:18:58,710 plus i, 1 plus r dollars next year. 423 00:18:58,710 --> 00:19:02,420 So, basically, what does the interest rate represent? 424 00:19:02,420 --> 00:19:03,370 This is important. 425 00:19:03,370 --> 00:19:08,160 The wage rate I defined as the price of leisure. 426 00:19:08,160 --> 00:19:09,260 Remember what the wage rate was? 427 00:19:09,260 --> 00:19:17,420 It was the price of leisure, that basically by working I 428 00:19:17,420 --> 00:19:21,360 forgoed the ability to-- 429 00:19:21,360 --> 00:19:23,510 I'm sorry, by taking leisure I forgoed the ability to 430 00:19:23,510 --> 00:19:25,270 earn a wage, w. 431 00:19:25,270 --> 00:19:27,645 So, literally, that was a price of sitting around on the 432 00:19:27,645 --> 00:19:29,740 couch was the wage, w, I could've earned. 433 00:19:29,740 --> 00:19:33,000 Likewise, the interest rate is the price of first period 434 00:19:33,000 --> 00:19:34,440 consumption. 435 00:19:34,440 --> 00:19:37,900 By consuming today, I'm forgoing the fact that I 436 00:19:37,900 --> 00:19:40,440 could've earned the interest on that money had I consumed 437 00:19:40,440 --> 00:19:43,060 it tomorrow or next year. 438 00:19:43,060 --> 00:19:45,200 So the interest rate is the price of first period 439 00:19:45,200 --> 00:19:50,570 consumption, just as the wage is the price of leisure. 440 00:19:50,570 --> 00:19:51,050 Yeah? 441 00:19:51,050 --> 00:19:53,445 AUDIENCE: You said before that r and i are used 442 00:19:53,445 --> 00:19:59,672 interchangeably for interest. Does that play into the cost 443 00:19:59,672 --> 00:20:01,826 function at all? 444 00:20:01,826 --> 00:20:05,358 Is the cost for capital going to be the interest rate? 445 00:20:05,358 --> 00:20:07,080 PROFESSOR: I'm going to come to that. 446 00:20:07,080 --> 00:20:12,300 That's exactly what I'll talk about next lecture. 447 00:20:12,300 --> 00:20:14,890 So, basically, this is the key thing, but the key thing to 448 00:20:14,890 --> 00:20:16,580 understand intertemporal choice-- and the other 449 00:20:16,580 --> 00:20:18,540 important point to understand on why it's a bit harder than 450 00:20:18,540 --> 00:20:20,070 labor is there's an extra-- 451 00:20:20,070 --> 00:20:20,950 well it's not harder. 452 00:20:20,950 --> 00:20:21,500 It's the same thing. 453 00:20:21,500 --> 00:20:23,940 Remember, we said we don't model bads in this course. 454 00:20:23,940 --> 00:20:25,330 We model goods. 455 00:20:25,330 --> 00:20:27,000 So we're modeling your choice of how hard to work. 456 00:20:27,000 --> 00:20:29,280 We model the trade-off between consumption and leisure. 457 00:20:29,280 --> 00:20:32,560 And then we said define labor as the total amount of hours 458 00:20:32,560 --> 00:20:33,750 available minus leisure. 459 00:20:33,750 --> 00:20:34,690 Same thing here. 460 00:20:34,690 --> 00:20:36,510 We don't model savings. 461 00:20:36,510 --> 00:20:38,450 That's a bad. 462 00:20:38,450 --> 00:20:39,310 Now you might not think [? some of these ?] 463 00:20:39,310 --> 00:20:41,410 things are good, but savings really by 464 00:20:41,410 --> 00:20:43,360 itself is not a good. 465 00:20:43,360 --> 00:20:44,700 Unless you're Scrooge McDuck-- 466 00:20:44,700 --> 00:20:47,340 does anyone know who Scrooge McDuck is? 467 00:20:47,340 --> 00:20:48,690 Wow, that hurts. 468 00:20:48,690 --> 00:20:50,546 OK, he was this old cartoon character when I was a kid who 469 00:20:50,546 --> 00:20:51,710 used to, like, fill a swimming pool with 470 00:20:51,710 --> 00:20:53,490 money and swim in it. 471 00:20:53,490 --> 00:20:55,940 Basically, unless you're like that, the savings itself does 472 00:20:55,940 --> 00:20:56,770 not give you utility. 473 00:20:56,770 --> 00:20:59,140 We don't have savings entering utility functions. 474 00:20:59,140 --> 00:21:01,460 We have consumption entering utility functions. 475 00:21:01,460 --> 00:21:02,810 Savings is a bad. 476 00:21:02,810 --> 00:21:05,350 Savings is the mean by which you translate consumption 477 00:21:05,350 --> 00:21:07,570 period one into consumption period two. 478 00:21:07,570 --> 00:21:09,800 But from the effect of today you wish you didn't have to 479 00:21:09,800 --> 00:21:10,910 save. You just do it because you want to make 480 00:21:10,910 --> 00:21:12,660 sure you eat tomorrow. 481 00:21:12,660 --> 00:21:14,560 So we model the good. 482 00:21:14,560 --> 00:21:18,040 The good is consumption in period one, and savings is the 483 00:21:18,040 --> 00:21:20,900 difference between income and consumption in period one. 484 00:21:20,900 --> 00:21:22,600 So we don't model savings. 485 00:21:22,600 --> 00:21:25,550 We define savings as y minus c1. 486 00:21:25,550 --> 00:21:31,570 We model c1, and define savings as y minus c1. 487 00:21:31,570 --> 00:21:34,040 You can see that there in the diagram. 488 00:21:34,040 --> 00:21:37,310 Now what happens when the interest rate changes? 489 00:21:37,310 --> 00:21:42,580 Let's go to Figure 21-3. 490 00:21:42,580 --> 00:21:44,550 What happens when the interest rate changes? 491 00:21:44,550 --> 00:21:45,670 Actually, go to 21-4. 492 00:21:45,670 --> 00:21:45,960 OK? 493 00:21:45,960 --> 00:21:46,680 Skip 21-3. 494 00:21:46,680 --> 00:21:48,990 Got to 21-4. 495 00:21:48,990 --> 00:21:51,190 What happens when the interest rate changes? 496 00:21:51,190 --> 00:21:54,850 So, initially, we're at a point like a and then the 497 00:21:54,850 --> 00:22:00,760 interest rate goes up from r to r2. 498 00:22:00,760 --> 00:22:03,960 The interest rate goes up. 499 00:22:03,960 --> 00:22:05,260 Now what does that do? 500 00:22:05,260 --> 00:22:08,290 Well, graphically, it steepens the budget constraint. 501 00:22:08,290 --> 00:22:13,120 What that means is it's raised the opportunity cost of first 502 00:22:13,120 --> 00:22:15,470 period consumption. 503 00:22:15,470 --> 00:22:17,550 First period consumption is now effectively more expensive 504 00:22:17,550 --> 00:22:22,040 because I'm forgoing a better savings rate by eating today. 505 00:22:22,040 --> 00:22:25,190 The more of my $80,000 I consume today, the less I get 506 00:22:25,190 --> 00:22:26,370 to save for tomorrow. 507 00:22:26,370 --> 00:22:28,390 And that's now a better deal to save for tomorrow because 508 00:22:28,390 --> 00:22:29,720 I'm getting a higher interest rate on that. 509 00:22:33,660 --> 00:22:34,730 So what does that do? 510 00:22:34,730 --> 00:22:36,380 Well that has two effects. 511 00:22:36,380 --> 00:22:38,640 Just like a change in the wage rate has two effects-- a 512 00:22:38,640 --> 00:22:41,920 substitution effect and an income effect. 513 00:22:41,920 --> 00:22:46,650 The substitution effect, which we can unambiguously sign, is 514 00:22:46,650 --> 00:22:50,760 the fact that now first period consumption's gotten more 515 00:22:50,760 --> 00:22:53,600 expensive, so we do less of it. 516 00:22:53,600 --> 00:22:55,570 Substitution effects are always price goes up, you do 517 00:22:55,570 --> 00:22:56,860 less of the activity. 518 00:22:56,860 --> 00:22:59,530 The substitution effect is first period consumption's 519 00:22:59,530 --> 00:23:01,180 gotten more expensive, there'll be less of it. 520 00:23:01,180 --> 00:23:03,510 Now here, once again, don't slip into thinking about 521 00:23:03,510 --> 00:23:04,200 savings yet. 522 00:23:04,200 --> 00:23:05,720 You'll really get yourself in trouble, and 523 00:23:05,720 --> 00:23:07,170 it's a natural tendency. 524 00:23:07,170 --> 00:23:10,000 Model consumption that makes savings a residual. 525 00:23:10,000 --> 00:23:11,880 So the activity we're modeling here is first period 526 00:23:11,880 --> 00:23:12,630 consumption. 527 00:23:12,630 --> 00:23:14,810 The price of first period consumption's gone up, so you 528 00:23:14,810 --> 00:23:15,800 do less of it. 529 00:23:15,800 --> 00:23:18,860 That's the substitution effect. 530 00:23:18,860 --> 00:23:22,670 The income effect is you're now richer. 531 00:23:22,670 --> 00:23:23,620 And you might say what do you mean I'm richer? 532 00:23:23,620 --> 00:23:26,860 I still have the same $80,000 in income. 533 00:23:26,860 --> 00:23:31,250 But any given dollar of savings yields more income in 534 00:23:31,250 --> 00:23:32,920 the second period. 535 00:23:32,920 --> 00:23:35,860 So, overall, you're richer. 536 00:23:35,860 --> 00:23:38,500 If you take the perspective of saying I have two periods in 537 00:23:38,500 --> 00:23:40,910 this model-- first and second period. 538 00:23:40,910 --> 00:23:42,920 Any given level of savings makes me richer 539 00:23:42,920 --> 00:23:43,490 in the second period. 540 00:23:43,490 --> 00:23:45,470 That means I'm richer. 541 00:23:45,470 --> 00:23:49,220 If I'm richer, I consume more of everything including first 542 00:23:49,220 --> 00:23:50,680 period consumption. 543 00:23:50,680 --> 00:23:52,140 So first period consumption goes up 544 00:23:52,140 --> 00:23:53,370 from the income effect. 545 00:23:53,370 --> 00:23:54,450 I find this confusing. 546 00:23:54,450 --> 00:23:56,440 I don't know if you guys do, but once again-- run through 547 00:23:56,440 --> 00:23:57,520 this again. 548 00:23:57,520 --> 00:24:00,840 I'm richer because for any given amount of savings I now 549 00:24:00,840 --> 00:24:03,770 have a total larger sum of money over both periods. 550 00:24:03,770 --> 00:24:06,770 When I'm richer I consume more of everything. 551 00:24:06,770 --> 00:24:09,060 One of the things that I consume more of is first 552 00:24:09,060 --> 00:24:10,070 period consumption. 553 00:24:10,070 --> 00:24:11,620 So, actually, first period consumption goes 554 00:24:11,620 --> 00:24:12,870 up, and I save less. 555 00:24:12,870 --> 00:24:15,160 It's sort of bizarre. 556 00:24:15,160 --> 00:24:16,500 Because I'm getting more return to my 557 00:24:16,500 --> 00:24:19,480 savings I save less. 558 00:24:19,480 --> 00:24:21,090 Here is the way I like to think of the 559 00:24:21,090 --> 00:24:24,080 intuition to make it easier. 560 00:24:24,080 --> 00:24:26,920 The way I like to think of the intuition is imagine that you 561 00:24:26,920 --> 00:24:29,510 have a goal for saving-- something I call a target 562 00:24:29,510 --> 00:24:30,620 savings level. 563 00:24:30,620 --> 00:24:33,280 Imagine you said, look. 564 00:24:33,280 --> 00:24:37,840 Imagine you said that I really want to make sure that I have 565 00:24:37,840 --> 00:24:41,950 certain level of savings to live on next year. 566 00:24:41,950 --> 00:24:45,450 Well if the interest rate goes up, I can save less to get to 567 00:24:45,450 --> 00:24:47,030 that target. 568 00:24:47,030 --> 00:24:47,350 Right? 569 00:24:47,350 --> 00:24:50,930 If I have a target, c2, and the interest rate is higher I 570 00:24:50,930 --> 00:24:54,490 can consume more c1 and still hit my target of c2. 571 00:24:54,490 --> 00:24:56,150 So that's the income effect. 572 00:24:56,150 --> 00:24:58,920 I can effectively consume more c1 because I'm made richer 573 00:24:58,920 --> 00:25:01,890 because any given level of savings allows me to consume 574 00:25:01,890 --> 00:25:03,270 more the next period. 575 00:25:03,270 --> 00:25:05,450 Now the target's an extreme case, but I find it a useful 576 00:25:05,450 --> 00:25:08,240 intuition for thinking about what's going on. 577 00:25:08,240 --> 00:25:11,190 And that's the income effect. 578 00:25:11,190 --> 00:25:14,240 Now, obviously, as with anything, this is ambiguous. 579 00:25:14,240 --> 00:25:17,810 If you go to Figure 21-3 now here's a case where the income 580 00:25:17,810 --> 00:25:20,070 effect dominates. 581 00:25:20,070 --> 00:25:21,360 Well, actually, go back to 21-4. 582 00:25:21,360 --> 00:25:22,710 Let's finish this example. 583 00:25:22,710 --> 00:25:25,280 So here with the substitution effect dominating, when the 584 00:25:25,280 --> 00:25:28,570 interest rate goes up I consume less in period one 585 00:25:28,570 --> 00:25:30,000 which means I save more. 586 00:25:30,000 --> 00:25:31,220 And that was prior intuition. 587 00:25:31,220 --> 00:25:32,890 A higher interest rate means you save more. 588 00:25:32,890 --> 00:25:35,270 But we'll work through the mechanics of how we get there. 589 00:25:35,270 --> 00:25:37,260 And the reason the mechanics is important is because of 590 00:25:37,260 --> 00:25:39,620 Figure 21-3. 591 00:25:39,620 --> 00:25:45,950 Which as in 21-3, the interest rate goes up, but I save less. 592 00:25:45,950 --> 00:25:50,110 The interest rate goes up, but I consume more in period one 593 00:25:50,110 --> 00:25:53,620 and therefore save less. 594 00:25:53,620 --> 00:25:56,270 And that's consistent with this target notion. 595 00:25:56,270 --> 00:25:57,520 That basically I'm so-- 596 00:25:57,520 --> 00:26:00,830 All I care about-- let's say in the limit if all I care 597 00:26:00,830 --> 00:26:02,650 about in the limit is exactly what I consume the second 598 00:26:02,650 --> 00:26:06,590 period, then, basically, my period one's consumption will 599 00:26:06,590 --> 00:26:09,470 definitely go up from a raise in the interest rate because, 600 00:26:09,470 --> 00:26:11,480 basically, I'm saying, look, all I care about is what I get 601 00:26:11,480 --> 00:26:11,950 in the second period. 602 00:26:11,950 --> 00:26:14,390 Now I can save less and get to that target. 603 00:26:14,390 --> 00:26:16,410 So my consumption first period goes up. 604 00:26:16,410 --> 00:26:19,580 The income effect dominates. 605 00:26:19,580 --> 00:26:21,800 So the bottom line is, just like with labor supply, we 606 00:26:21,800 --> 00:26:23,350 can't tell. 607 00:26:23,350 --> 00:26:26,900 Unlike with goods where it's rare to see a Giffen good, 608 00:26:26,900 --> 00:26:29,530 here we honestly don't know whether a raise in the 609 00:26:29,530 --> 00:26:31,870 interest rates will raise savings or lower savings. 610 00:26:31,870 --> 00:26:33,630 It all depends on the strength of the 611 00:26:33,630 --> 00:26:34,880 substitution and income effects. 612 00:26:38,040 --> 00:26:40,120 Let me actually say one of the most disturbing things in 613 00:26:40,120 --> 00:26:44,480 empirical economics is we actually do have no idea. 614 00:26:44,480 --> 00:26:46,830 Literally, there's no convincing study out there 615 00:26:46,830 --> 00:26:48,900 which even tells us which way the effect of interest rates 616 00:26:48,900 --> 00:26:49,890 goes on savings. 617 00:26:49,890 --> 00:26:52,380 We think probably the substitution effect dominates, 618 00:26:52,380 --> 00:26:54,490 but it's been very hard to find a 619 00:26:54,490 --> 00:26:56,090 convincing estimate of that. 620 00:26:56,090 --> 00:26:57,000 So it's a little bit disturbing 621 00:26:57,000 --> 00:26:58,370 for empirical economics. 622 00:26:58,370 --> 00:27:00,970 We'll typically assume it dominates, but don't 623 00:27:00,970 --> 00:27:03,660 necessarily assume that in the real world. 624 00:27:03,660 --> 00:27:05,700 OK, questions about that-- 625 00:27:05,700 --> 00:27:07,380 intertemporal choice framework? 626 00:27:07,380 --> 00:27:12,120 OK, now, with that in mind, let's now talk about how 627 00:27:12,120 --> 00:27:13,400 capital markets work. 628 00:27:17,660 --> 00:27:19,600 How do capital markets work? 629 00:27:19,600 --> 00:27:22,050 And the key concept for thinking about capital markets 630 00:27:22,050 --> 00:27:24,560 is the concept of present value. 631 00:27:30,180 --> 00:27:32,480 And the concept of the present value is simple. 632 00:27:32,480 --> 00:27:38,360 It's that $1 tomorrow is worth less than $1 today. 633 00:27:38,360 --> 00:27:42,660 $1 tomorrow is worth less than $1 today. 634 00:27:42,660 --> 00:27:43,880 And why is that? 635 00:27:43,880 --> 00:27:46,660 It's because if I had the dollar today, I could've 636 00:27:46,660 --> 00:27:49,670 invested it in something productive and had 1 plus i 637 00:27:49,670 --> 00:27:52,190 dollars tomorrow. 638 00:27:52,190 --> 00:27:54,230 So if you give me a dollar today I could have 1 plus i 639 00:27:54,230 --> 00:27:55,010 dollars tomorrow. 640 00:27:55,010 --> 00:27:57,740 If you give it to me tomorrow, I just have $1. 641 00:27:57,740 --> 00:28:00,610 So by definition, $1 today is worth more because I have the 642 00:28:00,610 --> 00:28:02,920 opportunity to save it. 643 00:28:02,920 --> 00:28:04,150 Whereas a $1 tomorrow I don't have the 644 00:28:04,150 --> 00:28:04,780 opportunity to save it. 645 00:28:04,780 --> 00:28:07,770 It's too late. 646 00:28:07,770 --> 00:28:12,510 So the key point is you can't add up dollars that you 647 00:28:12,510 --> 00:28:16,160 receive in different periods. 648 00:28:16,160 --> 00:28:17,920 So, in other words, if I said to you-- 649 00:28:17,920 --> 00:28:20,430 if this intertemporal choice graph was back pizzas and 650 00:28:20,430 --> 00:28:25,570 movies, and I said you have nine pizza plus movies. 651 00:28:25,570 --> 00:28:26,490 You have a total of nine. 652 00:28:26,490 --> 00:28:28,280 You'd be like, what the hell does that mean? 653 00:28:28,280 --> 00:28:31,960 It matters if it's nine pizzas and zero movies or five movies 654 00:28:31,960 --> 00:28:32,580 and four pizzas? 655 00:28:32,580 --> 00:28:33,370 I don't know what that means. 656 00:28:33,370 --> 00:28:33,910 Those are different things. 657 00:28:33,910 --> 00:28:35,800 You can't add them up. 658 00:28:35,800 --> 00:28:37,530 You can't just say I have nine. 659 00:28:37,530 --> 00:28:41,360 Well consumption over time-- it's the same thing. 660 00:28:41,360 --> 00:28:43,890 You can't just add up your consumption tomorrow and 661 00:28:43,890 --> 00:28:46,840 consumption today or a dollar tomorrow and a dollar today. 662 00:28:46,840 --> 00:28:50,200 They're different things. 663 00:28:50,200 --> 00:28:54,090 And so you have to account for the fact that $1 tomorrow is 664 00:28:54,090 --> 00:28:57,360 worth less than $1 today in trying to add them up. 665 00:28:57,360 --> 00:29:02,445 And the way we do that is we actually do it through the 666 00:29:02,445 --> 00:29:03,620 concept of present value. 667 00:29:03,620 --> 00:29:07,290 And the idea of present value is to translate all future 668 00:29:07,290 --> 00:29:10,550 dollars into today's dollars. 669 00:29:10,550 --> 00:29:12,920 Translate all future dollars into today's dollars 670 00:29:12,920 --> 00:29:17,550 recognizing the fact they're less valuable in the future. 671 00:29:17,550 --> 00:29:21,540 So the concept of present value is the concept of any 672 00:29:21,540 --> 00:29:26,500 future payment's value from the perspective of today. 673 00:29:26,500 --> 00:29:28,400 And you should know that any future payment will be worth 674 00:29:28,400 --> 00:29:30,050 less than a payment today. 675 00:29:30,050 --> 00:29:32,820 How much less-- that's what present value tells you. 676 00:29:32,820 --> 00:29:38,050 How much is a future payment worth in today's terms? 677 00:29:38,050 --> 00:29:43,010 So suppose that the interest rate is 10%. 678 00:29:43,010 --> 00:29:47,220 Suppose the interest rate is 10%, and you want to 679 00:29:47,220 --> 00:29:50,300 have $100 next year. 680 00:29:50,300 --> 00:29:53,170 So you know next year there's something you want to buy, and 681 00:29:53,170 --> 00:29:56,750 you have to decide how much do I have to save today to have 682 00:29:56,750 --> 00:30:02,970 $100 in period two. 683 00:30:02,970 --> 00:30:04,490 How much do I have to save today to have 684 00:30:04,490 --> 00:30:07,000 $100 in period two? 685 00:30:07,000 --> 00:30:11,290 Well if you put in an amount, PV, into the bank-- 686 00:30:11,290 --> 00:30:15,970 you put PV into the bank, then you know next year you're 687 00:30:15,970 --> 00:30:19,070 going to have-- if you put in PV in period one, next year 688 00:30:19,070 --> 00:30:25,210 you're going to have PV times 1 plus i. 689 00:30:25,210 --> 00:30:27,270 You're going to have your PV plus all the interest you 690 00:30:27,270 --> 00:30:34,730 earned on it, or in our example, PV times 1.1. 691 00:30:34,730 --> 00:30:38,870 So what that says is that, basically, you have to put in 692 00:30:38,870 --> 00:30:43,500 100 over 1.1 into the bank today, or 693 00:30:43,500 --> 00:30:48,300 90.9 dollars, $90.90. 694 00:30:48,300 --> 00:30:53,810 If you put $90.90 in the bank today, you will have $100 695 00:30:53,810 --> 00:30:56,730 tomorrow or $100 next year-- whenever the periodicity of 696 00:30:56,730 --> 00:30:59,940 the interest rate. 697 00:30:59,940 --> 00:31:05,280 So, basically, more generally, the present value of any 698 00:31:05,280 --> 00:31:12,570 stream of payments is equal to that stream's future value-- 699 00:31:12,570 --> 00:31:13,695 I'm going to write it over here. 700 00:31:13,695 --> 00:31:15,570 It's bigger. 701 00:31:15,570 --> 00:31:17,750 The present value of any stream of payments is that 702 00:31:17,750 --> 00:31:22,400 stream's future value over 1 plus the interest rate to the 703 00:31:22,400 --> 00:31:27,000 t, where t is the year in which you get the money. 704 00:31:27,000 --> 00:31:33,800 So any future money you get in year t is worth that amount 705 00:31:33,800 --> 00:31:37,806 you get over 1 plus the interest rate to the t. 706 00:31:40,610 --> 00:31:43,590 So, basically, the point is you have to weigt. 707 00:31:43,590 --> 00:31:46,300 Any money you're going to get, you to weight by how far into 708 00:31:46,300 --> 00:31:49,540 the future it is, just like if you're adding up these 709 00:31:49,540 --> 00:31:50,380 different goods. 710 00:31:50,380 --> 00:31:52,950 So, essentially, this is kind of like saying let's add a 711 00:31:52,950 --> 00:31:57,770 converter machine which can convert pizza into movies. 712 00:31:57,770 --> 00:32:00,425 Then I could say well I'll just take pizza, put it 713 00:32:00,425 --> 00:32:01,760 through the converter machine, and that'll tell me how many 714 00:32:01,760 --> 00:32:03,130 movies I have. That's what a utility 715 00:32:03,130 --> 00:32:05,590 function basically does. 716 00:32:05,590 --> 00:32:07,160 This we're saying the interest rate is 717 00:32:07,160 --> 00:32:09,100 the converter function. 718 00:32:09,100 --> 00:32:11,490 This present value formula is the converter function by 719 00:32:11,490 --> 00:32:14,080 which we convert two goods that are different 720 00:32:14,080 --> 00:32:15,350 into the same good. 721 00:32:15,350 --> 00:32:16,730 You convert them through this formula. 722 00:32:19,890 --> 00:32:24,800 So, basically, suppose that you say to me, "Look, loan me 723 00:32:24,800 --> 00:32:29,290 $30, and I'll pay you back $10 a year each of the next three 724 00:32:29,290 --> 00:32:33,450 years." Well I should say, "Wait a second. 725 00:32:33,450 --> 00:32:36,500 What's the value of that to me?" Well the present value of 726 00:32:36,500 --> 00:32:40,320 those repayments is I'm going to have $10 in one year, so 727 00:32:40,320 --> 00:32:42,470 that's $10 over 1 plus i. 728 00:32:42,470 --> 00:32:45,360 Let's say the interest rate's 10% again. 729 00:32:45,360 --> 00:32:46,145 Next year I got $10. 730 00:32:46,145 --> 00:32:48,510 That's worth 10 over 1 plus 1. 731 00:32:48,510 --> 00:32:50,260 The year after, you're going to give me 10 more dollars, 732 00:32:50,260 --> 00:32:53,610 but that's worth 10 over 1 plus 1 squared because that's 733 00:32:53,610 --> 00:32:54,700 in two years. 734 00:32:54,700 --> 00:32:57,730 If I had that money today, I could've invested it, earned 735 00:32:57,730 --> 00:33:00,600 10% and then 10% on that. 736 00:33:00,600 --> 00:33:02,770 And, likewise, the money you give me in the third year is 737 00:33:02,770 --> 00:33:05,180 worth 10 over 1.1 cubed. 738 00:33:05,180 --> 00:33:08,260 If you'd given me that money today, I could've invested it 739 00:33:08,260 --> 00:33:10,930 and and earned interest three times on it. 740 00:33:10,930 --> 00:33:13,770 So the bottom line is your repayments 741 00:33:13,770 --> 00:33:18,110 are only worth $24.87. 742 00:33:18,110 --> 00:33:22,030 So I've just given you $30 today in return for a stream 743 00:33:22,030 --> 00:33:24,740 of payments that's only worth $24.87 today. 744 00:33:24,740 --> 00:33:27,980 I've lost money from that loan because I gave you the money 745 00:33:27,980 --> 00:33:29,460 today, and you're paying me back in the future when the 746 00:33:29,460 --> 00:33:31,780 money's worth less. 747 00:33:31,780 --> 00:33:34,750 So, basically, the general formula we have is that the 748 00:33:34,750 --> 00:33:41,830 present value of any stream of future payments is that the 749 00:33:41,830 --> 00:33:45,040 amount of the future payment-- let's call it f for any fixed 750 00:33:45,040 --> 00:33:48,570 stream of future payments, $10 forever or $15 forever-- 751 00:33:48,570 --> 00:33:56,550 fixed stream of that amount, f, times 1 over 1 plus i, plus 752 00:33:56,550 --> 00:34:03,790 1 over 1 plus i squared, plus da da da da, plus 1 over 1 753 00:34:03,790 --> 00:34:06,850 plus i to the t. 754 00:34:06,850 --> 00:34:09,949 So if you're going to pay me a fixed amount, f, for t years, 755 00:34:09,949 --> 00:34:13,210 here what it's worth to me today. 756 00:34:13,210 --> 00:34:15,770 You pay me a fixed amount, f, for t years, it's worth this 757 00:34:15,770 --> 00:34:17,830 much to me today. 758 00:34:17,830 --> 00:34:19,680 I'm accounting for how far off in the future it is. 759 00:34:22,670 --> 00:34:25,989 Now one important trick we're going to do now for the rest 760 00:34:25,989 --> 00:34:28,710 of the semester is we're going to take the trick of saying 761 00:34:28,710 --> 00:34:29,540 this is actually-- 762 00:34:29,540 --> 00:34:31,210 well this is a messy formula. 763 00:34:31,210 --> 00:34:33,820 It's actually a rather easy formula to write down if the 764 00:34:33,820 --> 00:34:36,810 future stream of payments is infinite, if we have what we 765 00:34:36,810 --> 00:34:40,150 call a perpetuity. 766 00:34:40,150 --> 00:34:41,400 If we have what we call a perpetuity. 767 00:34:45,630 --> 00:34:48,010 A perpetuity is a future stream of payments that goes 768 00:34:48,010 --> 00:34:52,610 on forever or long enough that we'd consider it forever. 769 00:34:52,610 --> 00:34:55,199 Fifty years is probably good enough. 770 00:34:55,199 --> 00:34:58,990 If you have a perpetuity, then this formula 771 00:34:58,990 --> 00:35:02,940 can be reduced to-- 772 00:35:02,940 --> 00:35:06,140 the present value of any perpetuity is the amount of 773 00:35:06,140 --> 00:35:09,720 that perpetuity over the interest rate. 774 00:35:09,720 --> 00:35:12,150 It's just taking the infinite sum of that product. 775 00:35:12,150 --> 00:35:13,480 They're just taking the infinite sum. 776 00:35:13,480 --> 00:35:15,240 Those mathematically inclined will know this already. 777 00:35:15,240 --> 00:35:17,920 But it's just taking the infinite sum here, you can get 778 00:35:17,920 --> 00:35:19,390 this formula. 779 00:35:19,390 --> 00:35:22,980 So any perpetuity, if you're getting a payment forever, the 780 00:35:22,980 --> 00:35:25,660 value of that payment today-- so if I said I'll give you $10 781 00:35:25,660 --> 00:35:28,295 forever and the interest rate's going to be 10% then 782 00:35:28,295 --> 00:35:31,150 you'd say that's worth $100 to me. 783 00:35:31,150 --> 00:35:34,630 If I'm going to give you $10 forever at a 10% interest 784 00:35:34,630 --> 00:35:39,310 rate, then you'd say well that's worth $9.90 the next 785 00:35:39,310 --> 00:35:41,320 year and $8 something the next year, et cetera. 786 00:35:41,320 --> 00:35:46,640 And if I add all those up, I get approximately the amount 787 00:35:46,640 --> 00:35:48,270 of the payment over the interest rate. 788 00:35:51,600 --> 00:35:58,490 So, basically, that is what determines present value. 789 00:35:58,490 --> 00:36:02,530 Now we can flip this around and we could say, OK, well, if 790 00:36:02,530 --> 00:36:05,560 that's present value what determines future value? 791 00:36:05,560 --> 00:36:10,510 Well the future value of getting a payment today-- 792 00:36:10,510 --> 00:36:13,030 So that's the present value of getting payments tomorrow. 793 00:36:13,030 --> 00:36:17,120 The only other thing is what's the future value? 794 00:36:17,120 --> 00:36:21,610 What's the future value of getting a stream of payments 795 00:36:21,610 --> 00:36:22,710 starting today? 796 00:36:22,710 --> 00:36:25,390 So let's say, starting today, I'm going to get $10. 797 00:36:25,390 --> 00:36:27,060 I'm going to get it for a certain number of years. 798 00:36:27,060 --> 00:36:29,220 What's that going to be worth at the end of the day given 799 00:36:29,220 --> 00:36:31,070 that I can save it along the way. 800 00:36:31,070 --> 00:36:37,910 So, in other words, if you give me $10 today-- 801 00:36:37,910 --> 00:36:42,920 if you give me $10 today, well then in one year, next year, I 802 00:36:42,920 --> 00:36:48,150 have $11 because I got to save it at the interest rate. 803 00:36:48,150 --> 00:36:52,670 So if you give me $10 today, next year I'll have $11. 804 00:36:52,670 --> 00:36:57,870 Now let's say that I then keep it in the 805 00:36:57,870 --> 00:36:59,460 bank for another year. 806 00:36:59,460 --> 00:37:07,490 Well the next year, it's worth 10 times 1 plus i squared, so 807 00:37:07,490 --> 00:37:13,250 10 times 1.1 squared, 10 times 1.1 squared, or 808 00:37:13,250 --> 00:37:20,660 $12.10 and so on. 809 00:37:20,660 --> 00:37:27,700 So, basically, the point is that at the end of each year I 810 00:37:27,700 --> 00:37:31,280 earn the interest on my original $10, plus I earn the 811 00:37:31,280 --> 00:37:34,680 interest on the interest I earned the previous periods. 812 00:37:34,680 --> 00:37:38,750 So in the long run, at the end of t years, which of the 813 00:37:38,750 --> 00:37:43,140 future value, is the amount invested, f, times 1 814 00:37:43,140 --> 00:37:46,110 plus i to the t. 815 00:37:46,110 --> 00:37:47,600 That's your future value. 816 00:37:47,600 --> 00:37:49,970 So if you invest a given amount of money today for t 817 00:37:49,970 --> 00:37:54,570 years, you end up with that much. 818 00:37:54,570 --> 00:37:56,620 If you invest a given amount, f, today you end 819 00:37:56,620 --> 00:37:57,170 up with that much-- 820 00:37:57,170 --> 00:38:00,810 And the key point, the key insight, is the miracle of 821 00:38:00,810 --> 00:38:03,140 compounding. 822 00:38:03,140 --> 00:38:06,130 The miracle of compounding is the point that you earn 823 00:38:06,130 --> 00:38:13,580 interest on your interest. And what this means is the earlier 824 00:38:13,580 --> 00:38:18,110 you save, the more you'll have later on. 825 00:38:18,110 --> 00:38:22,420 So there's an example in the book which is very important. 826 00:38:22,420 --> 00:38:23,980 So it's actually thinking about-- 827 00:38:23,980 --> 00:38:25,540 let's think for a minute about retirement. 828 00:38:25,540 --> 00:38:26,720 You might say this is sort of crazy. 829 00:38:26,720 --> 00:38:28,650 Maybe not crazy for an old guy like me, but you're thinking 830 00:38:28,650 --> 00:38:30,010 I'm just starting on my career. 831 00:38:30,010 --> 00:38:31,320 Why would I think about retirement? 832 00:38:31,320 --> 00:38:33,340 Here's why you want to think about it. 833 00:38:33,340 --> 00:38:38,070 Let's say, for example, that you plan to work full time 834 00:38:38,070 --> 00:38:40,640 from age 22 to age 70. 835 00:38:40,640 --> 00:38:41,990 You've got a great idea. 836 00:38:41,990 --> 00:38:43,290 Screw grad school. 837 00:38:43,290 --> 00:38:44,900 You're going right to work. 838 00:38:44,900 --> 00:38:46,250 You've got a great idea, and you know you want 839 00:38:46,250 --> 00:38:47,020 to retire at 70. 840 00:38:47,020 --> 00:38:53,640 So you plan to work full time from age 22 to age 70. 841 00:38:53,640 --> 00:38:57,030 And let's say that you want to save money for your retirement 842 00:38:57,030 --> 00:38:58,030 because you're going to retire at 70. 843 00:38:58,030 --> 00:38:58,840 You're going to live forever. 844 00:38:58,840 --> 00:39:00,140 You're a healthy young person. 845 00:39:00,140 --> 00:39:02,000 You think you're going to live forever at 70. 846 00:39:02,000 --> 00:39:03,840 So you want to have money around when you retire. 847 00:39:03,840 --> 00:39:05,230 And let's say that the interest rate you 848 00:39:05,230 --> 00:39:08,680 can save at is 7%. 849 00:39:08,680 --> 00:39:13,120 So you can save money for your retirement at 7%, and that's 850 00:39:13,120 --> 00:39:13,600 your choice. 851 00:39:13,600 --> 00:39:16,830 Now let's consider two different savings plans. 852 00:39:16,830 --> 00:39:21,640 Savings plan one is that I'm going to save $3,000. 853 00:39:21,640 --> 00:39:24,960 You're going to save $3,000 right off the bat. 854 00:39:24,960 --> 00:39:27,390 And for the first 15 years of your working life-- 855 00:39:27,390 --> 00:39:29,550 so from 22 to 37-- 856 00:39:29,550 --> 00:39:32,450 you're going to save $3,000. 857 00:39:32,450 --> 00:39:44,690 You're going to save $3,000 a year savings for 15 years, and 858 00:39:44,690 --> 00:39:45,870 then nothing. 859 00:39:45,870 --> 00:39:47,890 And then once you're 37 and you've got to start worrying 860 00:39:47,890 --> 00:39:49,770 about kids' college and mortgage, you're not going to 861 00:39:49,770 --> 00:39:51,150 save anything. 862 00:39:51,150 --> 00:39:53,355 So from 22 to 37, when you're living high on the hog, you've 863 00:39:53,355 --> 00:39:56,440 got no obligations, you're going to save. Once you're 37, 864 00:39:56,440 --> 00:39:58,280 you've got a house, you've got kids, you've got things that 865 00:39:58,280 --> 00:39:59,730 are expensive, you're not going to save anymore. 866 00:39:59,730 --> 00:40:01,600 So then you go to zero. 867 00:40:01,600 --> 00:40:07,400 Zero savings from age 37 to age 70. 868 00:40:07,400 --> 00:40:09,590 That's a pretty bold plan. 869 00:40:09,590 --> 00:40:12,720 You're just going to save 15 years then zero savings. 870 00:40:12,720 --> 00:40:14,190 Well what do you get? 871 00:40:14,190 --> 00:40:19,360 Well after 15 years, if you use our future value formula, 872 00:40:19,360 --> 00:40:22,410 if you save $3,000 every year, you work out that you will 873 00:40:22,410 --> 00:40:27,670 have $75,387 in the bank. 874 00:40:27,670 --> 00:40:31,010 So it's more than 45-- is not just 3,000 times 15 because 875 00:40:31,010 --> 00:40:33,300 you get the compounding. 876 00:40:33,300 --> 00:40:34,760 It's not just 3,000 times 15. 877 00:40:34,760 --> 00:40:36,820 You actually get more than that because you got the 878 00:40:36,820 --> 00:40:38,980 compounding along the way. 879 00:40:38,980 --> 00:40:41,970 Then if you just let it sit there in the bank-- you don't 880 00:40:41,970 --> 00:40:42,500 do anything. 881 00:40:42,500 --> 00:40:43,300 No more active savings. 882 00:40:43,300 --> 00:40:44,670 You let it sit there. 883 00:40:44,670 --> 00:40:50,460 Then by the time you retire, you have that $75,387 times 884 00:40:50,460 --> 00:40:54,940 1.07 to the 33 because you let that money sit 885 00:40:54,940 --> 00:40:57,960 there for 33 years. 886 00:40:57,960 --> 00:40:59,720 You let that money sit there for 33 years. 887 00:40:59,720 --> 00:41:08,330 That works out to be $703,010. 888 00:41:08,330 --> 00:41:11,880 So by saving for 15 years-- all you did was save $3,000 889 00:41:11,880 --> 00:41:15,500 for 15 years, a fraction of your career. 890 00:41:15,500 --> 00:41:20,730 And you retire with $703,000. 891 00:41:20,730 --> 00:41:23,630 Now we'll contrast that with an alternative plan. 892 00:41:23,630 --> 00:41:27,490 My alternative plan is I'm going to save nothing for the 893 00:41:27,490 --> 00:41:31,460 first 15 years because I figure, like, I'm young. 894 00:41:31,460 --> 00:41:32,020 I'm gonna party. 895 00:41:32,020 --> 00:41:32,900 I'm going to use the money now. 896 00:41:32,900 --> 00:41:33,590 I'll save later. 897 00:41:33,590 --> 00:41:35,490 I'm nowhere near retirement. 898 00:41:35,490 --> 00:41:36,740 Then I get to 37. 899 00:41:36,740 --> 00:41:37,560 I say, wait a second, I'm 900 00:41:37,560 --> 00:41:38,690 starting to see more mortality. 901 00:41:38,690 --> 00:41:39,910 I better worry about retirement. 902 00:41:39,910 --> 00:41:43,700 Then I start to save, and I save for the next 33 years. 903 00:41:43,700 --> 00:41:51,270 So the new plan is zero per year from age 22 to 37, and 904 00:41:51,270 --> 00:41:56,980 then $3,000 a year from 37 to 70. 905 00:41:56,980 --> 00:41:58,580 So it's a lot more savings. 906 00:41:58,580 --> 00:42:02,400 You're saving for more than twice as long, more 907 00:42:02,400 --> 00:42:05,180 than twice as long. 908 00:42:05,180 --> 00:42:06,650 What do you end up with? 909 00:42:06,650 --> 00:42:13,760 You end up with $356,800-- 910 00:42:13,760 --> 00:42:19,050 half, just slightly more than half, than what you end up 911 00:42:19,050 --> 00:42:21,630 with the first plan, even though you save for twice as 912 00:42:21,630 --> 00:42:22,880 many years. 913 00:42:25,020 --> 00:42:29,220 This is like the parents' lecture why you should save. 914 00:42:29,220 --> 00:42:33,620 The point is that saving early lets you ride the wave of 915 00:42:33,620 --> 00:42:36,090 compounding for many, many years. 916 00:42:36,090 --> 00:42:39,520 Savings late does not let you do that. 917 00:42:39,520 --> 00:42:43,370 And as a result, you end up with less money. 918 00:42:43,370 --> 00:42:45,530 I take my kids to the science museum, and at the science 919 00:42:45,530 --> 00:42:46,960 museum they have these little ramps. 920 00:42:46,960 --> 00:42:48,010 And you can drop a ball. 921 00:42:48,010 --> 00:42:51,770 And one is flat then steep, and one is steep then flat. 922 00:42:51,770 --> 00:42:54,420 And the one that's steep then flat always wins because 923 00:42:54,420 --> 00:42:58,450 there's compounding in acceleration the same way. 924 00:42:58,450 --> 00:43:01,430 The point is building up early and then riding that velocity 925 00:43:01,430 --> 00:43:05,610 going forward is a lot better than starting late. 926 00:43:05,610 --> 00:43:08,070 Questions about that? 927 00:43:08,070 --> 00:43:10,640 So make sure when you get those jobs, and they offer 928 00:43:10,640 --> 00:43:12,245 you-- we'll talk next time about savings incentives-- and 929 00:43:12,245 --> 00:43:15,230 they offer you those good 401K packages, that you take them, 930 00:43:15,230 --> 00:43:17,810 and don't say I'll worry about that later. 931 00:43:17,810 --> 00:43:20,580 Now, one last thing. 932 00:43:20,580 --> 00:43:23,650 Last thing I want to cover is that we've ignored, so far, 933 00:43:23,650 --> 00:43:25,920 the whole concept of inflation. 934 00:43:25,920 --> 00:43:28,330 When I've talked about savings, I've presumed that 935 00:43:28,330 --> 00:43:29,660 you've saved the money and it's worth something. 936 00:43:29,660 --> 00:43:31,750 But who the hell knows what $703,000 will 937 00:43:31,750 --> 00:43:36,180 be worth in 48 years? 938 00:43:36,180 --> 00:43:37,450 What's that even going to be worth? 939 00:43:37,450 --> 00:43:38,750 How do we even think about that? 940 00:43:38,750 --> 00:43:41,160 Well we have to account for the fact that stuff's going to 941 00:43:41,160 --> 00:43:42,880 be more expensive. 942 00:43:42,880 --> 00:43:46,880 So we have to account for inflation in doing this. 943 00:43:46,880 --> 00:43:49,710 And the way we do this is by recognizing that what we've 944 00:43:49,710 --> 00:43:51,940 done so far is we've talked about the 945 00:43:51,940 --> 00:43:54,950 nominal interest rate. 946 00:43:54,950 --> 00:43:56,635 By the nominal interest rate, I meant the interest rate that 947 00:43:56,635 --> 00:43:59,620 you actually see posted in the bank. 948 00:43:59,620 --> 00:44:04,620 But what matters, ultimately for your well-being, is the 949 00:44:04,620 --> 00:44:09,400 real interest rate which is what your money can do in 950 00:44:09,400 --> 00:44:13,010 terms of actually buying goods. 951 00:44:13,010 --> 00:44:18,390 So I should not care about how much money I have next year. 952 00:44:18,390 --> 00:44:22,390 I should care about how many goods I can buy next year. 953 00:44:22,390 --> 00:44:23,940 The money's just paper. 954 00:44:23,940 --> 00:44:26,530 What matters is what I can get with it. 955 00:44:26,530 --> 00:44:28,760 That's what matters. 956 00:44:28,760 --> 00:44:30,700 So let's say, for example, I want to use 957 00:44:30,700 --> 00:44:32,190 all my money on Skittles. 958 00:44:32,190 --> 00:44:34,070 That's just what I want to use my money on. 959 00:44:34,070 --> 00:44:38,960 So let's say I have $100, and I want to spend 960 00:44:38,960 --> 00:44:41,230 that money on Skittles. 961 00:44:41,230 --> 00:44:43,530 And let's say Skittles today are $1 a bag. 962 00:44:47,330 --> 00:44:52,500 And let's say the interest rate, once again, is 10%. 963 00:44:52,500 --> 00:44:55,080 And let's say there's no inflation. 964 00:44:55,080 --> 00:44:56,330 Inflation equals zero. 965 00:44:59,990 --> 00:45:03,930 So my choice is I can spend $100 on Skittles 966 00:45:03,930 --> 00:45:06,020 today and get 100 bags. 967 00:45:06,020 --> 00:45:07,640 So I could have 100 bags today. 968 00:45:10,630 --> 00:45:15,050 Or I can save it, have $110 tomorrow and 969 00:45:15,050 --> 00:45:20,700 get 110 bags of Skittles. 970 00:45:20,700 --> 00:45:21,440 That's my choice. 971 00:45:21,440 --> 00:45:22,690 That's my trade-off. 972 00:45:24,620 --> 00:45:27,650 Now let's say there's inflation. 973 00:45:27,650 --> 00:45:33,450 Let's say that prices are rising at 10% a year, as well. 974 00:45:33,450 --> 00:45:35,910 So the prices are rising 10% a year, as well. 975 00:45:35,910 --> 00:45:40,580 What that means is next year Skittles cost $1.10 a bag. 976 00:45:40,580 --> 00:45:43,150 So now what's my trade-off? 977 00:45:43,150 --> 00:45:44,480 That means I could have 100 bags 978 00:45:44,480 --> 00:45:47,940 today or 100 bags tomorrow. 979 00:45:47,940 --> 00:45:50,650 I don't get any more Skittles tomorrow. 980 00:45:50,650 --> 00:45:53,820 I get 10 more dollars, but who cares? 981 00:45:53,820 --> 00:45:56,230 Everything costs more. 982 00:45:56,230 --> 00:45:59,930 If everything cost 10% more and I get a 10% interest rate, 983 00:45:59,930 --> 00:46:02,070 that interest rate is effectively zero in terms of 984 00:46:02,070 --> 00:46:03,200 what I can buy. 985 00:46:03,200 --> 00:46:07,410 The real interest rate is the nominal 986 00:46:07,410 --> 00:46:10,490 interest rate minus inflation. 987 00:46:13,070 --> 00:46:15,880 What I care about is what I can buy. 988 00:46:15,880 --> 00:46:18,560 So I have to take out of the interest rate 989 00:46:18,560 --> 00:46:21,700 what happens to prices. 990 00:46:21,700 --> 00:46:24,890 Because if prices go up, it offsets what I'm 991 00:46:24,890 --> 00:46:26,240 earning in the bank. 992 00:46:26,240 --> 00:46:31,270 And so what I care about is I care about what the bank posts 993 00:46:31,270 --> 00:46:32,790 minus what inflation will be. 994 00:46:32,790 --> 00:46:33,680 So it's even trickier, right? 995 00:46:33,680 --> 00:46:35,070 Because it's not about what inflation was, it's what 996 00:46:35,070 --> 00:46:35,710 inflation will be. 997 00:46:35,710 --> 00:46:39,310 You'll have to guess what inflation is going to be. 998 00:46:39,310 --> 00:46:41,840 And so what we care about is this real interest rate. 999 00:46:41,840 --> 00:46:45,680 And that's why the interest rate that banks pay, a primary 1000 00:46:45,680 --> 00:46:47,700 determinant of it is inflation. 1001 00:46:47,700 --> 00:46:51,320 Right now, we are in the lowest inflation period this 1002 00:46:51,320 --> 00:46:54,110 nation's seen since World War II. 1003 00:46:54,110 --> 00:46:55,380 Core inflation-- 1004 00:46:55,380 --> 00:46:56,920 we don't really get into inflation in this course-- but 1005 00:46:56,920 --> 00:46:59,170 core inflation, which is inflation minus some things 1006 00:46:59,170 --> 00:47:04,870 which fluctuate a lot, is basically zero in the US. 1007 00:47:04,870 --> 00:47:06,790 So, basically, nominal interest rates are the same as 1008 00:47:06,790 --> 00:47:08,770 real interest rates, and that's why the interest rates 1009 00:47:08,770 --> 00:47:12,290 you see posted are so incredibly low because there's 1010 00:47:12,290 --> 00:47:13,760 no inflation. 1011 00:47:13,760 --> 00:47:16,490 In the late 1970's, when inflation was running at 1012 00:47:16,490 --> 00:47:21,170 10-15% a year, interest rates were 15 to 20% a year. 1013 00:47:21,170 --> 00:47:23,110 Now it wasn't that you could get so much more for your 1014 00:47:23,110 --> 00:47:24,500 savings in the 1970's. 1015 00:47:24,500 --> 00:47:27,010 It was just that stuff was going to cost more next year, 1016 00:47:27,010 --> 00:47:29,820 so banks, if they wanted to induce you to save, had to pay 1017 00:47:29,820 --> 00:47:31,550 you a higher interest rate. 1018 00:47:31,550 --> 00:47:33,120 So, essentially, banks are going to have to pay you to 1019 00:47:33,120 --> 00:47:34,850 get you to put your money in. 1020 00:47:34,850 --> 00:47:40,230 If in 1978, when the inflation rate was 15%-- 1021 00:47:40,230 --> 00:47:43,500 if banks had offered a 3% interest rate no one would've 1022 00:47:43,500 --> 00:47:49,880 put money in the banks because you would end up losing 1023 00:47:49,880 --> 00:47:50,310 effectively. 1024 00:47:50,310 --> 00:47:52,760 Effectively, that's a negative 12% real interest rate. 1025 00:47:52,760 --> 00:47:56,020 So what matters is how much the bank pays you in cash 1026 00:47:56,020 --> 00:47:58,830 minus how much more stuff is going to cost. And that's 1027 00:47:58,830 --> 00:47:59,570 often what matters. 1028 00:47:59,570 --> 00:48:00,980 Now that's a distinction we won't spent a lot of 1029 00:48:00,980 --> 00:48:02,880 time on later on. 1030 00:48:02,880 --> 00:48:03,860 I'll just say interest rate. 1031 00:48:03,860 --> 00:48:05,370 I won't say real versus nominal. 1032 00:48:05,370 --> 00:48:07,840 But you've got to know in your head that what matters is the 1033 00:48:07,840 --> 00:48:09,480 interest rate is the real interest rate, what the bank 1034 00:48:09,480 --> 00:48:12,880 pays you, minus how much more stuff's going to cost. 1035 00:48:12,880 --> 00:48:14,800 Questions about that? 1036 00:48:14,800 --> 00:48:15,910 Alright, we'll come back next time. 1037 00:48:15,910 --> 00:48:16,740 There is class on Wednesday. 1038 00:48:16,740 --> 00:48:17,940 It does matter. 1039 00:48:17,940 --> 00:48:19,360 And on Wednesday we're going to talk about the rest of 1040 00:48:19,360 --> 00:48:21,000 capital markets and people's savings decisions.