1 00:00:00,000 --> 00:00:05,423 [SQUEAKING] [RUSTLING] [CLICKING] 2 00:00:11,350 --> 00:00:14,670 JONATHAN GRUBER: All right, let's get started. 3 00:00:14,670 --> 00:00:17,240 We have three weeks left in the class. 4 00:00:17,240 --> 00:00:19,460 And what we'll be doing for the next three weeks 5 00:00:19,460 --> 00:00:22,640 is really a series of applications 6 00:00:22,640 --> 00:00:26,270 of what we've learned so far to sort of help you understand how 7 00:00:26,270 --> 00:00:28,610 we add some richness to what we've learned 8 00:00:28,610 --> 00:00:32,119 and sort of take it to some more real world applications. 9 00:00:32,119 --> 00:00:33,830 So we're going to start that today 10 00:00:33,830 --> 00:00:37,010 by talking about something we've really ignored in the course 11 00:00:37,010 --> 00:00:44,150 so far, which is uncertainty and how uncertainty 12 00:00:44,150 --> 00:00:46,730 affects your decision making. 13 00:00:46,730 --> 00:00:49,210 So what we've done so far in this class is 14 00:00:49,210 --> 00:00:51,100 we've sort of said, look, we've assumed 15 00:00:51,100 --> 00:00:53,020 whenever you make decisions you make them 16 00:00:53,020 --> 00:00:55,390 with full knowledge and full certainty. 17 00:00:55,390 --> 00:00:58,000 But many, many decisions in life are 18 00:00:58,000 --> 00:01:01,450 made under conditions of uncertainty. 19 00:01:01,450 --> 00:01:02,890 So consider your decision to study 20 00:01:02,890 --> 00:01:05,379 for the final in this class. 21 00:01:05,379 --> 00:01:09,310 In our models so far, you could optimize your studying 22 00:01:09,310 --> 00:01:10,820 across different units of the class. 23 00:01:10,820 --> 00:01:13,180 So our model so far, you'd know on the final 24 00:01:13,180 --> 00:01:15,700 which unit would be represented with what proportion. 25 00:01:15,700 --> 00:01:17,680 You'd optimize your studying appropriately. 26 00:01:17,680 --> 00:01:19,450 But of course you don't know that. 27 00:01:19,450 --> 00:01:21,097 You face uncertainty about what will 28 00:01:21,097 --> 00:01:22,930 be covered in the final or upper proportion. 29 00:01:22,930 --> 00:01:24,347 You know the whole course-- you're 30 00:01:24,347 --> 00:01:25,798 responsible for the whole class. 31 00:01:25,798 --> 00:01:27,340 But obviously you allocate your time. 32 00:01:27,340 --> 00:01:29,110 You're uncertain about how to allocate 33 00:01:29,110 --> 00:01:31,660 your time across the different subjects on the test. 34 00:01:31,660 --> 00:01:34,480 So how do you make that decision? 35 00:01:34,480 --> 00:01:37,240 We need to bring our tools to bear 36 00:01:37,240 --> 00:01:39,910 on thinking about these kinds of decision making 37 00:01:39,910 --> 00:01:42,910 under uncertainty situations. 38 00:01:42,910 --> 00:01:45,040 And this isn't just about the test. 39 00:01:45,040 --> 00:01:47,300 I decide whether to bring my umbrella today. 40 00:01:47,300 --> 00:01:49,240 If I bring my umbrella, there's a chance I'm going to lose it. 41 00:01:49,240 --> 00:01:50,340 But I don't want to get wet. 42 00:01:50,340 --> 00:01:51,670 I have to think about whether it's going to rain. 43 00:01:51,670 --> 00:01:53,170 It all depends on how certain I am 44 00:01:53,170 --> 00:01:54,790 it's going to rain, et cetera. 45 00:01:54,790 --> 00:01:59,785 There's decisions about whether to bet on a sporting event. 46 00:01:59,785 --> 00:02:01,160 That's a decision of uncertainty. 47 00:02:01,160 --> 00:02:03,010 And that's all the fun stuff in your life. 48 00:02:03,010 --> 00:02:05,067 When you get to the anxiety ridden adult life, 49 00:02:05,067 --> 00:02:07,150 you've got things like whether to buy a seven year 50 00:02:07,150 --> 00:02:10,060 mortgage or a 30 year mortgage, whether to buy 51 00:02:10,060 --> 00:02:13,330 health insurance, what school to put your kids in. 52 00:02:13,330 --> 00:02:16,780 All these things involve a huge amount of uncertainty. 53 00:02:16,780 --> 00:02:20,600 And we have not yet developed the tools to deal with this. 54 00:02:20,600 --> 00:02:23,620 What's really cool is that economics 55 00:02:23,620 --> 00:02:28,180 has a very useful tool to think about exactly 56 00:02:28,180 --> 00:02:29,707 these kinds of situations. 57 00:02:29,707 --> 00:02:32,290 That much like the other tools we've dealt with this semester, 58 00:02:32,290 --> 00:02:34,330 it's pretty easy once you understand it. 59 00:02:34,330 --> 00:02:37,900 But it's a huge amount of power for explaining the world. 60 00:02:37,900 --> 00:02:40,990 And that's the tool of expected utility theory. 61 00:02:46,178 --> 00:02:47,720 And that's what we'll focus on today. 62 00:02:47,720 --> 00:02:50,178 That's what we'll learn today, the tool of expected utility 63 00:02:50,178 --> 00:02:51,758 theory. 64 00:02:51,758 --> 00:02:53,300 Now, I'm going to ask you a question. 65 00:02:53,300 --> 00:02:55,460 As always, I don't want you try to outsmart me. 66 00:02:55,460 --> 00:02:58,152 I just want a quick, gut reaction. 67 00:02:58,152 --> 00:02:59,360 I'm going to offer you a bet. 68 00:02:59,360 --> 00:03:01,115 Not really, but imagine I was. 69 00:03:01,115 --> 00:03:03,080 I'm going to flip a coin. 70 00:03:03,080 --> 00:03:05,540 Heads you get $125. 71 00:03:05,540 --> 00:03:08,070 Tails you give me $100. 72 00:03:08,070 --> 00:03:09,730 So you win $125 versus lose $100. 73 00:03:09,730 --> 00:03:10,980 How many of you take that bet? 74 00:03:13,840 --> 00:03:14,715 So yeah. 75 00:03:14,715 --> 00:03:16,840 You're a slightly more aggressive class than usual. 76 00:03:16,840 --> 00:03:18,310 About 40% of you taking the bet. 77 00:03:18,310 --> 00:03:20,800 Usually I get more about 20%, 25%. 78 00:03:20,800 --> 00:03:21,480 OK. 79 00:03:21,480 --> 00:03:23,050 Now-- yeah. 80 00:03:23,050 --> 00:03:24,177 AUDIENCE: [INAUDIBLE] 81 00:03:24,177 --> 00:03:25,010 JONATHAN GRUBER: No. 82 00:03:25,010 --> 00:03:27,310 It's a one time bet. 83 00:03:27,310 --> 00:03:30,867 So basically-- now how do we think about this, 84 00:03:30,867 --> 00:03:32,200 whether it's a good idea or not? 85 00:03:32,200 --> 00:03:36,220 Now those who raised your hand probably quickly did the math 86 00:03:36,220 --> 00:03:39,880 and did in your head what we call an expected value 87 00:03:39,880 --> 00:03:41,300 calculation. 88 00:03:41,300 --> 00:03:43,600 What's the expected value of any gamble? 89 00:03:43,600 --> 00:03:46,840 The expected value of any gamble is the probability 90 00:03:46,840 --> 00:03:53,470 that you win times what you win plus the probability that you 91 00:03:53,470 --> 00:03:57,070 lose times what you lose. 92 00:03:57,070 --> 00:03:58,840 So you did that calculation in your head. 93 00:03:58,840 --> 00:04:01,750 You said, as long as he's not cheating, using a fair coin, 94 00:04:01,750 --> 00:04:11,460 there's a 0.5 times 125 plus 0.5 times minus 100. 95 00:04:11,460 --> 00:04:17,885 And that is an expected value of $12.50. 96 00:04:17,885 --> 00:04:19,760 So those of you who raised your hand probably 97 00:04:19,760 --> 00:04:21,700 did that calculation quickly in your head 98 00:04:21,700 --> 00:04:24,880 and said, yeah, this is a positive expected value. 99 00:04:24,880 --> 00:04:31,440 This is what we call in economics a more than fair bet. 100 00:04:31,440 --> 00:04:32,670 More than fair. 101 00:04:32,670 --> 00:04:36,970 A fair bet is one with an expected value of 0. 102 00:04:36,970 --> 00:04:39,910 So a fair bet is one with an expected value of 0. 103 00:04:39,910 --> 00:04:41,830 So a bet with a positive expected value 104 00:04:41,830 --> 00:04:43,793 is more than fair. 105 00:04:43,793 --> 00:04:45,710 And you in your head said, I did that through. 106 00:04:45,710 --> 00:04:48,950 It's more than fair. 107 00:04:48,950 --> 00:04:50,960 And that's why some of you raised your hands. 108 00:04:50,960 --> 00:04:52,840 But many of you didn't. 109 00:04:52,840 --> 00:04:54,860 And that doesn't mean you were wrong. 110 00:04:54,860 --> 00:04:58,550 It just means this is not the right way to think about it. 111 00:04:58,550 --> 00:05:01,040 The right way to think about it is that what you care about 112 00:05:01,040 --> 00:05:02,480 is not dollars. 113 00:05:02,480 --> 00:05:04,870 What you care about is utility. 114 00:05:04,870 --> 00:05:06,470 Dollars are meaningless. 115 00:05:06,470 --> 00:05:10,790 What you care about as a consumer is your utility. 116 00:05:10,790 --> 00:05:13,610 And so we don't want to think about expected value. 117 00:05:13,610 --> 00:05:16,850 We want to think about expected utility. 118 00:05:16,850 --> 00:05:18,320 Now, what is expected utility? 119 00:05:18,320 --> 00:05:22,480 It's the same kind of formula as this but with one change. 120 00:05:22,480 --> 00:05:25,510 Expected utility is the probability 121 00:05:25,510 --> 00:05:32,240 that you win times your utility if you win plus the probability 122 00:05:32,240 --> 00:05:36,780 that you lose times your utility if you lose. 123 00:05:39,560 --> 00:05:43,040 And that is somewhat different than expected value. 124 00:05:43,040 --> 00:05:46,120 And the reason is because utility is not 125 00:05:46,120 --> 00:05:48,290 a linear weighting of dollars. 126 00:05:48,290 --> 00:05:53,330 Utility is a concave weighting of dollars. 127 00:05:53,330 --> 00:05:56,870 As such, because you utility is a concave weighting of dollars, 128 00:05:56,870 --> 00:06:01,220 it exhibits diminishing marginal utility. 129 00:06:01,220 --> 00:06:03,830 Diminishing marginal rate of substitution. 130 00:06:03,830 --> 00:06:05,720 Diminishing marginal rate of substitution, 131 00:06:05,720 --> 00:06:08,240 as we talked about ad nauseam in consumer theory. 132 00:06:11,330 --> 00:06:15,700 That means that the next dollar is worth less to you 133 00:06:15,700 --> 00:06:16,930 than the previous dollar. 134 00:06:19,500 --> 00:06:21,677 The next dollars worth diminishing utility. 135 00:06:21,677 --> 00:06:23,510 The next slice of pizza is worth less to you 136 00:06:23,510 --> 00:06:24,930 than the previous slice of pizza. 137 00:06:24,930 --> 00:06:27,060 Likewise, the next dollar's worth less to you 138 00:06:27,060 --> 00:06:28,950 than the previous dollar. 139 00:06:28,950 --> 00:06:33,270 As a result, losing $1 makes you sadder 140 00:06:33,270 --> 00:06:35,790 than winning $1 makes you happy. 141 00:06:35,790 --> 00:06:38,190 There's a nonlinearity that comes 142 00:06:38,190 --> 00:06:39,810 from diminishing marginal utility 143 00:06:39,810 --> 00:06:42,510 and diminishing marginal rate of substitution. 144 00:06:42,510 --> 00:06:45,240 So for example, let's think about our typical utility 145 00:06:45,240 --> 00:06:47,850 function that we use previously in consumer theory. 146 00:06:47,850 --> 00:06:50,302 Utility equals the square root of consumption. 147 00:06:50,302 --> 00:06:52,260 And let's just say you consume all your income, 148 00:06:52,260 --> 00:06:53,100 as we always did. 149 00:06:53,100 --> 00:06:55,200 We've talked about savings the last couple of lectures. 150 00:06:55,200 --> 00:06:57,120 Let's put savings aside again and just assume 151 00:06:57,120 --> 00:06:59,510 people consume all their income. 152 00:06:59,510 --> 00:07:03,030 And so you utility is the square root of consumption. 153 00:07:03,030 --> 00:07:08,760 And let's say you start your initial consumption, c0 is 100. 154 00:07:08,760 --> 00:07:13,670 You start with $100 of consumption. 155 00:07:13,670 --> 00:07:15,270 Your c0 is 100. 156 00:07:15,270 --> 00:07:18,890 So your initial utility u0 is 10. 157 00:07:21,460 --> 00:07:23,430 Now, I give you-- 158 00:07:23,430 --> 00:07:25,020 I offer you this bet. 159 00:07:25,020 --> 00:07:27,270 What's the expected utility of this bet? 160 00:07:27,270 --> 00:07:29,370 Well, the expected utility of this bet 161 00:07:29,370 --> 00:07:34,960 is the probability you win, 0.5, times utility if you win, 162 00:07:34,960 --> 00:07:38,040 where utility if you win is the square root of your consumption 163 00:07:38,040 --> 00:07:39,370 if you win. 164 00:07:39,370 --> 00:07:43,190 What is your consumption if you win? 165 00:07:43,190 --> 00:07:46,025 If you win the bet, what is your consumption? 166 00:07:46,025 --> 00:07:48,950 Somebody raise your hand and tell me. 167 00:07:48,950 --> 00:07:51,540 Starting with 100 and I made this bet with. 168 00:07:51,540 --> 00:07:52,150 Yeah. 169 00:07:52,150 --> 00:07:52,733 AUDIENCE: 225. 170 00:07:52,733 --> 00:07:54,060 JONATHAN GRUBER: 225. 171 00:07:54,060 --> 00:07:56,880 You started with 100 and you won 125. 172 00:07:56,880 --> 00:08:00,520 If you lose the bet, what do you have? 173 00:08:04,900 --> 00:08:07,400 What do you have if you lose the bet? 174 00:08:07,400 --> 00:08:08,540 0. 175 00:08:08,540 --> 00:08:09,710 OK? 176 00:08:09,710 --> 00:08:12,650 So your expected utility is 0.5 times 177 00:08:12,650 --> 00:08:14,600 this utility of what you get if you 178 00:08:14,600 --> 00:08:19,700 win plus 0.5 times utility what if you lose. 179 00:08:19,700 --> 00:08:26,920 Now if you do that math, you will find that that is 7.5. 180 00:08:26,920 --> 00:08:28,570 Your expected utility of this bet 181 00:08:28,570 --> 00:08:34,429 is 7.5, which is less than your initial utility. 182 00:08:34,429 --> 00:08:39,014 So you should not take the bet, which is through the mechanism 183 00:08:39,014 --> 00:08:43,010 of psychology why many of you didn't. 184 00:08:43,010 --> 00:08:45,650 You should not take the bet. 185 00:08:45,650 --> 00:08:51,020 And the reason is because you are what we call risk-- 186 00:08:51,020 --> 00:08:53,570 and humans are what we call risk averse. 187 00:08:57,570 --> 00:09:02,660 That risk is inherently negative value to us. 188 00:09:02,660 --> 00:09:05,610 A certain dollar is worth much more to us 189 00:09:05,610 --> 00:09:07,440 than an uncertain dollar. 190 00:09:07,440 --> 00:09:10,440 Just like $1 today is worth more than $1 tomorrow, 191 00:09:10,440 --> 00:09:14,190 a certain dollar is worth much more than an uncertain dollar. 192 00:09:14,190 --> 00:09:17,850 To see why, the best way-- this intuition here is graphical. 193 00:09:17,850 --> 00:09:20,910 So let's go to figure 20-1 and just sort of slowly 194 00:09:20,910 --> 00:09:21,690 walk through this. 195 00:09:21,690 --> 00:09:23,700 It's a little confusing graph. 196 00:09:23,700 --> 00:09:26,960 On the x-axis is your wealth, your total consumption or money 197 00:09:26,960 --> 00:09:27,460 you have. 198 00:09:27,460 --> 00:09:28,850 You consume everything you have. 199 00:09:28,850 --> 00:09:31,650 So it's wealth, or alternatively consumption. 200 00:09:31,650 --> 00:09:35,640 On the y-axis of figure 20-1 is your utility. 201 00:09:35,640 --> 00:09:39,080 It's the graph of how much you consume against utility. 202 00:09:39,080 --> 00:09:43,160 And as you can see, this is a concave graph. 203 00:09:43,160 --> 00:09:47,660 It's exhibiting diminishing marginal utility. 204 00:09:47,660 --> 00:09:52,400 Each dollar of wealth adds utility but less and less 205 00:09:52,400 --> 00:09:53,510 over time. 206 00:09:53,510 --> 00:09:55,730 Just like a slice of pizza makes you happier 207 00:09:55,730 --> 00:09:59,040 but less and less over time. 208 00:09:59,040 --> 00:10:00,000 You get that. 209 00:10:00,000 --> 00:10:04,958 So the shape of this curve is true for any utility function 210 00:10:04,958 --> 00:10:06,750 that features diminishing marginal utility. 211 00:10:06,750 --> 00:10:08,292 That pretty much any utility function 212 00:10:08,292 --> 00:10:09,580 we haven't used this semester. 213 00:10:09,580 --> 00:10:11,700 It's not as if we're trying to trick you. 214 00:10:11,700 --> 00:10:13,800 Has diminishing marginal utility. 215 00:10:13,800 --> 00:10:17,550 So as a result, it has this shape. 216 00:10:17,550 --> 00:10:21,560 Now, with the utility function of this shape, 217 00:10:21,560 --> 00:10:25,820 let's evaluate the gamble I just gave you. 218 00:10:25,820 --> 00:10:29,610 You start with wealth of 100. 219 00:10:29,610 --> 00:10:32,920 So you see on the x-axis the 100 point, that 220 00:10:32,920 --> 00:10:36,880 corresponds to utility of 10. 221 00:10:36,880 --> 00:10:40,600 So you can trace up that 100 to utility curve, 222 00:10:40,600 --> 00:10:42,790 and then you go over to the y-axis. 223 00:10:42,790 --> 00:10:45,590 So that corresponds to a utility of 10. 224 00:10:45,590 --> 00:10:49,180 Now, think about what the gamble does. 225 00:10:49,180 --> 00:10:51,070 What the gamble does is say look. 226 00:10:51,070 --> 00:10:54,160 There's two possible outcomes with 50% chance each. 227 00:10:54,160 --> 00:10:57,100 One is wealth of 225. 228 00:10:57,100 --> 00:10:59,560 That is the point all the way to the right. 229 00:10:59,560 --> 00:11:02,560 That leaves utility of 15. 230 00:11:02,560 --> 00:11:04,660 The other's wealth of 0. 231 00:11:04,660 --> 00:11:06,970 That's the point all the way to the left. 232 00:11:06,970 --> 00:11:10,080 That was utility of 0. 233 00:11:10,080 --> 00:11:11,580 What is the average of those two? 234 00:11:11,580 --> 00:11:13,680 Well, it's just a linear combination. 235 00:11:13,680 --> 00:11:15,720 So 50% chance of each. 236 00:11:15,720 --> 00:11:21,770 So the average of those two is a wealth of 112.5 237 00:11:21,770 --> 00:11:24,960 but an expected utility of 7.5. 238 00:11:24,960 --> 00:11:29,210 So you draw a cord between those two points, between the 0 point 239 00:11:29,210 --> 00:11:32,810 and point B. You find the midpoint of that cord. 240 00:11:32,810 --> 00:11:34,550 That's wealth of 112.5. 241 00:11:34,550 --> 00:11:37,970 But then you trace that over to utility function. 242 00:11:37,970 --> 00:11:43,620 And you see the expected utility is only 7.5. 243 00:11:43,620 --> 00:11:47,610 And that's because we're not using a linear combination. 244 00:11:47,610 --> 00:11:49,710 We're using a nonlinear combination-- 245 00:11:49,710 --> 00:11:51,930 a nonlinear concave combination-- 246 00:11:51,930 --> 00:11:54,960 which means that moving up in terms of wealth 247 00:11:54,960 --> 00:11:57,720 makes you less happy than moving down in terms of wealth 248 00:11:57,720 --> 00:11:58,740 makes you sad. 249 00:11:58,740 --> 00:12:01,220 And you're really sad at 0. 250 00:12:01,220 --> 00:12:03,590 So going for 100 down to 0 makes you 251 00:12:03,590 --> 00:12:08,683 way sadder than going from 100 up to 225 makes you happier. 252 00:12:08,683 --> 00:12:10,100 And that's all because diminishing 253 00:12:10,100 --> 00:12:12,500 marginal utility of income. 254 00:12:12,500 --> 00:12:16,720 So it's natural that this gamble would make you worse off, even 255 00:12:16,720 --> 00:12:19,950 though it's more than fair, because, yeah, you're 256 00:12:19,950 --> 00:12:21,300 somewhat happier if you win. 257 00:12:21,300 --> 00:12:24,540 If you win, utility goes up from 10 to 15. 258 00:12:24,540 --> 00:12:26,000 That's great. 259 00:12:26,000 --> 00:12:28,340 But if you lose, utility goes down from 10 to 0. 260 00:12:28,340 --> 00:12:30,090 That's really bad. 261 00:12:30,090 --> 00:12:33,760 So you don't want to take this risk, which 262 00:12:33,760 --> 00:12:37,240 is why, although you may not realize it, many of you 263 00:12:37,240 --> 00:12:39,880 wouldn't want to take that gamble. 264 00:12:39,880 --> 00:12:41,590 So using this graphic, let's ask-- 265 00:12:41,590 --> 00:12:43,940 are there questions about that? 266 00:12:43,940 --> 00:12:44,629 Yeah. 267 00:12:44,629 --> 00:12:46,046 AUDIENCE: So would we take the bet 268 00:12:46,046 --> 00:12:48,541 if our gain utility outweighs our loss utility, 269 00:12:48,541 --> 00:12:51,970 or we would not take the bet if our utility [INAUDIBLE].. 270 00:12:51,970 --> 00:12:54,820 JONATHAN GRUBER: Well, you've answered-- 271 00:12:54,820 --> 00:12:56,998 it's the same-- those two questions are the same. 272 00:12:56,998 --> 00:12:58,540 It just depends on the probabilities. 273 00:12:58,540 --> 00:13:00,347 If the probabilities are 0.5 each, 274 00:13:00,347 --> 00:13:01,930 then those two answers-- two questions 275 00:13:01,930 --> 00:13:04,060 are exactly the same because 0.5 each 276 00:13:04,060 --> 00:13:07,840 would be gain outweighing losses the same as on net positive. 277 00:13:07,840 --> 00:13:09,340 But if the probabilities aren't 0.5, 278 00:13:09,340 --> 00:13:11,055 you want to use this equation. 279 00:13:11,055 --> 00:13:13,180 So you basically want to say is the weighted-- it's 280 00:13:13,180 --> 00:13:15,055 about the weighted average change in utility, 281 00:13:15,055 --> 00:13:19,170 essentially, where the weights are these probabilities. 282 00:13:19,170 --> 00:13:19,760 Yeah. 283 00:13:19,760 --> 00:13:21,510 AUDIENCE: Is there any utility calculation 284 00:13:21,510 --> 00:13:22,480 in actually gambling. 285 00:13:22,480 --> 00:13:24,430 Like can someone dislike gambling-- 286 00:13:24,430 --> 00:13:24,700 JONATHAN GRUBER: Hold on. 287 00:13:24,700 --> 00:13:25,810 I'm going to come to that. 288 00:13:25,810 --> 00:13:27,227 We're going come back to gambling. 289 00:13:27,227 --> 00:13:29,990 We talk all about the lottery at the end. 290 00:13:29,990 --> 00:13:30,490 OK. 291 00:13:30,490 --> 00:13:34,170 But do people understand the basics of this graph? 292 00:13:34,170 --> 00:13:38,110 So using this graph, tell me the following. 293 00:13:38,110 --> 00:13:43,125 How much-- answer the following question. 294 00:13:48,530 --> 00:13:50,915 How much-- let's say-- 295 00:13:50,915 --> 00:13:51,790 it's a hard question. 296 00:13:51,790 --> 00:13:53,010 See if you can get this. 297 00:13:53,010 --> 00:13:54,920 Let's say that I said, you know what, class, 298 00:13:54,920 --> 00:13:56,753 I'm going to force you to take this gamble. 299 00:13:56,753 --> 00:13:58,170 I'm going to come in here, and I'm 300 00:13:58,170 --> 00:13:59,930 going to tell you I'm locking the door. 301 00:13:59,930 --> 00:14:04,160 You're not leaving without taking this gamble unless you 302 00:14:04,160 --> 00:14:07,350 pay me not to force you. 303 00:14:07,350 --> 00:14:10,900 So I'm going to offer you a more than fair bet. 304 00:14:10,900 --> 00:14:14,050 Would you be willing to pay me to get out of that bet? 305 00:14:14,050 --> 00:14:16,330 And how much would you be willing to pay me? 306 00:14:16,330 --> 00:14:16,830 Yeah. 307 00:14:16,830 --> 00:14:21,410 AUDIENCE: I'd be willing to pay you up to 2 and 1/2 dollars. 308 00:14:21,410 --> 00:14:23,144 JONATHAN GRUBER: Up to 2 and 1/2 dollars. 309 00:14:23,144 --> 00:14:26,442 AUDIENCE: [INAUDIBLE] 310 00:14:26,442 --> 00:14:27,900 JONATHAN GRUBER: 2 and 1/2 dollars. 311 00:14:27,900 --> 00:14:28,692 I don't understand. 312 00:14:28,692 --> 00:14:31,260 AUDIENCE: Sorry, [INAUDIBLE]. 313 00:14:31,260 --> 00:14:32,760 JONATHAN GRUBER: Well, OK, that's-- 314 00:14:32,760 --> 00:14:33,927 AUDIENCE: $100 start, right? 315 00:14:33,927 --> 00:14:35,354 JONATHAN GRUBER: Yeah. $100 start. 316 00:14:35,354 --> 00:14:36,067 AUDIENCE: $25. 317 00:14:36,067 --> 00:14:36,900 JONATHAN GRUBER: OK. 318 00:14:36,900 --> 00:14:38,923 You're thinking about that sort of right, 319 00:14:38,923 --> 00:14:41,340 but you're still thinking in a linear world, not nonlinear 320 00:14:41,340 --> 00:14:41,850 world. 321 00:14:41,850 --> 00:14:42,680 Look at the graph. 322 00:14:42,680 --> 00:14:43,180 OK. 323 00:14:43,180 --> 00:14:43,980 Yeah. 324 00:14:43,980 --> 00:14:46,075 AUDIENCE: Would it be $43.75? 325 00:14:46,075 --> 00:14:48,060 JONATHAN GRUBER: It would be exactly $43.75. 326 00:14:48,060 --> 00:14:48,960 Why? 327 00:14:48,960 --> 00:14:51,930 AUDIENCE: Because right now the bet essentially 328 00:14:51,930 --> 00:14:54,807 gives me the utility of $56.25. 329 00:14:54,807 --> 00:14:56,640 JONATHAN GRUBER: So your answer in the front 330 00:14:56,640 --> 00:14:58,800 was exactly right in a linear world. 331 00:14:58,800 --> 00:15:00,550 But in a nonlinear world, you've got 332 00:15:00,550 --> 00:15:02,320 to account for the curvature. 333 00:15:02,320 --> 00:15:05,010 So the way to think about it is right now your utility 334 00:15:05,010 --> 00:15:07,440 from that bet, if I force you to take it, 335 00:15:07,440 --> 00:15:11,550 it leaves you a utility of $56.25. 336 00:15:11,550 --> 00:15:12,420 You can see that. 337 00:15:12,420 --> 00:15:15,240 Just go backwards from the 7.5 utility down 338 00:15:15,240 --> 00:15:17,610 to what level of wealth that's equivalent. 339 00:15:17,610 --> 00:15:25,590 What that means is you would rather pay me $43.74 than take 340 00:15:25,590 --> 00:15:26,540 that bet. 341 00:15:26,540 --> 00:15:28,650 Think about how crazy that is for one second. 342 00:15:28,650 --> 00:15:33,590 I'm offering you a bet that is more than fair, 343 00:15:33,590 --> 00:15:37,530 and you will pay me almost half of your entire wealth 344 00:15:37,530 --> 00:15:39,787 to avoid taking that bet. 345 00:15:39,787 --> 00:15:41,870 And that's only with our standard utility function 346 00:15:41,870 --> 00:15:43,960 we always use. 347 00:15:43,960 --> 00:15:45,250 That's risk aversion. 348 00:15:45,250 --> 00:15:49,720 And the reason is because 0 sucks so badly. 349 00:15:49,720 --> 00:15:52,780 The reason is because you're so sad going to 0 350 00:15:52,780 --> 00:15:55,990 that you really don't want to be in that situation. 351 00:15:55,990 --> 00:15:59,890 And so you will actually pay me $43.75 352 00:15:59,890 --> 00:16:02,410 to avoid a more than fair bet. 353 00:16:02,410 --> 00:16:05,380 That's what's crazy. 354 00:16:05,380 --> 00:16:06,970 So another way to see this-- 355 00:16:06,970 --> 00:16:09,090 let me ask you another question. 356 00:16:09,090 --> 00:16:12,120 How large-- let's offer you the same bet. 357 00:16:12,120 --> 00:16:13,910 Flip a coin. 358 00:16:13,910 --> 00:16:15,500 Tails, you lose 100. 359 00:16:15,500 --> 00:16:17,690 Heads, you win x. 360 00:16:17,690 --> 00:16:22,420 How large would x have to be for you to take the bet? 361 00:16:22,420 --> 00:16:24,010 Tails, you lose 100. 362 00:16:24,010 --> 00:16:25,230 Heads, you win x. 363 00:16:25,230 --> 00:16:25,730 Yeah. 364 00:16:25,730 --> 00:16:26,355 AUDIENCE: $300. 365 00:16:26,355 --> 00:16:27,272 JONATHAN GRUBER: $300. 366 00:16:27,272 --> 00:16:27,850 Why? 367 00:16:27,850 --> 00:16:30,160 AUDIENCE: Because then your expected utility is 10. 368 00:16:30,160 --> 00:16:30,430 JONATHAN GRUBER: Right. 369 00:16:30,430 --> 00:16:31,210 Exactly. 370 00:16:31,210 --> 00:16:33,920 If it's $300, then I'm doing the square root 371 00:16:33,920 --> 00:16:37,192 of 400, which is 20, and the square root of 0. 372 00:16:37,192 --> 00:16:38,650 You average those, and you're going 373 00:16:38,650 --> 00:16:41,350 to get expected utility of 10. 374 00:16:41,350 --> 00:16:44,290 So for you to take that bet, I would have to say, 375 00:16:44,290 --> 00:16:47,620 tails, you lose 100, heads, you win 300. 376 00:16:47,620 --> 00:16:51,180 I need to give you a monstrously more than fair bet. 377 00:16:51,180 --> 00:16:56,070 And that is due to the principle of risk aversion. 378 00:16:56,070 --> 00:16:58,445 That basically, because of diminishing marginal utility-- 379 00:16:58,445 --> 00:17:00,028 risk aversion isn't something made up. 380 00:17:00,028 --> 00:17:01,380 It's not some crazy concept. 381 00:17:01,380 --> 00:17:05,010 It just falls naturally out of diminishing margin utility 382 00:17:05,010 --> 00:17:09,869 because making you sad, because losing, because moving down 383 00:17:09,869 --> 00:17:13,589 makes you sadder than moving up makes you happier. 384 00:17:13,589 --> 00:17:14,640 Any questions about that? 385 00:17:14,640 --> 00:17:16,109 Yeah. 386 00:17:16,109 --> 00:17:17,849 AUDIENCE: I guess the question is, 387 00:17:17,849 --> 00:17:19,724 doesn't this kind of more depende on utility? 388 00:17:19,724 --> 00:17:20,730 Because I know that-- 389 00:17:20,730 --> 00:17:21,000 JONATHAN GRUBER: OK. 390 00:17:21,000 --> 00:17:21,579 Stop there. 391 00:17:21,579 --> 00:17:22,787 Let's go to the next section. 392 00:17:22,787 --> 00:17:24,420 You guys are way ahead of me as always. 393 00:17:24,420 --> 00:17:26,265 Let's talk about a couple extensions. 394 00:17:31,490 --> 00:17:33,310 Let's talk about a couple extensions. 395 00:17:33,310 --> 00:17:37,600 First extension, change utility function. 396 00:17:37,600 --> 00:17:40,930 Suppose your utility function was of the form u 397 00:17:40,930 --> 00:17:44,652 equals 0.1 times c. 398 00:17:44,652 --> 00:17:46,110 Now I've chose this particular form 399 00:17:46,110 --> 00:17:48,120 because the initial conditions are the same. 400 00:17:48,120 --> 00:17:52,170 With c0 of 100, u0 is still 10. 401 00:17:52,170 --> 00:17:56,160 So I'm starting from the same point as I was before. 402 00:17:56,160 --> 00:17:59,220 But now, would you take the bet, and why? 403 00:18:02,290 --> 00:18:07,520 If that's utility function, would you take the bet and why? 404 00:18:07,520 --> 00:18:09,930 Just do the math. 405 00:18:09,930 --> 00:18:10,980 Do the math. 406 00:18:10,980 --> 00:18:13,080 What's your expected utility of that bet? 407 00:18:13,080 --> 00:18:18,780 Your expected utility is 0.5 times your utility of 225. 408 00:18:18,780 --> 00:18:28,110 So it's times 0.1 times 225 plus 0.5 times your utility of 0. 409 00:18:28,110 --> 00:18:30,090 So it's 0.1 times 0. 410 00:18:33,140 --> 00:18:35,540 And if you write that out and solve it, 411 00:18:35,540 --> 00:18:40,860 you get 11.25, which is greater than 10. 412 00:18:40,860 --> 00:18:43,880 So you would take the bet. 413 00:18:43,880 --> 00:18:46,180 Any questions about the math? 414 00:18:46,180 --> 00:18:49,000 I just did the expected utility evaluation. 415 00:18:49,000 --> 00:18:50,860 So you would take the bet. 416 00:18:50,860 --> 00:18:52,130 What's the difference? 417 00:18:52,130 --> 00:18:55,020 Why do you take the bet here? 418 00:18:55,020 --> 00:18:55,670 Yeah. 419 00:18:55,670 --> 00:18:56,170 Yeah. 420 00:18:56,170 --> 00:18:57,280 Let me get-- go ahead. 421 00:18:57,280 --> 00:18:59,460 AUDIENCE: This is a linear utility function. 422 00:18:59,460 --> 00:18:59,992 So-- 423 00:18:59,992 --> 00:19:02,200 JONATHAN GRUBER: If you're a linear utility function, 424 00:19:02,200 --> 00:19:05,300 what you care about is expected value. 425 00:19:05,300 --> 00:19:06,970 So you can see that-- 426 00:19:06,970 --> 00:19:08,440 do I have that, yeah-- 427 00:19:08,440 --> 00:19:10,540 in figure 22. 428 00:19:10,540 --> 00:19:14,530 This is the case we call risk neutrality. 429 00:19:14,530 --> 00:19:16,510 With the linear utility function, 430 00:19:16,510 --> 00:19:19,930 you're risk neutral because your linear utility 431 00:19:19,930 --> 00:19:23,630 function does not have what? 432 00:19:23,630 --> 00:19:26,120 Does not have diminishing margin utility. 433 00:19:26,120 --> 00:19:30,493 As a result, you just care about expected value. 434 00:19:30,493 --> 00:19:32,660 There's no difference in expected value and expected 435 00:19:32,660 --> 00:19:33,805 utility. 436 00:19:33,805 --> 00:19:35,180 Now, the numbers are a little bit 437 00:19:35,180 --> 00:19:36,680 different because the functional form, 438 00:19:36,680 --> 00:19:37,930 but it gives the same outcome. 439 00:19:37,930 --> 00:19:39,890 You always take a more than fair bet 440 00:19:39,890 --> 00:19:41,930 and you reject a less than fair bet. 441 00:19:41,930 --> 00:19:47,240 So as people move from risk averse to risk neutral, 442 00:19:47,240 --> 00:19:49,130 or as utility features less and less 443 00:19:49,130 --> 00:19:50,870 diminishing margin utility, they'll 444 00:19:50,870 --> 00:19:53,713 be more and more willing to take gambles. 445 00:19:53,713 --> 00:19:55,130 But it doesn't have to stop there. 446 00:19:55,130 --> 00:19:56,450 We can go further. 447 00:19:56,450 --> 00:20:02,130 Imagine that I wrote utility of the form-- 448 00:20:02,130 --> 00:20:07,000 utility was of the form c squared over 1,000. 449 00:20:07,000 --> 00:20:09,810 A weird utility function but once again created 450 00:20:09,810 --> 00:20:16,430 so that if c0 equals 100, u0 equals 10. 451 00:20:16,430 --> 00:20:19,120 Now let's do the expected value calculation. 452 00:20:19,120 --> 00:20:21,340 Well, if you take the gamble, there's 453 00:20:21,340 --> 00:20:24,770 a 0.5 probability that you win. 454 00:20:24,770 --> 00:20:25,900 So then you would have-- 455 00:20:25,900 --> 00:20:33,820 utility B would be 225 squared over 1,000 and a 0.5 456 00:20:33,820 --> 00:20:35,530 probability that you lose. 457 00:20:35,530 --> 00:20:38,600 So you just get 0. 458 00:20:38,600 --> 00:20:43,020 And the expected utility in that case is 25.3. 459 00:20:43,020 --> 00:20:45,210 The expected utility equals 25.3, 460 00:20:45,210 --> 00:20:48,410 which is way bigger than 10. 461 00:20:48,410 --> 00:20:50,020 So you take this gamble. 462 00:20:50,020 --> 00:20:50,830 Why? 463 00:20:50,830 --> 00:20:52,705 Because now you're risk loving. 464 00:20:52,705 --> 00:20:55,080 Because what does this say about the diminishing marginal 465 00:20:55,080 --> 00:20:58,025 utility of income? 466 00:20:58,025 --> 00:20:59,900 This actually says you have increasing margin 467 00:20:59,900 --> 00:21:01,700 utility of consumption. 468 00:21:01,700 --> 00:21:04,310 A utility function like this says the next slice of pizza 469 00:21:04,310 --> 00:21:06,740 makes you even happier than the previous slice of pizza. 470 00:21:06,740 --> 00:21:08,990 So go figure 22-3. 471 00:21:08,990 --> 00:21:12,810 This is the risk loving case, where you actually 472 00:21:12,810 --> 00:21:15,380 have increasing marginal utility of consumption. 473 00:21:15,380 --> 00:21:16,880 We don't really talk about this case 474 00:21:16,880 --> 00:21:18,500 because it doesn't make sense. 475 00:21:18,500 --> 00:21:22,040 But just to understand how this works, 476 00:21:22,040 --> 00:21:27,010 same calculations before you start at a point like A. 477 00:21:27,010 --> 00:21:31,030 If you win, you go to B. If you lose, you go to 0. 478 00:21:31,030 --> 00:21:33,940 Well, this shape utility function, going to B 479 00:21:33,940 --> 00:21:37,600 makes you way happier than going to 0 makes you sad. 480 00:21:37,600 --> 00:21:40,740 So you love the gamble. 481 00:21:40,740 --> 00:21:43,110 In fact, with this utility function, 482 00:21:43,110 --> 00:21:44,690 you would take an unfair bet. 483 00:21:47,550 --> 00:21:50,445 So for example, imagine I change the gamble to one 484 00:21:50,445 --> 00:21:52,620 where it's win 100, lose-- 485 00:21:52,620 --> 00:21:56,253 I'm sorry, win 75, lose 100. 486 00:21:56,253 --> 00:21:57,420 So I changed the gamble now. 487 00:21:57,420 --> 00:21:58,590 Win 75, lose 100. 488 00:21:58,590 --> 00:22:00,240 I made an unfair bet. 489 00:22:00,240 --> 00:22:03,340 The expected value was negative. 490 00:22:03,340 --> 00:22:06,270 Well, this person will still take that bet. 491 00:22:06,270 --> 00:22:11,790 If you do the math, if they win, 75, they get 175. 492 00:22:11,790 --> 00:22:15,120 Just replace this with 175. 493 00:22:15,120 --> 00:22:17,450 And you do the math. 494 00:22:17,450 --> 00:22:21,480 You're going to find that the expected utility in that case 495 00:22:21,480 --> 00:22:28,470 is 15.3, which is greater than 10. 496 00:22:28,470 --> 00:22:30,830 So even an unfair bet-- 497 00:22:30,830 --> 00:22:33,070 lose 100, win 75-- 498 00:22:33,070 --> 00:22:36,260 will still leave these risk loving people better off than 499 00:22:36,260 --> 00:22:38,489 if they hadn't taken a bet. 500 00:22:38,489 --> 00:22:39,375 Yeah. 501 00:22:39,375 --> 00:22:42,083 AUDIENCE: So when we're doing the losses, when 502 00:22:42,083 --> 00:22:44,500 we set that to 0, we're assuming that they're starting off 503 00:22:44,500 --> 00:22:46,982 with the amount that they could possibly lose, correct? 504 00:22:46,982 --> 00:22:48,190 JONATHAN GRUBER: Oh, that's-- 505 00:22:48,190 --> 00:22:48,560 OK. 506 00:22:48,560 --> 00:22:48,830 Great. 507 00:22:48,830 --> 00:22:49,970 I'm going to come to that next. 508 00:22:49,970 --> 00:22:51,060 That's in these examples. 509 00:22:51,060 --> 00:22:53,018 But you've called me on an important assumption 510 00:22:53,018 --> 00:22:54,170 I'm making. 511 00:22:54,170 --> 00:22:55,250 These examples I have. 512 00:22:55,250 --> 00:22:57,708 Let's make sure we understand risk neutral and risk loving. 513 00:22:57,708 --> 00:22:59,950 People understand that? 514 00:22:59,950 --> 00:23:05,437 So now let's-- now you actually raised another issue. 515 00:23:05,437 --> 00:23:06,520 Let me ask a new question. 516 00:23:06,520 --> 00:23:09,000 Once again, forget everything you've learned. 517 00:23:09,000 --> 00:23:09,927 Gut instincts. 518 00:23:09,927 --> 00:23:11,260 Here's the bet I'm offering you. 519 00:23:11,260 --> 00:23:12,610 Flip a coin. 520 00:23:12,610 --> 00:23:14,980 Heads, you win 1,250. 521 00:23:14,980 --> 00:23:16,160 Tails, you lose $10. 522 00:23:16,160 --> 00:23:18,330 Who takes that bet? 523 00:23:18,330 --> 00:23:21,020 Raise your hands if you take that bet. 524 00:23:21,020 --> 00:23:21,520 OK. 525 00:23:21,520 --> 00:23:22,570 That's backwards. 526 00:23:22,570 --> 00:23:25,870 More of you should take that bet, not less of you. 527 00:23:25,870 --> 00:23:26,905 And why is that? 528 00:23:26,905 --> 00:23:30,060 It's because of exactly what you just pointed out. 529 00:23:30,060 --> 00:23:34,340 It's because basically if you think about that-- 530 00:23:34,340 --> 00:23:35,470 think about that bet. 531 00:23:35,470 --> 00:23:38,340 Think about-- let's go back to our old utility function, 532 00:23:38,340 --> 00:23:41,500 u equals square root of c. 533 00:23:41,500 --> 00:23:43,270 Let's think about that bet. 534 00:23:43,270 --> 00:23:45,790 So what's the expected utility? 535 00:23:45,790 --> 00:23:49,960 It's 0.5 times you win 1,250. 536 00:23:49,960 --> 00:23:56,540 So it's square root of 112.5 plus 0.5 times 537 00:23:56,540 --> 00:24:00,010 you lose 10 square root of 90. 538 00:24:00,010 --> 00:24:07,860 And that expected utility is 10.5, which is greater than 10. 539 00:24:07,860 --> 00:24:10,620 So you should take that bet. 540 00:24:10,620 --> 00:24:11,970 What changed? 541 00:24:11,970 --> 00:24:13,530 You're still risk averse. 542 00:24:13,530 --> 00:24:17,310 The guy who would've paid me $44 to avoid the other bet 543 00:24:17,310 --> 00:24:19,530 is now happy to take this bet. 544 00:24:19,530 --> 00:24:20,880 Same person. 545 00:24:20,880 --> 00:24:23,398 What changed? 546 00:24:23,398 --> 00:24:23,940 What changed? 547 00:24:23,940 --> 00:24:24,200 Yeah. 548 00:24:24,200 --> 00:24:26,180 AUDIENCE: Smaller portion of [INAUDIBLE].. 549 00:24:26,180 --> 00:24:26,570 JONATHAN GRUBER: Right. 550 00:24:26,570 --> 00:24:28,670 And why does a smaller portion of the income 551 00:24:28,670 --> 00:24:30,042 change things here? 552 00:24:30,042 --> 00:24:32,338 AUDIENCE: [INAUDIBLE] 553 00:24:32,338 --> 00:24:33,380 JONATHAN GRUBER: Exactly. 554 00:24:33,380 --> 00:24:35,990 Because ultimately, infinitesimally, it's 555 00:24:35,990 --> 00:24:37,130 a linear curve. 556 00:24:37,130 --> 00:24:42,920 So if you go back to Figure 21, for any given epsilon change 557 00:24:42,920 --> 00:24:46,200 from point A it's linear. 558 00:24:46,200 --> 00:24:50,030 So essentially as gambles get smaller and smaller relative 559 00:24:50,030 --> 00:24:52,750 to your starting point, you become more and more risk 560 00:24:52,750 --> 00:24:53,250 neutral. 561 00:24:56,350 --> 00:24:58,940 Because, yeah, you're a bit sadder than happier 562 00:24:58,940 --> 00:25:00,377 but just a bit. 563 00:25:00,377 --> 00:25:01,460 And remember, it's linear. 564 00:25:01,460 --> 00:25:07,040 You just take-- so if I did 12 and 1/2 cents versus $0.10, 565 00:25:07,040 --> 00:25:08,840 then unless you were crazy risk averse, 566 00:25:08,840 --> 00:25:11,990 you should take that bet because essentially you only care-- 567 00:25:11,990 --> 00:25:14,240 at that point it's so tiny relative to your wealth you 568 00:25:14,240 --> 00:25:17,750 might as well use expected value. 569 00:25:17,750 --> 00:25:21,660 So as gambles become smaller relative to your income, 570 00:25:21,660 --> 00:25:26,200 the utility function becomes locally flatter. 571 00:25:26,200 --> 00:25:28,780 Utility function goes locally flatter. 572 00:25:28,780 --> 00:25:31,780 And as a result, you become more and more risk neutral. 573 00:25:35,550 --> 00:25:37,720 Question about that? 574 00:25:37,720 --> 00:25:38,890 Last point. 575 00:25:38,890 --> 00:25:42,740 Why did so many of you still not take that bet? 576 00:25:42,740 --> 00:25:46,250 Well, the answer is that even the model we've talked so far 577 00:25:46,250 --> 00:25:48,727 misses an important psychological phenomena. 578 00:25:48,727 --> 00:25:50,810 So now I'm stepping out of standard microeconomics 579 00:25:50,810 --> 00:25:52,435 into the realm of behavioral economics. 580 00:25:52,435 --> 00:25:54,200 Unfortunately, due to time this semester, 581 00:25:54,200 --> 00:25:55,100 I'm not going to get to my lecture 582 00:25:55,100 --> 00:25:56,430 on behavioral economics. 583 00:25:56,430 --> 00:25:57,110 But you guys want to learn-- 584 00:25:57,110 --> 00:25:58,580 I'll talk a little bit about it in the next few lectures. 585 00:25:58,580 --> 00:25:59,840 I'll sprinkle it in. 586 00:25:59,840 --> 00:26:01,940 But course 1113 is a fascinating course 587 00:26:01,940 --> 00:26:03,918 we offer here about how you build psychology 588 00:26:03,918 --> 00:26:05,210 when you think about economics. 589 00:26:05,210 --> 00:26:06,830 And here's one example. 590 00:26:06,830 --> 00:26:09,350 Why is it that even with this gamble, 591 00:26:09,350 --> 00:26:11,840 even if I'd done the 12 and 1/2, $0.10 gamble, 592 00:26:11,840 --> 00:26:13,940 a bunch of you still wouldn't have taken it. 593 00:26:13,940 --> 00:26:14,970 Why is that? 594 00:26:14,970 --> 00:26:18,380 That's because humans not only feature risk aversion, humans 595 00:26:18,380 --> 00:26:23,450 also feature loss aversion, which 596 00:26:23,450 --> 00:26:26,750 is we have an irrational behavioral bias 597 00:26:26,750 --> 00:26:32,580 that losing by itself makes us sad relative to winning. 598 00:26:32,580 --> 00:26:35,550 Taking away something we have makes us sadder 599 00:26:35,550 --> 00:26:37,710 than getting something new. 600 00:26:37,710 --> 00:26:39,510 So here's a standard experiment that's run. 601 00:26:42,660 --> 00:26:45,150 They get a bunch of $5 mugs. 602 00:26:45,150 --> 00:26:47,040 Mugs worth about $5. 603 00:26:47,040 --> 00:26:48,030 They take people. 604 00:26:48,030 --> 00:26:52,320 And randomly half of the people they ask, how much would you 605 00:26:52,320 --> 00:26:54,300 pay for this mug? 606 00:26:54,300 --> 00:26:56,460 And half the people they give them the mug 607 00:26:56,460 --> 00:26:59,490 and say, how much would you sell your mug for? 608 00:26:59,490 --> 00:27:01,590 Half people they say, here's a mug, 609 00:27:01,590 --> 00:27:02,873 how much would you pay for it? 610 00:27:02,873 --> 00:27:04,290 Half the people say, here's a mug. 611 00:27:04,290 --> 00:27:04,827 It's yours. 612 00:27:04,827 --> 00:27:05,910 But I want to buy it back. 613 00:27:05,910 --> 00:27:08,060 How much would you sell it to me for? 614 00:27:08,060 --> 00:27:12,350 The average person will pay $3, but the average person 615 00:27:12,350 --> 00:27:14,900 wants $7 to sell it back. 616 00:27:14,900 --> 00:27:16,640 That makes no sense. 617 00:27:16,640 --> 00:27:18,673 Either way, it's trivial. 618 00:27:18,673 --> 00:27:19,340 It's just a mug. 619 00:27:19,340 --> 00:27:21,423 It's trivial relative to your wealth. 620 00:27:21,423 --> 00:27:22,090 It's just a mug. 621 00:27:22,090 --> 00:27:23,530 It doesn't really matter. 622 00:27:23,530 --> 00:27:26,307 But once people have it, they feel like, no, 623 00:27:26,307 --> 00:27:27,140 that's already mine. 624 00:27:27,140 --> 00:27:28,390 I don't want to sell it. 625 00:27:28,390 --> 00:27:30,670 That's loss aversion. 626 00:27:30,670 --> 00:27:35,360 People are biased by their starting points. 627 00:27:35,360 --> 00:27:38,470 Your very starting point dictates your willingness 628 00:27:38,470 --> 00:27:41,680 to take a gamble, which is not true 629 00:27:41,680 --> 00:27:43,390 in a standard economic model. 630 00:27:43,390 --> 00:27:48,540 But it's true in all laboratory experiments in psychology. 631 00:27:48,540 --> 00:27:52,790 So the reason people don't like gambles are not only 632 00:27:52,790 --> 00:27:54,360 because they're risk averse. 633 00:27:54,360 --> 00:27:56,180 But even more, they're loss averse. 634 00:27:56,180 --> 00:27:58,880 So for example, there's great economic studies 635 00:27:58,880 --> 00:28:04,810 which show that there's a massive bias against selling 636 00:28:04,810 --> 00:28:08,180 your house for anything under the price you paid for it. 637 00:28:08,180 --> 00:28:09,250 That people sort of-- 638 00:28:09,250 --> 00:28:10,520 they're very sort of linear, and they're 639 00:28:10,520 --> 00:28:12,220 willing to sell the house above the price you paid for it. 640 00:28:12,220 --> 00:28:14,140 But there's this huge notch at the price you paid for it. 641 00:28:14,140 --> 00:28:16,550 They simply don't want to sell less they paid for it. 642 00:28:16,550 --> 00:28:18,460 And that's just loss aversion idea. 643 00:28:18,460 --> 00:28:20,950 This comes up in many other contexts. 644 00:28:20,950 --> 00:28:23,577 So there's two reasons why people are risk averse, 645 00:28:23,577 --> 00:28:25,660 that people won't take gambles-- a standard reason 646 00:28:25,660 --> 00:28:29,290 and the sort of extra psychological bias. 647 00:28:29,290 --> 00:28:33,650 Now, this raises-- this leads us naturally to the next section 648 00:28:33,650 --> 00:28:35,320 I want to go to, which is to talk 649 00:28:35,320 --> 00:28:41,920 about applications of this theory and why it's important. 650 00:28:41,920 --> 00:28:47,190 And the first application I want to talk about is insurance. 651 00:28:47,190 --> 00:28:50,710 Insurance is big business in America. 652 00:28:50,710 --> 00:28:54,260 Individuals in America pay individuals-- 653 00:28:54,260 --> 00:28:56,610 forgetting the government, just people-- 654 00:28:56,610 --> 00:29:01,320 spend $1.5 trillion a year on insurance products. 655 00:29:01,320 --> 00:29:03,265 Almost 10% of GDP. 656 00:29:03,265 --> 00:29:07,140 10% of our entire economy is people buying insurance. 657 00:29:07,140 --> 00:29:10,050 Health insurance is the biggest, life insurance, 658 00:29:10,050 --> 00:29:14,010 casualty and property insurance, auto insurance, et cetera. 659 00:29:14,010 --> 00:29:18,270 Added all up, it's almost a tenth of our entire economy. 660 00:29:18,270 --> 00:29:19,780 Why? 661 00:29:19,780 --> 00:29:22,058 Because they're risk averse, and also loss averse. 662 00:29:22,058 --> 00:29:24,100 I'm going to put loss aversion aside and just use 663 00:29:24,100 --> 00:29:25,120 the standard framework. 664 00:29:25,120 --> 00:29:27,040 That just strengthens the argument. 665 00:29:27,040 --> 00:29:29,710 But it's because they're risk averse. 666 00:29:29,710 --> 00:29:32,530 So let's do the math. 667 00:29:32,530 --> 00:29:35,505 Imagine you're a single 25-year-old male. 668 00:29:35,505 --> 00:29:36,880 I'm only being gender biased here 669 00:29:36,880 --> 00:29:39,220 because there's no risk of pregnancy. 670 00:29:39,220 --> 00:29:42,130 So you're a single 25-year-old male in perfect health. 671 00:29:42,130 --> 00:29:46,045 So the only risk you face health wise is getting hit by a car. 672 00:29:46,045 --> 00:29:47,170 That's basically your risk. 673 00:29:47,170 --> 00:29:50,980 Otherwise, you're basically not going to go to the doctor. 674 00:29:50,980 --> 00:29:56,770 So essentially, let's say your income is $40,000. 675 00:29:56,770 --> 00:29:58,690 That's your income. 676 00:29:58,690 --> 00:30:01,930 And let's say that there's a 1%-- since it's Cambridge, 677 00:30:01,930 --> 00:30:04,870 there's a non-trivial chance you get hit by a car. 678 00:30:04,870 --> 00:30:09,940 Let's say there's a 1% chance, probability 0.01, 679 00:30:09,940 --> 00:30:13,460 you'll get hit by a car every year. 680 00:30:13,460 --> 00:30:19,890 And if you do, you're going to face $30,000 in medical bills. 681 00:30:19,890 --> 00:30:22,970 So you have a $40,000 income. 682 00:30:22,970 --> 00:30:25,370 There's a 1% chance you get hit by a car. 683 00:30:25,370 --> 00:30:28,515 And if you do, you'll face $30,000 in medical bills. 684 00:30:28,515 --> 00:30:30,890 And let's assume for the minute you'll still get to work. 685 00:30:30,890 --> 00:30:32,240 Your income will always be there. 686 00:30:32,240 --> 00:30:33,710 You're just going to have to face a bunch of medical bills. 687 00:30:33,710 --> 00:30:34,670 There's a separate issue about whether you 688 00:30:34,670 --> 00:30:35,870 might have to miss your job. 689 00:30:35,870 --> 00:30:37,200 That makes this even worse. 690 00:30:37,200 --> 00:30:38,207 But let's ignore that. 691 00:30:38,207 --> 00:30:39,290 You get to go to your job. 692 00:30:39,290 --> 00:30:41,748 You're just going to have to take a week to get patched up. 693 00:30:41,748 --> 00:30:45,530 And $30,000 is nothing, by the way, for a hospital bill. 694 00:30:45,530 --> 00:30:47,990 A typical, for example, heart attack hospital bill 695 00:30:47,990 --> 00:30:49,686 is well over $100,000. 696 00:30:49,686 --> 00:30:51,500 So $30,000 is pretty modest. 697 00:30:51,500 --> 00:30:52,376 Yeah. 698 00:30:52,376 --> 00:30:54,445 AUDIENCE: Wouldn't the person that hit the guy 699 00:30:54,445 --> 00:30:56,570 have to get their insurance cover the medical bill? 700 00:30:56,570 --> 00:30:58,770 JONATHAN GRUBER: Well, let's ignore that for a second. 701 00:30:58,770 --> 00:31:01,070 Right now we're talking about why you want insurance overall. 702 00:31:01,070 --> 00:31:02,120 We'll later get into who-- 703 00:31:02,120 --> 00:31:04,240 we can discuss later who should own that insurance, who 704 00:31:04,240 --> 00:31:05,115 should bear the risk. 705 00:31:05,115 --> 00:31:09,440 Right now it's just simply why you'd want insurance. 706 00:31:09,440 --> 00:31:14,930 So the expected cost of getting hit by a car-- 707 00:31:14,930 --> 00:31:18,980 the expected value or expected cost because it's negative-- 708 00:31:18,980 --> 00:31:21,230 is minus 300. 709 00:31:21,230 --> 00:31:24,290 So every year you have a $300 expected cost 710 00:31:24,290 --> 00:31:26,970 of getting hit by a car. 711 00:31:26,970 --> 00:31:30,660 And let's say your utility function is 712 00:31:30,660 --> 00:31:32,640 u equal square root of c. 713 00:31:32,640 --> 00:31:34,140 And let's assume there's no savings. 714 00:31:34,140 --> 00:31:35,307 You consume all your income. 715 00:31:38,590 --> 00:31:43,050 How much will this person be willing to pay for insurance? 716 00:31:43,050 --> 00:31:46,670 Well, we can solve that by asking 717 00:31:46,670 --> 00:31:50,300 at what insurance price would they be better off 718 00:31:50,300 --> 00:31:54,080 being insured versus uninsured. 719 00:31:54,080 --> 00:31:56,740 So let's just do the math. 720 00:31:56,740 --> 00:32:03,680 If they're uninsured what's going to happen to them? 721 00:32:03,680 --> 00:32:05,290 Well, what's their expected utility? 722 00:32:05,290 --> 00:32:12,230 Well, there's a 0.1 chance that they are going to get hit. 723 00:32:12,230 --> 00:32:17,110 And so their net income will drop from 40,000 to 10,000 724 00:32:17,110 --> 00:32:19,340 because they'll have to pay $30,000 in medical bills. 725 00:32:19,340 --> 00:32:23,900 So 0.1% chance their net income be $10,000. 726 00:32:23,900 --> 00:32:30,010 And there's a 99% chance that their net income 727 00:32:30,010 --> 00:32:35,230 will be $40,000. 728 00:32:35,230 --> 00:32:37,990 That's utility without insurance. 729 00:32:37,990 --> 00:32:40,720 Add that up and you get 199. 730 00:32:40,720 --> 00:32:44,950 So their expected utility without insurance is 199. 731 00:32:44,950 --> 00:32:50,662 That's their expected utility with no insurance. 732 00:32:50,662 --> 00:32:52,120 Now let's do their expected utility 733 00:32:52,120 --> 00:32:53,740 with insurance but with insurance 734 00:32:53,740 --> 00:32:55,480 with an uncertain price. 735 00:32:55,480 --> 00:32:56,710 Let's call the price x. 736 00:32:59,480 --> 00:33:02,180 What's the utility with insurance? 737 00:33:02,180 --> 00:33:09,190 Well, with insurance there's a 0.1% chance that they get hit. 738 00:33:09,190 --> 00:33:09,930 0.01, I'm sorry. 739 00:33:09,930 --> 00:33:10,820 It should be an .01. 740 00:33:10,820 --> 00:33:12,150 My bad. 741 00:33:12,150 --> 00:33:12,650 Wow. 742 00:33:12,650 --> 00:33:13,300 I can't believe you guys missed that. 743 00:33:13,300 --> 00:33:15,380 You guys are a little tired today. 744 00:33:15,380 --> 00:33:18,760 0.01. 745 00:33:18,760 --> 00:33:22,510 0.01% chance that I get hit. 746 00:33:22,510 --> 00:33:24,430 Now, if I get hit with insurance, 747 00:33:24,430 --> 00:33:26,900 I don't have to pay my medical bill. 748 00:33:26,900 --> 00:33:29,790 But I do have to pay my insurance premium. 749 00:33:29,790 --> 00:33:35,530 So what I have is I have $40,000 minus x, 750 00:33:35,530 --> 00:33:36,780 which is my insurance premium. 751 00:33:36,780 --> 00:33:38,488 I always have to pay my insurance premium 752 00:33:38,488 --> 00:33:40,660 every year, no matter what. 753 00:33:40,660 --> 00:33:45,697 If I don't get hit, then I get my 40,000, 754 00:33:45,697 --> 00:33:47,530 but I also have to pay my insurance premium. 755 00:33:50,820 --> 00:33:52,680 So basically these things are the same. 756 00:33:52,680 --> 00:33:58,650 So my expected utility is square root of $40,000 minus x. 757 00:33:58,650 --> 00:34:02,010 That's my expected utility. 758 00:34:02,010 --> 00:34:04,280 So how do I solve for the optimal x? 759 00:34:04,280 --> 00:34:07,610 Well, I ask at what x am I better off 760 00:34:07,610 --> 00:34:09,650 than being uninsured? 761 00:34:09,650 --> 00:34:13,630 So I set this equal to 199. 762 00:34:13,630 --> 00:34:16,940 I ask at what x would I be better off 763 00:34:16,940 --> 00:34:18,870 than being uninsured? 764 00:34:18,870 --> 00:34:25,010 And if you solve that, you get that the x star, the point 765 00:34:25,010 --> 00:34:27,230 at which you would rather be insured than uninsured, 766 00:34:27,230 --> 00:34:32,650 is a premium of $399. 767 00:34:32,650 --> 00:34:34,889 So you will pay-- 768 00:34:34,889 --> 00:34:39,360 you would rather have insurance at a cost of 399 769 00:34:39,360 --> 00:34:42,790 than you would go uninsured. 770 00:34:42,790 --> 00:34:45,100 Clear on that? 771 00:34:45,100 --> 00:34:47,440 You'd rather pay a premium of 399 772 00:34:47,440 --> 00:34:50,130 than you would go uninsured. 773 00:34:50,130 --> 00:34:51,659 Now think about what that means. 774 00:34:51,659 --> 00:34:56,560 Remember, the expected cost of this accident was only $300. 775 00:34:56,560 --> 00:35:02,575 That means that you have a $99 risk premium. 776 00:35:06,150 --> 00:35:10,430 You are willing to pay $99 to avoid bearing this risk. 777 00:35:10,430 --> 00:35:11,930 That is what you're willing to pay-- 778 00:35:11,930 --> 00:35:14,610 before you were willing to pay me $43.75 to get out 779 00:35:14,610 --> 00:35:15,600 of that gamble. 780 00:35:15,600 --> 00:35:17,390 That was your risk premium. 781 00:35:17,390 --> 00:35:21,540 It's how much you'll pay to get out of taking a gamble. 782 00:35:21,540 --> 00:35:24,690 Now before I was offering a gamble. 783 00:35:24,690 --> 00:35:25,680 But here's the thing. 784 00:35:25,680 --> 00:35:28,710 Being uninsured is a gamble. 785 00:35:28,710 --> 00:35:31,260 Being uninsured is like taking the gamble. 786 00:35:31,260 --> 00:35:33,540 So the example I had before, I locked you in the room. 787 00:35:33,540 --> 00:35:35,880 And you have to pay me if you want avoid the bet. 788 00:35:35,880 --> 00:35:37,353 That's insurance. 789 00:35:37,353 --> 00:35:38,520 You are locked in this life. 790 00:35:38,520 --> 00:35:40,590 You're locked into being in Cambridge. 791 00:35:40,590 --> 00:35:43,590 You're dealing with a 1% risk getting hit by a car always. 792 00:35:43,590 --> 00:35:47,720 So the question is, how much will you pay to avoid at least 793 00:35:47,720 --> 00:35:51,090 the financial cost-- forget the trauma, the financial costs-- 794 00:35:51,090 --> 00:35:53,220 of being hit by that car? 795 00:35:53,220 --> 00:35:57,090 And the answer is, you'll pay $99 above the expected damage 796 00:35:57,090 --> 00:35:59,490 it will do. 797 00:35:59,490 --> 00:36:03,190 And that is why insurance is big business 798 00:36:03,190 --> 00:36:10,100 because people will pay to avoid being put in risky situations. 799 00:36:10,100 --> 00:36:12,262 So insurance is a very profitable exploit. 800 00:36:12,262 --> 00:36:14,220 Now, in fact, of course, the insurance industry 801 00:36:14,220 --> 00:36:15,080 is like any other industry. 802 00:36:15,080 --> 00:36:17,330 The supply side and competition, and whether that 803 00:36:17,330 --> 00:36:19,310 will lead to profits and stuff like that. 804 00:36:19,310 --> 00:36:21,080 Depends on the whole supply side. 805 00:36:21,080 --> 00:36:22,822 This is just the demand side. 806 00:36:22,822 --> 00:36:24,280 But the point is that there's going 807 00:36:24,280 --> 00:36:26,310 to be huge demand for insurance, and people 808 00:36:26,310 --> 00:36:29,330 will be willing to pay much more than it costs the insurance 809 00:36:29,330 --> 00:36:29,960 companies. 810 00:36:29,960 --> 00:36:32,720 The consumers expect to pay the $300 a year. 811 00:36:32,720 --> 00:36:35,400 And they're getting almost $400 a year in premium. 812 00:36:35,400 --> 00:36:39,290 So the insurance company makes that money. 813 00:36:39,290 --> 00:36:42,780 And basically, that's why insurance is big business. 814 00:36:42,780 --> 00:36:45,280 Now, here's a couple of things I'd like you to show yourself 815 00:36:45,280 --> 00:36:49,160 in your copious spare time. 816 00:36:49,160 --> 00:36:52,190 First of all, this risk premium should be 817 00:36:52,190 --> 00:36:55,900 bigger as the loss gets bigger. 818 00:36:55,900 --> 00:36:56,400 Why? 819 00:36:56,400 --> 00:36:58,400 Because you're moving away from that linear part 820 00:36:58,400 --> 00:37:01,500 towards the nonlinear part of the utility function. 821 00:37:01,500 --> 00:37:03,990 Similarly, this risk premium should 822 00:37:03,990 --> 00:37:07,470 fall as your income is higher. 823 00:37:07,470 --> 00:37:07,970 Why? 824 00:37:07,970 --> 00:37:09,387 Because once again, that makes you 825 00:37:09,387 --> 00:37:11,440 more towards the linear part. 826 00:37:11,440 --> 00:37:13,780 The bottom line is the bigger the risk is 827 00:37:13,780 --> 00:37:17,313 relative to your income, the more risk averse you become. 828 00:37:17,313 --> 00:37:19,480 The more you move from that linear part of the curve 829 00:37:19,480 --> 00:37:22,330 onto the nonlinear part of the curve. 830 00:37:22,330 --> 00:37:24,840 So that's the key thing. 831 00:37:24,840 --> 00:37:28,520 What matters is risk relative to your income. 832 00:37:28,520 --> 00:37:30,920 That's going to determine your value, your willingness 833 00:37:30,920 --> 00:37:32,130 to pay for insurance. 834 00:37:32,130 --> 00:37:35,890 So for example, let's think of your decision 835 00:37:35,890 --> 00:37:39,200 to go buy consumer electronics and the warranty. 836 00:37:39,200 --> 00:37:41,400 And they always offer you a warranty. 837 00:37:41,400 --> 00:37:46,100 Now, those warranties are expected value negative. 838 00:37:46,100 --> 00:37:48,680 If you take the odds of your machine 839 00:37:48,680 --> 00:37:51,500 breaking-- if you go to buy a new stereo. 840 00:37:51,500 --> 00:37:53,360 As if people buy stereos anymore. 841 00:37:53,360 --> 00:37:55,940 You're going to buy a car stereo. 842 00:37:55,940 --> 00:37:56,945 People still buy those. 843 00:37:56,945 --> 00:37:59,780 You're going to buy a car stereo. 844 00:37:59,780 --> 00:38:02,510 You take the odds of that breaking times the cost 845 00:38:02,510 --> 00:38:04,160 it would take to fix it. 846 00:38:04,160 --> 00:38:06,920 Those multiplied are less than what they'll charge you 847 00:38:06,920 --> 00:38:09,260 for the insurance premium. 848 00:38:09,260 --> 00:38:12,995 It's a bad bet but it's insurance. 849 00:38:12,995 --> 00:38:14,870 And so the question is, should you take that? 850 00:38:14,870 --> 00:38:18,240 Well, that depends on how wealthy you are. 851 00:38:18,240 --> 00:38:22,830 I should never take that because my car radio cost is tiny 852 00:38:22,830 --> 00:38:24,610 relative to my income. 853 00:38:24,610 --> 00:38:26,680 Someone who has low income might decide 854 00:38:26,680 --> 00:38:29,030 that's a large gamble relative my income. 855 00:38:29,030 --> 00:38:30,140 I don't want to take that. 856 00:38:30,140 --> 00:38:35,250 So I want to buy the insurance offered by the manufacturer. 857 00:38:35,250 --> 00:38:37,950 So once again, it's all about the size of the risk 858 00:38:37,950 --> 00:38:39,120 relative to your income. 859 00:38:39,120 --> 00:38:39,620 Yeah. 860 00:38:39,620 --> 00:38:41,360 AUDIENCE: What if I have increased 861 00:38:41,360 --> 00:38:43,260 chance of breaking my phone? 862 00:38:43,260 --> 00:38:44,160 JONATHAN GRUBER: Well, that's a separate issue. 863 00:38:44,160 --> 00:38:45,327 We'll talk about that later. 864 00:38:45,327 --> 00:38:47,230 That's called moral hazard. 865 00:38:47,230 --> 00:38:48,990 You might-- well, it's not moral hazard. 866 00:38:48,990 --> 00:38:51,390 What you're saying is there's heterogeneity. 867 00:38:51,390 --> 00:38:54,900 And you know you're actually-- that for you it is a fair bet 868 00:38:54,900 --> 00:38:55,922 because you're clumsy. 869 00:38:55,922 --> 00:38:57,630 Well, then you should definitely take it. 870 00:38:57,630 --> 00:38:58,920 This is saying risk aversion works 871 00:38:58,920 --> 00:38:59,690 in favor of you taking it. 872 00:38:59,690 --> 00:39:01,855 Clumsiness further works in favor of you taking it. 873 00:39:01,855 --> 00:39:03,730 And we'll talk about that in a lecture or two 874 00:39:03,730 --> 00:39:08,790 when we talk about government provision of insurance. 875 00:39:08,790 --> 00:39:10,775 So that's sort of the first application, 876 00:39:10,775 --> 00:39:12,150 which is thinking about insurance 877 00:39:12,150 --> 00:39:13,900 and why it's such big business in America. 878 00:39:13,900 --> 00:39:17,070 And it is huge business in America. 879 00:39:17,070 --> 00:39:19,140 The second application is thinking 880 00:39:19,140 --> 00:39:21,420 about our friend the lottery. 881 00:39:21,420 --> 00:39:22,150 Big news lately. 882 00:39:22,150 --> 00:39:22,650 We talked. 883 00:39:22,650 --> 00:39:26,003 There was a couple of huge lottery payouts. 884 00:39:26,003 --> 00:39:27,920 So let's talk about-- actually, let's do this. 885 00:39:27,920 --> 00:39:31,430 Let's talk about the lottery. 886 00:39:31,430 --> 00:39:36,620 Now, the lottery is a total rip off. 887 00:39:36,620 --> 00:39:41,103 The expected value of a lottery purchase is 50%. 888 00:39:41,103 --> 00:39:43,520 So every dollar you spend on the lottery, over all lottery 889 00:39:43,520 --> 00:39:44,450 options-- 890 00:39:44,450 --> 00:39:48,740 for every dollar you spend, the expected payout is $0.50, 891 00:39:48,740 --> 00:39:53,000 is a much, much less than fair bet. 892 00:39:53,000 --> 00:39:55,010 And yet lotteries are wildly popular. 893 00:39:55,010 --> 00:39:57,800 Actually, the beginnings of this country, the US 894 00:39:57,800 --> 00:39:58,925 were financed by a lottery. 895 00:39:58,925 --> 00:40:01,008 Much of the money they government raised initially 896 00:40:01,008 --> 00:40:02,840 to set up America came from a lottery. 897 00:40:02,840 --> 00:40:05,660 And state lotteries are a huge source of public financing 898 00:40:05,660 --> 00:40:08,960 right now across America. 899 00:40:08,960 --> 00:40:13,790 Now, why do people play lotteries. 900 00:40:13,790 --> 00:40:15,920 Well, there's basically four theories 901 00:40:15,920 --> 00:40:17,870 for why people play lotteries. 902 00:40:17,870 --> 00:40:20,330 The first is that people are risk loving. 903 00:40:23,980 --> 00:40:26,140 In fact, that were wrong, people are risk loving. 904 00:40:26,140 --> 00:40:27,580 That's why they play lotteries. 905 00:40:27,580 --> 00:40:29,080 How do we know that theory is wrong? 906 00:40:31,395 --> 00:40:33,270 How do we know that theory is its face wrong, 907 00:40:33,270 --> 00:40:34,437 that people are risk loving? 908 00:40:36,788 --> 00:40:37,348 Yeah. 909 00:40:37,348 --> 00:40:38,890 AUDIENCE: The demonstration in class. 910 00:40:38,890 --> 00:40:41,353 Lots of didn't raise their hands. 911 00:40:41,353 --> 00:40:43,520 JONATHAN GRUBER: Well, that's one way we might know. 912 00:40:43,520 --> 00:40:45,320 But how do we know more globally? 913 00:40:45,320 --> 00:40:47,180 You guys could just be a weird bunch. 914 00:40:47,180 --> 00:40:47,940 How do you we know more globally? 915 00:40:47,940 --> 00:40:48,440 Yeah. 916 00:40:48,440 --> 00:40:49,973 AUDIENCE: Because of [INAUDIBLE].. 917 00:40:49,973 --> 00:40:50,890 JONATHAN GRUBER: Yeah. 918 00:40:50,890 --> 00:40:53,762 But that's absolutely right, theoretically. 919 00:40:53,762 --> 00:40:54,720 But that's theoretical. 920 00:40:54,720 --> 00:40:56,570 In the real world, what piece of evidence can 921 00:40:56,570 --> 00:40:57,800 you immediately point to that I recently 922 00:40:57,800 --> 00:40:59,780 pointed out that could show you this is wrong. 923 00:40:59,780 --> 00:40:59,990 Yeah. 924 00:40:59,990 --> 00:41:01,190 AUDIENCE: People buy insurance. 925 00:41:01,190 --> 00:41:02,420 JONATHAN GRUBER: People buy insurance. 926 00:41:02,420 --> 00:41:04,610 If they're risk loving, why are they buying insurance? 927 00:41:04,610 --> 00:41:06,210 So clearly people aren't risk loving. 928 00:41:06,210 --> 00:41:08,230 We wouldn't spend 10% of GDP on insurance. 929 00:41:08,230 --> 00:41:10,660 So that theory is clearly wrong. 930 00:41:10,660 --> 00:41:11,420 OK. 931 00:41:11,420 --> 00:41:13,150 That's theory one. 932 00:41:13,150 --> 00:41:16,270 Now, the second theory is a somewhat subtler version 933 00:41:16,270 --> 00:41:19,150 of this theory, which is quite interesting, 934 00:41:19,150 --> 00:41:23,980 which is that people are both risk averse and risk loving. 935 00:41:23,980 --> 00:41:26,920 So that risk aversion varies. 936 00:41:26,920 --> 00:41:31,870 Risk tolerance, let's call it, varies. 937 00:41:31,870 --> 00:41:33,520 And then in particular, people are 938 00:41:33,520 --> 00:41:36,760 risk averse over small gambles, but risk 939 00:41:36,760 --> 00:41:38,860 loving over big gambles. 940 00:41:38,860 --> 00:41:41,813 So let's look at figure 20-4. 941 00:41:41,813 --> 00:41:43,230 This is an example of what we call 942 00:41:43,230 --> 00:41:44,703 Friedman-Savage preferences. 943 00:41:44,703 --> 00:41:45,870 You don't need to know that. 944 00:41:45,870 --> 00:41:48,480 But they had this idea that maybe people are locally 945 00:41:48,480 --> 00:41:51,870 risk averse but globally risk loving. 946 00:41:51,870 --> 00:41:53,170 Let's see what this-- 947 00:41:53,170 --> 00:41:55,380 let me explain this. 948 00:41:55,380 --> 00:41:57,160 This is sort of complicated. 949 00:41:57,160 --> 00:42:00,420 So imagine that I'm going to offer you 950 00:42:00,420 --> 00:42:07,970 a 50-50 gamble between w1 and w3. 951 00:42:07,970 --> 00:42:10,850 So a gamble leaves you at w1 and a gamble leaves you at w3 952 00:42:10,850 --> 00:42:13,460 at 50% chance. 953 00:42:13,460 --> 00:42:15,650 Well, if we look at between w1 and w3, 954 00:42:15,650 --> 00:42:19,020 we're on the concave part of the utility function. 955 00:42:19,020 --> 00:42:21,680 And as a result, I will not take that gamble. 956 00:42:21,680 --> 00:42:27,470 That gamble leaves me at point B, which is below B star. 957 00:42:27,470 --> 00:42:30,020 So basically, I will not take that gamble. 958 00:42:30,020 --> 00:42:33,500 That leaves me worse off than just having w1 plus w3 over 2 959 00:42:33,500 --> 00:42:34,190 with certainty. 960 00:42:34,190 --> 00:42:36,050 This is just if you hold your hand-- 961 00:42:36,050 --> 00:42:38,210 if you hold your hands between w1 and w3, 962 00:42:38,210 --> 00:42:40,400 that's just the graph we saw before. 963 00:42:40,400 --> 00:42:43,240 You won't take that bet. 964 00:42:43,240 --> 00:42:45,700 But now let's say once you get above w3, 965 00:42:45,700 --> 00:42:49,900 once you're rich enough, you're risk loving. 966 00:42:49,900 --> 00:42:52,150 Let's say people are risk averse at first 967 00:42:52,150 --> 00:42:53,680 but then get risk loving. 968 00:42:53,680 --> 00:42:55,240 So if you started it-- 969 00:42:55,240 --> 00:42:59,570 if you said you were starting at w3 plus w5 over 2, 970 00:42:59,570 --> 00:43:01,870 I'd offer you a gamble between w3 and w5. 971 00:43:01,870 --> 00:43:04,300 Then you're risk loving in that range. 972 00:43:04,300 --> 00:43:05,973 And you take it. 973 00:43:05,973 --> 00:43:08,390 So once you get rich enough, you start to get risk loving. 974 00:43:08,390 --> 00:43:10,370 So I talked about before getting rich or getting more and more 975 00:43:10,370 --> 00:43:11,662 risk neutral as you get richer. 976 00:43:11,662 --> 00:43:12,912 What if it goes the other way? 977 00:43:12,912 --> 00:43:15,410 What if you actually get risk loving when you get richer? 978 00:43:15,410 --> 00:43:18,770 Well, then, if you think about the whole Mega Millions thing, 979 00:43:18,770 --> 00:43:21,670 you could see that over the whole distribution from w1 980 00:43:21,670 --> 00:43:25,110 to w5, people might want to take that risk. 981 00:43:25,110 --> 00:43:29,250 That you could actually be risk loving over these gambles, 982 00:43:29,250 --> 00:43:30,740 over these giant gambles. 983 00:43:30,740 --> 00:43:33,630 And that could explain why people play Mega Millions. 984 00:43:33,630 --> 00:43:35,130 That over the giant gambles, they're 985 00:43:35,130 --> 00:43:38,000 risk loving, even if over more moderate gambles 986 00:43:38,000 --> 00:43:39,190 they're risk averse. 987 00:43:39,190 --> 00:43:41,190 You don't insure yourself for a billion dollars. 988 00:43:41,190 --> 00:43:43,180 You insure yourself for a few thousand dollars. 989 00:43:43,180 --> 00:43:43,420 Yeah. 990 00:43:43,420 --> 00:43:45,810 AUDIENCE: How does the size of the gamble we're talking about 991 00:43:45,810 --> 00:43:47,768 determine-- we're talking about small bets that 992 00:43:47,768 --> 00:43:51,210 are more linear, is it based on what the player puts in 993 00:43:51,210 --> 00:43:52,830 or what they get in return? 994 00:43:52,830 --> 00:43:54,141 JONATHAN GRUBER: Both. 995 00:43:54,141 --> 00:43:54,820 Both. 996 00:43:54,820 --> 00:43:57,430 It's basically about-- it's about expected utility 997 00:43:57,430 --> 00:43:58,373 calculations. 998 00:43:58,373 --> 00:43:59,790 Yes, it's true, for Mega Millions, 999 00:43:59,790 --> 00:44:02,590 you put in $2 for the chance of winning $1.6 billion. 1000 00:44:02,590 --> 00:44:06,830 But your probability is way, way lower than 2 in 1.6 billion. 1001 00:44:06,830 --> 00:44:09,510 So it's still unfair. 1002 00:44:09,510 --> 00:44:12,057 So the Friedman-Savage hypothesis-- 1003 00:44:12,057 --> 00:44:13,890 you don't need to know the name, once again. 1004 00:44:13,890 --> 00:44:15,930 This hypothesis is that what's happening 1005 00:44:15,930 --> 00:44:20,030 is that people are first risk averse, but then risk loving. 1006 00:44:20,030 --> 00:44:24,350 Well, how could we test and actually disprove this theory? 1007 00:44:24,350 --> 00:44:25,032 Yeah. 1008 00:44:25,032 --> 00:44:26,450 AUDIENCE: Like scratch offs. 1009 00:44:26,450 --> 00:44:27,367 JONATHAN GRUBER: Yeah. 1010 00:44:27,367 --> 00:44:29,600 If this is true, people would love Mega Millions 1011 00:44:29,600 --> 00:44:31,940 but hate $10 scratch offs. 1012 00:44:31,940 --> 00:44:34,400 In fact, the vast majority of lottery playing 1013 00:44:34,400 --> 00:44:35,690 is not Mega Millions. 1014 00:44:35,690 --> 00:44:37,340 It's $10 scratch off. 1015 00:44:37,340 --> 00:44:40,600 Most money spent on lotteries are $10 and $20 gambles 1016 00:44:40,600 --> 00:44:43,720 where you bet $1 to win $10 or $20. 1017 00:44:43,720 --> 00:44:46,660 You should be risk averse over that, or at best risk neutral. 1018 00:44:46,660 --> 00:44:49,480 You shouldn't be risk loving over those tiny gambles. 1019 00:44:49,480 --> 00:44:52,310 And yet that's most of what lottery players do. 1020 00:44:52,310 --> 00:44:55,570 AUDIENCE: Wouldn't not really a scratch off be 1021 00:44:55,570 --> 00:45:00,700 counted internally as not getting money instead of losing 1022 00:45:00,700 --> 00:45:01,460 money? 1023 00:45:01,460 --> 00:45:01,870 JONATHAN GRUBER: Well, no, but you've 1024 00:45:01,870 --> 00:45:03,250 lost the dollar you spent. 1025 00:45:03,250 --> 00:45:04,480 And that dollar-- 1026 00:45:04,480 --> 00:45:07,380 I still offered you a gamble. 1027 00:45:07,380 --> 00:45:11,310 Spend $1, win $10, with a 0.05 probability. 1028 00:45:11,310 --> 00:45:13,750 AUDIENCE: I mean, in the loss averse sense. 1029 00:45:13,750 --> 00:45:14,880 JONATHAN GRUBER: Well, we're not doing loss aversion. 1030 00:45:14,880 --> 00:45:15,840 Loss aversion is sort of hard. 1031 00:45:15,840 --> 00:45:16,860 You don't have to think about gambling. 1032 00:45:16,860 --> 00:45:18,240 Loss aversion is more about losing. 1033 00:45:18,240 --> 00:45:20,310 But in the regular-- you can see you shouldn't do 1034 00:45:20,310 --> 00:45:21,900 that unless you're risk loving. 1035 00:45:21,900 --> 00:45:24,730 But even this theory would say you're not locally risk loving. 1036 00:45:24,730 --> 00:45:26,940 So this theory is out, which leaves us 1037 00:45:26,940 --> 00:45:28,590 with two more theories. 1038 00:45:28,590 --> 00:45:33,920 The first theory is that this is entertainment. 1039 00:45:33,920 --> 00:45:37,360 That in people's utility function 1040 00:45:37,360 --> 00:45:39,450 is not just consumption but the thrill 1041 00:45:39,450 --> 00:45:42,430 of finding out if they won. 1042 00:45:42,430 --> 00:45:43,930 My wife, against my better judgment, 1043 00:45:43,930 --> 00:45:46,860 went out and bought a Mega Millions ticket. 1044 00:45:46,860 --> 00:45:49,320 And she got utility out of waiting 1045 00:45:49,320 --> 00:45:50,807 for that number to come up. 1046 00:45:50,807 --> 00:45:52,140 And it was pretty cheap utility. 1047 00:45:52,140 --> 00:45:54,210 Cost her $2. 1048 00:45:54,210 --> 00:45:57,260 So in that sense, maybe you play the lottery a lot 1049 00:45:57,260 --> 00:45:59,150 for entertainment. 1050 00:45:59,150 --> 00:46:01,520 That's one theory, unfortunately, 1051 00:46:01,520 --> 00:46:07,600 the other theory is ignorance. 1052 00:46:07,600 --> 00:46:09,560 That basically, the saying is the lottery 1053 00:46:09,560 --> 00:46:12,380 is a tax on the stupid. 1054 00:46:12,380 --> 00:46:16,860 Basically just don't understand what a bad deal this is. 1055 00:46:16,860 --> 00:46:19,440 And the problem is we don't know which of these theories 1056 00:46:19,440 --> 00:46:20,880 is right. 1057 00:46:20,880 --> 00:46:22,933 And they have very different implications 1058 00:46:22,933 --> 00:46:23,850 for government policy. 1059 00:46:26,790 --> 00:46:29,950 If this theory is right, if this theory is right, 1060 00:46:29,950 --> 00:46:32,460 then the government should support lotteries, 1061 00:46:32,460 --> 00:46:34,470 where essentially the government is essentially 1062 00:46:34,470 --> 00:46:37,450 getting paid for providing entertainment. 1063 00:46:37,450 --> 00:46:40,682 It's what the lotteries often call the voluntary tax. 1064 00:46:40,682 --> 00:46:42,640 That I am basically giving the government money 1065 00:46:42,640 --> 00:46:43,840 that can run our schools in return 1066 00:46:43,840 --> 00:46:45,550 for the government giving me the entertainment value of seeing 1067 00:46:45,550 --> 00:46:46,840 if my scratch off won. 1068 00:46:46,840 --> 00:46:48,100 That's great. 1069 00:46:48,100 --> 00:46:51,080 That's welfare improving. 1070 00:46:51,080 --> 00:46:58,345 Under this theory, we should be discouraging lotteries. 1071 00:46:58,345 --> 00:47:00,720 That all we're doing is taking a bunch of ignorant people 1072 00:47:00,720 --> 00:47:03,054 and getting them to waste their money. 1073 00:47:03,054 --> 00:47:04,445 Yeah. 1074 00:47:04,445 --> 00:47:06,070 AUDIENCE: Is there almost a possibility 1075 00:47:06,070 --> 00:47:09,300 that there is this concept of having nothing to lose. 1076 00:47:09,300 --> 00:47:12,650 If you're already too poor to be able to afford 1077 00:47:12,650 --> 00:47:14,830 your basic needs, then you might feel 1078 00:47:14,830 --> 00:47:17,270 like, I may as well try and win the lottery 1079 00:47:17,270 --> 00:47:18,910 and then I would be all set. 1080 00:47:18,910 --> 00:47:19,580 That is-- 1081 00:47:19,580 --> 00:47:20,413 [INTERPOSING VOICES] 1082 00:47:20,413 --> 00:47:23,980 AUDIENCE: [INAUDIBLE] 1083 00:47:23,980 --> 00:47:26,060 JONATHAN GRUBER: That's exactly this. 1084 00:47:26,060 --> 00:47:28,705 That wouldn't explain why I'd pay the $20 scratch off. 1085 00:47:28,705 --> 00:47:30,080 That's an absolute reason why I'd 1086 00:47:30,080 --> 00:47:31,455 go ahead, even if I was starving, 1087 00:47:31,455 --> 00:47:32,730 and play the Mega Millions. 1088 00:47:32,730 --> 00:47:35,120 And that's the Friedman-Savage hypothesis, absolutely. 1089 00:47:35,120 --> 00:47:38,330 But that can't explain why in fact, in some low income 1090 00:47:38,330 --> 00:47:40,730 communities, among some low income groups, 1091 00:47:40,730 --> 00:47:43,070 they'll spend as much as 20% of their income 1092 00:47:43,070 --> 00:47:47,030 every year on the lottery, a net. 1093 00:47:47,030 --> 00:47:51,260 They're losing huge amounts of money on scratch off tickets. 1094 00:47:51,260 --> 00:47:54,140 So the question is, is that a rational decision 1095 00:47:54,140 --> 00:47:55,910 because they find it entertaining 1096 00:47:55,910 --> 00:47:57,952 or an irrational decision because they just don't 1097 00:47:57,952 --> 00:47:59,840 understand what's going on? 1098 00:47:59,840 --> 00:48:02,270 And unfortunately, we don't know the answer. 1099 00:48:02,270 --> 00:48:05,013 But we do know it's very important. 1100 00:48:05,013 --> 00:48:06,680 It's important because there's big bucks 1101 00:48:06,680 --> 00:48:08,720 and in many low income communities 1102 00:48:08,720 --> 00:48:10,785 it's a huge source of expenditure. 1103 00:48:10,785 --> 00:48:12,410 So I can't give you the answer to that. 1104 00:48:12,410 --> 00:48:13,490 I can just tell you it's an important question. 1105 00:48:13,490 --> 00:48:14,990 I hope someday someone to figure out 1106 00:48:14,990 --> 00:48:16,657 how to think about this because it's got 1107 00:48:16,657 --> 00:48:18,060 very important implications. 1108 00:48:18,060 --> 00:48:19,040 So let me stop there. 1109 00:48:19,040 --> 00:48:20,832 That's all I want to say about uncertainty. 1110 00:48:20,832 --> 00:48:25,000 And we'll come back and do another topic on Wednesday.