1 00:00:00,040 --> 00:00:02,460 The following content is provided under a Creative 2 00:00:02,460 --> 00:00:03,870 Commons license. 3 00:00:03,870 --> 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 --> 00:00:18,090 hundreds of MIT courses, visit MIT OpenCourseWare at 7 00:00:18,090 --> 00:00:19,340 ocw.mit.edu. 8 00:00:21,640 --> 00:00:24,730 PROFESSOR: All right, so today we're going to continue our 9 00:00:24,730 --> 00:00:29,250 discussion of consumer choice. 10 00:00:29,250 --> 00:00:32,759 If you remember the set-up from last time, the main 11 00:00:32,759 --> 00:00:35,450 motivation is you're trying to understand what underlies 12 00:00:35,450 --> 00:00:39,790 demand curves, how consumers ultimately decide to trade off 13 00:00:39,790 --> 00:00:41,860 price and quantity of goods. 14 00:00:41,860 --> 00:00:44,315 We said that ultimately that came from the principle of 15 00:00:44,315 --> 00:00:49,530 utility maximization, and that utility is maximized when 16 00:00:49,530 --> 00:00:53,770 individuals maximize the utility function, which is 17 00:00:53,770 --> 00:00:56,580 this mathematical representation of preferences. 18 00:00:56,580 --> 00:00:59,730 And last time we talked about how if individuals were 19 00:00:59,730 --> 00:01:02,240 unconstrained how they choose what they want, they would 20 00:01:02,240 --> 00:01:05,940 just like more of everything, and their ranking across 21 00:01:05,940 --> 00:01:07,590 different bundles would depend on that 22 00:01:07,590 --> 00:01:09,520 underlying utility function. 23 00:01:09,520 --> 00:01:11,390 Now, of course, what's stopping individuals from 24 00:01:11,390 --> 00:01:14,300 consuming everything they want is their budget constraints. 25 00:01:14,300 --> 00:01:16,690 And so today we're going to turn to the second part of the 26 00:01:16,690 --> 00:01:19,930 problem, which is talking about budget constraints. 27 00:01:19,930 --> 00:01:22,060 Now, we're going to make a very simplifying assumption 28 00:01:22,060 --> 00:01:26,000 here for most of the semester, which is we are going to 29 00:01:26,000 --> 00:01:28,920 assume that your income equals your budget. 30 00:01:28,920 --> 00:01:31,010 That is, you spend your entire income. 31 00:01:31,010 --> 00:01:33,600 That is, we're going to ignore the possibility of savings 32 00:01:33,600 --> 00:01:36,370 until about the third lecture from the end. 33 00:01:36,370 --> 00:01:38,430 Now, this turns out not to be a terrible assumption for the 34 00:01:38,430 --> 00:01:39,230 typical American. 35 00:01:39,230 --> 00:01:42,600 The typical American doesn't save. So actually, it's not a 36 00:01:42,600 --> 00:01:45,050 terrible assumption for us to work with if we think about 37 00:01:45,050 --> 00:01:46,680 typical consumers. 38 00:01:46,680 --> 00:01:48,610 In practice, savings is going to turn out to be a very 39 00:01:48,610 --> 00:01:52,650 critical part of what we're going to do to think about 40 00:01:52,650 --> 00:01:54,405 economics, so we'll come back to that. 41 00:01:54,405 --> 00:01:56,470 But we're going to ignore savings for now and assume 42 00:01:56,470 --> 00:01:58,680 that your budget equals your income. 43 00:01:58,680 --> 00:02:01,910 So let's say that your parents, probably a good model 44 00:02:01,910 --> 00:02:04,020 is you guys, you guys probably aren't in saving mode. 45 00:02:04,020 --> 00:02:06,780 You've got some budget saved from your parents. 46 00:02:06,780 --> 00:02:09,000 Let's call it y. 47 00:02:09,000 --> 00:02:10,979 And let's say that your parents give you some budget 48 00:02:10,979 --> 00:02:13,430 at the start of the semester, y, and they say this is your 49 00:02:13,430 --> 00:02:15,520 money you have to spend, say each month or 50 00:02:15,520 --> 00:02:16,770 for the whole semester. 51 00:02:18,670 --> 00:02:22,070 And let's imagine that you have to allocate that budget 52 00:02:22,070 --> 00:02:24,840 only across two goods, pizza and movies. 53 00:02:24,840 --> 00:02:27,650 So once again, unrealistic, but this is the kind of 54 00:02:27,650 --> 00:02:29,850 simplifying assumption that lets us understand how people 55 00:02:29,850 --> 00:02:31,260 make decisions. 56 00:02:31,260 --> 00:02:35,000 So that gives you your budget constraint. 57 00:02:35,000 --> 00:02:39,590 You've got some income y that your parents have given you, 58 00:02:39,590 --> 00:02:42,750 and you can allocate that across pizza and movies. 59 00:02:42,750 --> 00:02:46,100 So how do you allocate that? 60 00:02:46,100 --> 00:02:49,770 Well, you can buy movies, the number of movies you can get, 61 00:02:49,770 --> 00:02:52,130 plus the number of pizzas. 62 00:02:52,130 --> 00:02:53,790 Well, how many of each you can get, that 63 00:02:53,790 --> 00:02:55,100 depends on their price. 64 00:02:55,100 --> 00:02:57,130 In particular, budget constraint is the number of 65 00:02:57,130 --> 00:03:00,920 movies times the price per movie plus the 66 00:03:00,920 --> 00:03:03,220 number of pizzas -- 67 00:03:03,220 --> 00:03:07,310 plus the number of pizzas times the price for pizza. 68 00:03:07,310 --> 00:03:08,960 That's your budget constraint. 69 00:03:08,960 --> 00:03:11,880 It's the number of movies times the price per movie or 70 00:03:11,880 --> 00:03:13,630 the number of pizzas times the price for pizza. 71 00:03:13,630 --> 00:03:15,900 And this is easiest to see graphically. 72 00:03:15,900 --> 00:03:19,850 If you go to figure 5-1, this is a graphical illustration of 73 00:03:19,850 --> 00:03:22,630 a budget constraint. 74 00:03:22,630 --> 00:03:26,450 Now, let's just carefully talk through this for a moment. 75 00:03:26,450 --> 00:03:28,190 You're going to be really good at dealing with budget 76 00:03:28,190 --> 00:03:28,730 constraints. 77 00:03:28,730 --> 00:03:29,930 You're going to have to be this semester. 78 00:03:29,930 --> 00:03:33,410 So let's carefully talk about where this comes from. 79 00:03:33,410 --> 00:03:38,050 OK, the x-axis is going to be how many movies you could have 80 00:03:38,050 --> 00:03:40,850 if all you did with your income was consume movies. 81 00:03:40,850 --> 00:03:43,020 Well, if all you did with your income was consume movies, you 82 00:03:43,020 --> 00:03:45,385 could have y over p sub m movies. 83 00:03:49,340 --> 00:03:52,640 If you decided to devote your income solely to movies, then 84 00:03:52,640 --> 00:03:59,340 you could have y times y over p sub m movies. 85 00:03:59,340 --> 00:04:03,080 If instead you decided to devote all your income to 86 00:04:03,080 --> 00:04:07,360 pizza, then you could have y over p sub p pizza. 87 00:04:07,360 --> 00:04:10,990 So the y-axis is going to be the point where you consume 88 00:04:10,990 --> 00:04:12,730 zero movies and all pizza. 89 00:04:12,730 --> 00:04:14,070 It's going to be where you devote your 90 00:04:14,070 --> 00:04:15,940 entire budget to pizzas. 91 00:04:15,940 --> 00:04:17,890 And then there'll be some combination in between, which 92 00:04:17,890 --> 00:04:20,220 is our budget line. 93 00:04:20,220 --> 00:04:22,620 Which is the combinations of pizzas and movies you can 94 00:04:22,620 --> 00:04:26,277 consume given your total income y. 95 00:04:29,270 --> 00:04:32,040 And the slope of that line is going to be the price ratio. 96 00:04:32,040 --> 00:04:35,620 Or the negative of the price ratio. 97 00:04:35,620 --> 00:04:59,500 The slope of that line is going to be minus pp over pm. 98 00:04:59,500 --> 00:05:04,180 The slope of that line is going to be the change in the 99 00:05:04,180 --> 00:05:09,540 ratio of the price of pizza to the price of movies. 100 00:05:09,540 --> 00:05:11,030 OK, what am I doing wrong here? 101 00:05:13,920 --> 00:05:15,260 Negative of the price ratio. 102 00:05:15,260 --> 00:05:16,400 Have I got this right? 103 00:05:16,400 --> 00:05:17,493 Rise over run. 104 00:05:17,493 --> 00:05:18,743 Yeah. 105 00:05:24,845 --> 00:05:27,914 Have I got this right? 106 00:05:27,914 --> 00:05:28,405 Yeah. 107 00:05:28,405 --> 00:05:31,351 AUDIENCE: I think that the pp and the pm's are in the 108 00:05:31,351 --> 00:05:33,806 denominators, because it's y over pp [INAUDIBLE PHRASE]. 109 00:05:38,225 --> 00:05:38,716 PROFESSOR: Right. 110 00:05:38,716 --> 00:05:40,189 It's the denominators, that's what I did wrong. 111 00:05:40,189 --> 00:05:41,439 Right, so it is pm over pp. 112 00:05:44,150 --> 00:05:45,050 Sorry, my bad. 113 00:05:45,050 --> 00:05:46,130 OK, right. 114 00:05:46,130 --> 00:05:46,830 Because they're the denominators. 115 00:05:46,830 --> 00:05:48,300 Because it's the rise over run in terms of the quantity. 116 00:05:48,300 --> 00:05:49,290 So that's what I did wrong. 117 00:05:49,290 --> 00:05:51,980 OK, so basically it's the negative of the price ratio, 118 00:05:51,980 --> 00:05:54,150 minus the price of movies over the price of pizzas because 119 00:05:54,150 --> 00:05:56,170 they're in the denominators as you said, because as the price 120 00:05:56,170 --> 00:05:57,790 goes up, the quantity goes down. 121 00:05:57,790 --> 00:06:01,320 So the negative of the price ratio of the price of movies 122 00:06:01,320 --> 00:06:02,850 to the price of pizzas is the slope. 123 00:06:02,850 --> 00:06:04,820 So let's just do a simple example. 124 00:06:04,820 --> 00:06:09,490 Imagine that income equals $96. 125 00:06:09,490 --> 00:06:13,080 Imagine your parents give you $96, say 126 00:06:13,080 --> 00:06:15,340 a month or a semester. 127 00:06:15,340 --> 00:06:21,420 Imagine that the price of movies is $8 and imagine the 128 00:06:21,420 --> 00:06:24,480 price of a pizza is $16. 129 00:06:24,480 --> 00:06:27,420 It's a good pizza. 130 00:06:27,420 --> 00:06:32,240 So what this means is that with your income of $96, you 131 00:06:32,240 --> 00:06:38,220 could either get eight pizzas or 12 movies. 132 00:06:38,220 --> 00:06:41,180 So that means that the price ratio of the slope of your 133 00:06:41,180 --> 00:06:45,020 budget constraint is minus 1/2. 134 00:06:45,020 --> 00:06:47,540 The price ratio is minus 1/2. 135 00:06:47,540 --> 00:06:51,550 So the slope of that budget constraint is minus 1/2. 136 00:06:51,550 --> 00:06:53,910 Now, we have a name for this slope. 137 00:06:53,910 --> 00:06:56,740 We're going to call this the marginal rate of 138 00:06:56,740 --> 00:06:59,580 transformation. 139 00:06:59,580 --> 00:07:03,030 The marginal rate of transformation is our label 140 00:07:03,030 --> 00:07:05,220 for this slope. 141 00:07:05,220 --> 00:07:07,460 Now, why do we use that name? 142 00:07:07,460 --> 00:07:09,830 Well, it means that's the marginal rate at which you can 143 00:07:09,830 --> 00:07:17,170 transform pizzas into movies. 144 00:07:17,170 --> 00:07:19,320 The rate at which you can turn pizzas into movies. 145 00:07:19,320 --> 00:07:21,950 Now, once again, like I talked about last time, you're not an 146 00:07:21,950 --> 00:07:25,690 alchemist. You're not actually turning pizzas into movies. 147 00:07:25,690 --> 00:07:28,890 But the market essentially is giving you a rate at which you 148 00:07:28,890 --> 00:07:31,770 can do that given a budget, given that you have a certain 149 00:07:31,770 --> 00:07:34,410 amount of money. 150 00:07:34,410 --> 00:07:41,200 Given that you have a certain amount of money, $96, and 151 00:07:41,200 --> 00:07:44,340 given the prices that you face in the market, you could 152 00:07:44,340 --> 00:07:48,170 transform pizzas into movies by trading one 153 00:07:48,170 --> 00:07:50,770 pizza for 1/2 a movie. 154 00:07:50,770 --> 00:07:52,850 Now, once again, you're not actually doing the physical 155 00:07:52,850 --> 00:07:56,700 transformation, but that's the trade-off that you face when 156 00:07:56,700 --> 00:07:59,300 you're trying to transform one to the other. 157 00:07:59,300 --> 00:08:01,760 So effectively, it's the same as if you're trading them for 158 00:08:01,760 --> 00:08:02,650 each other. 159 00:08:02,650 --> 00:08:04,090 As I talked about last time. 160 00:08:04,090 --> 00:08:07,160 it's essentially the same as you're trading, and that's 161 00:08:07,160 --> 00:08:09,350 because of the key economic concept we'll come back to 162 00:08:09,350 --> 00:08:10,540 over and over again in this course-- 163 00:08:10,540 --> 00:08:20,360 the concept of opportunity cost. 164 00:08:20,360 --> 00:08:24,660 The opportunity cost is the value of the forgone 165 00:08:24,660 --> 00:08:25,910 alternative. 166 00:08:39,740 --> 00:08:42,250 The value of the forgone alternative is the opportunity 167 00:08:42,250 --> 00:08:48,120 cost. So basically what that means is if you decide to 168 00:08:48,120 --> 00:08:59,970 forgo a pizza, that's the same as forgoing two movies. 169 00:08:59,970 --> 00:09:03,150 Likewise, if you decide to forgo a movie, it's the same 170 00:09:03,150 --> 00:09:05,660 as forgoing half a pizza. 171 00:09:05,660 --> 00:09:09,270 So the opportunity cost of a movie, what essentially the 172 00:09:09,270 --> 00:09:12,780 movie is costing you, is 1/2 a pizza. 173 00:09:12,780 --> 00:09:16,100 Now, really it's costing you $8 and a pizza costs you $16. 174 00:09:16,100 --> 00:09:17,850 But when we think about trading off goods, the 175 00:09:17,850 --> 00:09:20,770 opportunity cost of that movie is that you've forgone the 176 00:09:20,770 --> 00:09:23,300 ability to eat half a pizza. 177 00:09:23,300 --> 00:09:27,510 That's the opportunity cost of the situation. 178 00:09:27,510 --> 00:09:28,630 So that's basically how we're going to 179 00:09:28,630 --> 00:09:31,000 think about this trade-off. 180 00:09:31,000 --> 00:09:32,430 We're going to think about trading off goods as the 181 00:09:32,430 --> 00:09:35,900 opportunity cost of consuming one good instead of another. 182 00:09:35,900 --> 00:09:38,730 The opportunity cost of that movie is that you haven't 183 00:09:38,730 --> 00:09:39,730 gotten to eat 1/2 a pizza. 184 00:09:39,730 --> 00:09:42,130 The opportunity cost of the pizza is that you've forgone 185 00:09:42,130 --> 00:09:43,860 seeing two movies. 186 00:09:43,860 --> 00:09:46,640 And the reason is because you have a fixed budget. 187 00:09:46,640 --> 00:09:48,750 If you had an infinite budget, there'd be no opportunity 188 00:09:48,750 --> 00:09:52,410 cost. But because you have a fixed budget and you have to 189 00:09:52,410 --> 00:09:57,570 allocate that budget, there's an opportunity cost. If you 190 00:09:57,570 --> 00:10:01,340 choose not to decide, you've still made a choice. 191 00:10:01,340 --> 00:10:02,940 I don't know whether that quote's due to Shakespeare or 192 00:10:02,940 --> 00:10:03,850 Rush, I'm not sure. 193 00:10:03,850 --> 00:10:05,060 I have to look that up. 194 00:10:05,060 --> 00:10:09,880 But basically, if you choose to have one thing, then by 195 00:10:09,880 --> 00:10:11,890 definition you're forgoing another. 196 00:10:11,890 --> 00:10:14,470 Now, to understand the budget constraint, let's talk about 197 00:10:14,470 --> 00:10:16,240 what happens when we shock the budget constraint. 198 00:10:22,210 --> 00:10:29,000 Let's imagine the price of pizzas rose from $16 to $24. 199 00:10:29,000 --> 00:10:31,270 Pizzas got really expensive. 200 00:10:31,270 --> 00:10:33,780 We decided we only want gourmet pizzas or something. 201 00:10:33,780 --> 00:10:37,930 The price of pizzas went from $16 to $24. 202 00:10:37,930 --> 00:10:38,540 What does this do? 203 00:10:38,540 --> 00:10:40,180 Well, let's look at figure 5-2. 204 00:10:40,180 --> 00:10:42,120 It'll show what that does. 205 00:10:42,120 --> 00:10:45,930 What that does is it says our new budget constraint, instead 206 00:10:45,930 --> 00:10:51,320 of being 16p plus 8m equals 96, which is what the budget 207 00:10:51,320 --> 00:10:55,680 constraint was in our example, it's now 24p 208 00:10:55,680 --> 00:10:58,370 plus 8m equals 96. 209 00:10:58,370 --> 00:11:00,020 That's the new equation for the budget constraint. 210 00:11:00,020 --> 00:11:02,940 Or, more relevantly, the slope of the budget constraint has 211 00:11:02,940 --> 00:11:07,370 flattened from minus 1/2 to minus 1/3. 212 00:11:07,370 --> 00:11:11,240 The slope has fallen from minus 1/2 to minus 1/3. 213 00:11:11,240 --> 00:11:18,390 The price ratio has been reduced from 1/2 to 1/3. 214 00:11:18,390 --> 00:11:21,530 Now, forget utility for a second. 215 00:11:21,530 --> 00:11:23,790 Forget the fact that we thought about utility. 216 00:11:23,790 --> 00:11:29,390 Just looking at this, can you tell whether you are better or 217 00:11:29,390 --> 00:11:33,010 worse off from this price change? 218 00:11:33,010 --> 00:11:34,950 You shook your head no, why not? 219 00:11:34,950 --> 00:11:36,151 AUDIENCE: Because you don't know if you like pizzas enough 220 00:11:36,151 --> 00:11:38,360 to get any. 221 00:11:38,360 --> 00:11:41,420 PROFESSOR: OK, well in particular, 222 00:11:41,420 --> 00:11:43,180 you can almost tell. 223 00:11:43,180 --> 00:11:45,010 Who's the only person who doesn't care 224 00:11:45,010 --> 00:11:47,589 about this price change? 225 00:11:47,589 --> 00:11:49,068 AUDIENCE: [INAUDIBLE] 226 00:11:49,068 --> 00:11:51,050 PROFESSOR: No, no no. 227 00:11:51,050 --> 00:11:53,080 Think about consumers, people with different preferences for 228 00:11:53,080 --> 00:11:53,960 pizzas and movies. 229 00:11:53,960 --> 00:11:56,850 What would your preference for pizzas and movies have to be 230 00:11:56,850 --> 00:12:00,610 for you not to care about this price change? 231 00:12:00,610 --> 00:12:01,830 All movies. 232 00:12:01,830 --> 00:12:04,280 So long as you care about pizza at all, 233 00:12:04,280 --> 00:12:05,790 you're worse off. 234 00:12:05,790 --> 00:12:09,880 So in fact, the answer is your opportunity set has been 235 00:12:09,880 --> 00:12:10,940 restricted. 236 00:12:10,940 --> 00:12:12,960 So we can think about the opportunity set. 237 00:12:17,290 --> 00:12:21,430 Your opportunity set is the set of choices you can make 238 00:12:21,430 --> 00:12:24,550 given your budget. 239 00:12:24,550 --> 00:12:26,470 Before, you could make choices all the way up 240 00:12:26,470 --> 00:12:28,070 to the upper line. 241 00:12:28,070 --> 00:12:29,540 Now your set of choices that are 242 00:12:29,540 --> 00:12:31,640 available have just fallen. 243 00:12:31,640 --> 00:12:33,720 Now, you're no poorer-- it's not like your parents 244 00:12:33,720 --> 00:12:34,890 have cut you off. 245 00:12:34,890 --> 00:12:37,390 They still give you the $96. 246 00:12:37,390 --> 00:12:39,990 But you're effectively poorer. 247 00:12:39,990 --> 00:12:41,620 You're effectively worse off, and why is that? 248 00:12:41,620 --> 00:12:44,620 Because the set of things you could afford with that $96 has 249 00:12:44,620 --> 00:12:45,850 just been restricted. 250 00:12:45,850 --> 00:12:49,310 And unless you truly have no value on pizza, unless all you 251 00:12:49,310 --> 00:12:49,840 care about's the movie-- 252 00:12:49,840 --> 00:12:56,600 you're gluten and cheese allergic or something, you 253 00:12:56,600 --> 00:12:57,850 have no value on pizza-- 254 00:13:00,660 --> 00:13:01,790 then you're worse off. 255 00:13:01,790 --> 00:13:02,835 Your opportunity set's restricted. 256 00:13:02,835 --> 00:13:06,000 And that's the key insight here, is that you are worse 257 00:13:06,000 --> 00:13:08,410 off because the price has increased. 258 00:13:08,410 --> 00:13:09,950 A price increase makes you worse off. 259 00:13:09,950 --> 00:13:12,950 It restricts your opportunity set, because with the same 260 00:13:12,950 --> 00:13:17,300 amount of income, you can now afford fewer goods. 261 00:13:17,300 --> 00:13:21,000 Your opportunity set has been restricted. 262 00:13:21,000 --> 00:13:23,020 Likewise, now let's talk about what happens 263 00:13:23,020 --> 00:13:24,840 when your income falls. 264 00:13:24,840 --> 00:13:26,620 That's the next figure. 265 00:13:26,620 --> 00:13:28,460 Now, let's suppose your parents are pissed at you and 266 00:13:28,460 --> 00:13:30,470 they cut you down to $80. 267 00:13:30,470 --> 00:13:33,340 Because you didn't do something. 268 00:13:33,340 --> 00:13:34,970 You don't write enough or call enough, so they 269 00:13:34,970 --> 00:13:37,280 cut you down to $80. 270 00:13:37,280 --> 00:13:39,490 Well, here the slope of the budget 271 00:13:39,490 --> 00:13:40,610 constraint has not changed. 272 00:13:40,610 --> 00:13:42,430 Because what determines the slope of the budget 273 00:13:42,430 --> 00:13:42,870 constraint? 274 00:13:42,870 --> 00:13:46,260 It's prices, and no prices have changed. 275 00:13:46,260 --> 00:13:48,000 The slope of the budget constraint is unchanged 276 00:13:48,000 --> 00:13:50,070 because prices haven't changed, but your opportunity 277 00:13:50,070 --> 00:13:52,400 set is once again restricted because you 278 00:13:52,400 --> 00:13:53,980 now have lower income. 279 00:13:53,980 --> 00:13:57,740 So you can now afford fewer pizzas and movies. 280 00:13:57,740 --> 00:14:01,370 So now, instead of being able to afford up to six pizzas and 281 00:14:01,370 --> 00:14:05,010 up to 12 movies, you can now only afford up to five pizzas 282 00:14:05,010 --> 00:14:08,240 and up to 10 movies because your income has fallen. 283 00:14:08,240 --> 00:14:10,620 So once again, you're unambiguously worse off. 284 00:14:10,620 --> 00:14:13,560 Your opportunity set has contracted. 285 00:14:13,560 --> 00:14:17,600 So your opportunity set will contract whenever income falls 286 00:14:17,600 --> 00:14:20,230 or whenever price increases. 287 00:14:20,230 --> 00:14:22,710 And how it affects the graph will depend on whether it 288 00:14:22,710 --> 00:14:25,170 affects prices, which affects the slope, or just income, 289 00:14:25,170 --> 00:14:27,650 which affects the intercepts. 290 00:14:27,650 --> 00:14:30,830 Now, questions about the budget constraints and 291 00:14:30,830 --> 00:14:33,790 opportunity sets? 292 00:14:33,790 --> 00:14:34,450 Armed with that-- 293 00:14:34,450 --> 00:14:36,214 Yeah, I'm sorry, go ahead. 294 00:14:36,214 --> 00:14:37,438 AUDIENCE: Is the area under the curve at all 295 00:14:37,438 --> 00:14:38,688 indicative of utility? 296 00:14:41,690 --> 00:14:43,410 PROFESSOR:No, it's not, because that's going to be 297 00:14:43,410 --> 00:14:44,350 determined by your preferences. 298 00:14:44,350 --> 00:14:47,170 It's indicative of, if you will, potential utility, 299 00:14:47,170 --> 00:14:48,710 because that's your opportunity set. 300 00:14:48,710 --> 00:14:52,240 But as the example here points out, if you don't like pizzas 301 00:14:52,240 --> 00:14:55,890 at all, you'll feel very differently than if you like 302 00:14:55,890 --> 00:14:56,900 pizzas a lot. 303 00:14:56,900 --> 00:14:59,610 So it's indicative of sort of your potential utility, but 304 00:14:59,610 --> 00:15:01,160 not your actual well-being. 305 00:15:01,160 --> 00:15:02,920 But now that's a great segue to the next step. 306 00:15:02,920 --> 00:15:06,395 Let's put that together and talk about constrained choice. 307 00:15:11,650 --> 00:15:13,820 Which is now, let's put together-- 308 00:15:13,820 --> 00:15:16,200 we know what your preferences are, we've mathematically 309 00:15:16,200 --> 00:15:18,820 represented those by utility function. 310 00:15:18,820 --> 00:15:21,600 We know what your budget set is, we've mathematically 311 00:15:21,600 --> 00:15:24,410 represented that based on your income and prices. 312 00:15:24,410 --> 00:15:26,060 Now let's put them together and talk about 313 00:15:26,060 --> 00:15:28,580 how you make choices. 314 00:15:28,580 --> 00:15:34,940 And the basic question you want to ask is, what's the 315 00:15:34,940 --> 00:15:39,050 highest utility you can achieve given the constraints 316 00:15:39,050 --> 00:15:41,880 your budget constraints put on you? 317 00:15:41,880 --> 00:15:43,820 Or, graphically-- 318 00:15:43,820 --> 00:15:46,110 so let's say you wanted to understand this intuitively, 319 00:15:46,110 --> 00:15:47,530 graphically, and mathematically. 320 00:15:47,530 --> 00:15:51,120 Intuitively the idea is quite simple, I think, which is 321 00:15:51,120 --> 00:15:55,775 just, what's the most you can have given the constraints 322 00:15:55,775 --> 00:15:57,170 that are placed on you? 323 00:15:57,170 --> 00:16:00,010 Graphically, we represent that as asking, what is the 324 00:16:00,010 --> 00:16:02,640 furthest out indifference curve you can achieve? 325 00:16:02,640 --> 00:16:04,080 Because remember, more is better. 326 00:16:04,080 --> 00:16:06,260 Indifference curves that are further out make you happier. 327 00:16:06,260 --> 00:16:08,190 So what's the furthest out indifference curve that you 328 00:16:08,190 --> 00:16:11,950 can achieve given your budget constraint? 329 00:16:11,950 --> 00:16:14,260 So to do that, let's actually do an example. 330 00:16:14,260 --> 00:16:17,250 Let's imagine, as last time, your utility is the square 331 00:16:17,250 --> 00:16:19,640 root of pizza times movies. 332 00:16:19,640 --> 00:16:22,050 Once again, this has no fundamental meaning, it's just 333 00:16:22,050 --> 00:16:25,080 a mathematical representation of your preferences. 334 00:16:25,080 --> 00:16:27,310 So your preferences are mathematically represented by 335 00:16:27,310 --> 00:16:29,450 utility equals square root of pizza times movies. 336 00:16:29,450 --> 00:16:31,330 And let's have the same budget constraint 337 00:16:31,330 --> 00:16:32,120 that we have up here. 338 00:16:32,120 --> 00:16:38,660 Income is $96, price of movies is $8, price of pizza is $16. 339 00:16:38,660 --> 00:16:41,300 Now let's go to the next graph. 340 00:16:41,300 --> 00:16:43,410 Figure 5-4. 341 00:16:43,410 --> 00:16:46,570 What this does is put together our indifference curve 342 00:16:46,570 --> 00:16:49,670 analysis with our budget constraint analysis. 343 00:16:49,670 --> 00:16:50,680 It's a little complicated. 344 00:16:50,680 --> 00:16:58,140 The budget constraint line is the vertical line running from 345 00:16:58,140 --> 00:17:01,340 a y-intercept of six to an x-intercept of 12. 346 00:17:01,340 --> 00:17:05,058 The-- not the vertical line, the straight line running from 347 00:17:05,058 --> 00:17:07,740 a y-intercept of six to an x-intercept of 12. 348 00:17:07,740 --> 00:17:08,720 That's your budget constraint. 349 00:17:08,720 --> 00:17:10,369 We saw that before. 350 00:17:10,369 --> 00:17:13,290 Then we have here a series of indifference curves. 351 00:17:13,290 --> 00:17:15,440 These curves are drawn-- these are a mathematical 352 00:17:15,440 --> 00:17:18,230 representative of this utility function. 353 00:17:18,230 --> 00:17:21,280 These are points among which you're indifferent if you have 354 00:17:21,280 --> 00:17:22,920 that utility function. 355 00:17:22,920 --> 00:17:26,079 And what we see is that the best you can do is to choose 356 00:17:26,079 --> 00:17:32,620 point D. Point D, with six movies and three pizzas-- 357 00:17:32,620 --> 00:17:39,070 OK, that should be p on the y-axis, not C. It should be 358 00:17:39,070 --> 00:17:41,600 movies on the x-axis and pizzas on the y-axis. 359 00:17:41,600 --> 00:17:44,130 That should be p on the y-axis. 360 00:17:44,130 --> 00:17:49,170 The best you can do is to choose a point D. 361 00:17:49,170 --> 00:17:50,470 Now, to see that. 362 00:17:50,470 --> 00:17:51,790 And that gives utility. 363 00:17:51,790 --> 00:17:53,820 What's the value of your utility at point D? 364 00:17:53,820 --> 00:17:55,890 We understand value's meaningless, but just so we 365 00:17:55,890 --> 00:18:00,096 can compare, what's the value of your utility at point D? 366 00:18:00,096 --> 00:18:02,620 The square root of 18. 367 00:18:02,620 --> 00:18:05,760 The value of utility is the square root of 6 times 3, 368 00:18:05,760 --> 00:18:13,890 which is the square root of 18. 369 00:18:13,890 --> 00:18:17,720 Which is going to be square root of two, or three times 370 00:18:17,720 --> 00:18:19,500 square root of two, but we'll just call it square root of 18 371 00:18:19,500 --> 00:18:22,090 for comparison. 372 00:18:22,090 --> 00:18:25,990 Now, let's talk about why that's the best point for you. 373 00:18:25,990 --> 00:18:27,470 Let's think about some alternative points. 374 00:18:27,470 --> 00:18:29,950 For instance, why is that better than point E? 375 00:18:33,460 --> 00:18:35,622 Somebody raise their hand and tell me, why is point D better 376 00:18:35,622 --> 00:18:36,680 than point E? 377 00:18:36,680 --> 00:18:36,900 Yeah? 378 00:18:36,900 --> 00:18:38,870 AUDIENCE: E is unattainable with your budget. 379 00:18:38,870 --> 00:18:40,910 PROFESSOR: E would be better, that'd be great. 380 00:18:40,910 --> 00:18:45,270 We'd love eight movies and four pizzas, but 381 00:18:45,270 --> 00:18:46,560 we can't reach it. 382 00:18:46,560 --> 00:18:47,710 So E's unattainable. 383 00:18:47,710 --> 00:18:51,170 Why is it better than point A? 384 00:18:51,170 --> 00:18:53,160 Point A you can afford. 385 00:18:53,160 --> 00:18:55,660 So why's point E better than point A? 386 00:18:55,660 --> 00:18:56,890 You could afford point A just like you can 387 00:18:56,890 --> 00:18:58,960 afford point D. Yeah? 388 00:18:58,960 --> 00:19:02,180 AUDIENCE: Because the utility's only root 10. 389 00:19:02,180 --> 00:19:02,980 PROFESSOR: Because what? 390 00:19:02,980 --> 00:19:04,700 AUDIENCE: It's only root 10. 391 00:19:04,700 --> 00:19:06,350 PROFESSOR: Yes, exactly, because the utilitity's only 392 00:19:06,350 --> 00:19:08,140 the square root of 10. 393 00:19:08,140 --> 00:19:11,650 You're on a lower indifference curve at point A. So it's true 394 00:19:11,650 --> 00:19:14,110 you could afford point A, but you're on a lower 395 00:19:14,110 --> 00:19:14,795 indifference curve. 396 00:19:14,795 --> 00:19:17,590 Your utility's a lower value, it's only square root of 10. 397 00:19:17,590 --> 00:19:22,420 So point A is dominated by point D. What about point C? 398 00:19:22,420 --> 00:19:28,050 Well, point C you have the same-- 399 00:19:28,050 --> 00:19:31,410 point C is just an inward shift from point D, but here 400 00:19:31,410 --> 00:19:32,530 that's a dominated choice. 401 00:19:32,530 --> 00:19:34,480 Once again your utility's lower. 402 00:19:34,480 --> 00:19:38,220 It's the square root of 4.5 times 2.2. 403 00:19:38,220 --> 00:19:42,690 And basically that's dominated because you could afford more. 404 00:19:42,690 --> 00:19:46,200 So basically, the point is that the point which will make 405 00:19:46,200 --> 00:19:49,040 you happiest is the point at which your indifference curve 406 00:19:49,040 --> 00:19:52,490 is tangent to the budget constraint. 407 00:19:52,490 --> 00:19:55,440 Because that is the point of the farthest out indifference 408 00:19:55,440 --> 00:19:57,750 curve that you can reach given your budget constraint. 409 00:19:57,750 --> 00:20:00,610 The tangency of the indifference curve and the 410 00:20:00,610 --> 00:20:03,360 budget constraint is the point which makes you best off given 411 00:20:03,360 --> 00:20:04,985 your available budget and the available prices. 412 00:20:07,630 --> 00:20:11,330 And that's the point where the slope of the indifference 413 00:20:11,330 --> 00:20:14,990 curve equals the slope of the budget constraint. 414 00:20:14,990 --> 00:20:17,490 The tangency is the point where the slope of the 415 00:20:17,490 --> 00:20:19,700 indifference curve equals the slope of the budget 416 00:20:19,700 --> 00:20:22,110 constraint. 417 00:20:22,110 --> 00:20:25,570 Or, more relevantly-- 418 00:20:25,570 --> 00:20:26,280 OK, let me stop there. 419 00:20:26,280 --> 00:20:27,850 That's the graphic intuition. 420 00:20:27,850 --> 00:20:29,410 With a sloping indifference curve because the slope of the 421 00:20:29,410 --> 00:20:31,850 budget constraint is the optimum, because by 422 00:20:31,850 --> 00:20:34,640 definition, that is the point of the furthest out 423 00:20:34,640 --> 00:20:37,580 indifference curve you can reach given your budget. 424 00:20:37,580 --> 00:20:40,540 The point of tangency is the point of equal slopes. 425 00:20:40,540 --> 00:20:44,520 Are there questions about the graphical analysis here? 426 00:20:44,520 --> 00:20:46,270 This is very, very important, so. 427 00:20:46,270 --> 00:20:46,950 Yeah? 428 00:20:46,950 --> 00:20:48,620 AUDIENCE: This is sort of about the graphical analysis, 429 00:20:48,620 --> 00:20:51,070 but if it only matters in terms of the ordinal values of 430 00:20:51,070 --> 00:20:55,858 the utility function and p and M are always positive, does it 431 00:20:55,858 --> 00:20:57,230 matter if you got rid of the square root? 432 00:20:57,230 --> 00:20:58,210 Would anything change if it was u equals pm? 433 00:20:58,210 --> 00:21:01,700 Because the the marginal rate of substitution, 434 00:21:01,700 --> 00:21:04,080 transformation, all that would still be the same, right? 435 00:21:08,180 --> 00:21:09,920 PROFESSOR: In this particular example, it would not. 436 00:21:09,920 --> 00:21:11,390 So actually, you're asking a great question. 437 00:21:11,390 --> 00:21:15,720 Because it's ordinal, you can typically do transformations 438 00:21:15,720 --> 00:21:18,220 for the ranking of bundles. 439 00:21:18,220 --> 00:21:20,290 You will always get the same ranking with a monotone 440 00:21:20,290 --> 00:21:22,260 transformation of the utility function. 441 00:21:22,260 --> 00:21:23,510 That's exactly right. 442 00:21:27,770 --> 00:21:29,580 Later in the course, we'll show different ways why the 443 00:21:29,580 --> 00:21:31,940 functional form matters, and I'll show you why I did square 444 00:21:31,940 --> 00:21:34,780 root, because it's going to turn out that 445 00:21:34,780 --> 00:21:36,930 that's going to matter. 446 00:21:36,930 --> 00:21:39,790 But for other things-- but for the ranking 447 00:21:39,790 --> 00:21:40,530 bundles, you're right. 448 00:21:40,530 --> 00:21:42,610 The ranking of bundles is consistent with the 449 00:21:42,610 --> 00:21:43,860 transformation. 450 00:21:45,970 --> 00:21:47,170 So that's the graphical. 451 00:21:47,170 --> 00:21:49,300 Now let's come to the mathematical 452 00:21:49,300 --> 00:21:51,080 derivation of this. 453 00:21:51,080 --> 00:21:53,010 So let's talk about the mathematics of utility 454 00:21:53,010 --> 00:21:53,970 maximization. 455 00:21:53,970 --> 00:21:55,790 Now what I'm going to do here is, I'm going to do this sort 456 00:21:55,790 --> 00:21:57,680 of casually, as is my wont. 457 00:21:57,680 --> 00:22:00,730 Friday in section, you're going to work on the 458 00:22:00,730 --> 00:22:04,240 underlying calculus that lies behind the mathematics that 459 00:22:04,240 --> 00:22:07,640 I'm going to present here. 460 00:22:07,640 --> 00:22:13,020 Now, let's talk about what it means that 461 00:22:13,020 --> 00:22:14,700 these slopes are equal. 462 00:22:14,700 --> 00:22:17,610 Well, remember, what is-- does anyone remember what the slope 463 00:22:17,610 --> 00:22:18,590 of the indifference curve is? 464 00:22:18,590 --> 00:22:20,150 What do we call the slope of the indifference curve? 465 00:22:20,150 --> 00:22:20,430 Yeah? 466 00:22:20,430 --> 00:22:21,490 AUDIENCE: The MRS. 467 00:22:21,490 --> 00:22:23,190 PROFESSOR: The MRS. The slope of the indifference curve is 468 00:22:23,190 --> 00:22:26,810 the marginal rate of substitution. 469 00:22:26,810 --> 00:22:30,210 Which is defined as what? 470 00:22:30,210 --> 00:22:34,000 What is the marginal rate of substitution? 471 00:22:34,000 --> 00:22:35,450 The ratio of what? 472 00:22:35,450 --> 00:22:37,090 AUDIENCE: [INAUDIBLE] 473 00:22:37,090 --> 00:22:38,982 PROFESSOR: No, the marginal rate of substitution. 474 00:22:38,982 --> 00:22:41,290 This is just about preferences. 475 00:22:41,290 --> 00:22:43,125 What's the marginal rate of substitution defined as? 476 00:22:43,125 --> 00:22:44,310 It's the ratio of what to what? 477 00:22:44,310 --> 00:22:44,810 Yeah? 478 00:22:44,810 --> 00:22:46,074 AUDIENCE: The amount of one good you have to get to give 479 00:22:46,074 --> 00:22:47,310 up a unit of the other good. 480 00:22:47,310 --> 00:22:48,810 PROFESSOR: I'm sorry? 481 00:22:48,810 --> 00:22:49,872 AUDIENCE: The amount of one good you have to get to give 482 00:22:49,872 --> 00:22:51,310 up a unit of the other good. 483 00:22:51,310 --> 00:22:52,450 PROFESSOR: So graphically that's what 484 00:22:52,450 --> 00:22:53,665 it's defined as, exactly. 485 00:22:53,665 --> 00:22:55,710 It's the slope of the indifference curve. 486 00:22:55,710 --> 00:22:57,400 Mathematically, what was it? 487 00:22:57,400 --> 00:22:59,720 What was it in terms of utility? 488 00:22:59,720 --> 00:23:00,440 Does anyone remember? 489 00:23:00,440 --> 00:23:00,680 Yeah. 490 00:23:00,680 --> 00:23:02,190 AUDIENCE: The ratio of the partials. 491 00:23:02,190 --> 00:23:05,000 PROFESSOR: Ratio of the marginal utilities. 492 00:23:05,000 --> 00:23:08,210 In particular, it's the negative of the marginal 493 00:23:08,210 --> 00:23:11,110 utility of movies over the marginal utility of pizza. 494 00:23:11,110 --> 00:23:12,622 Remember, it's the negative of the marginal utility of the 495 00:23:12,622 --> 00:23:14,950 x-axis over the marginal utility of the y-axis. 496 00:23:14,950 --> 00:23:17,630 So marginal rate of substitution is the rate at 497 00:23:17,630 --> 00:23:21,650 which you're willing to substitute between movies and 498 00:23:21,650 --> 00:23:25,700 pizza, which is a function of your marginal utilities. 499 00:23:25,700 --> 00:23:30,360 If your marginal utility for movies is very high, then you 500 00:23:30,360 --> 00:23:31,560 need a lot of pizzas. 501 00:23:31,560 --> 00:23:33,190 Then you wouldn't trade a movie unless you get a lot of 502 00:23:33,190 --> 00:23:34,450 pizza for it. 503 00:23:34,450 --> 00:23:36,930 If your marginal utility of movies is very low, you'd be 504 00:23:36,930 --> 00:23:38,630 happy to give up a movie even for a small 505 00:23:38,630 --> 00:23:40,970 fraction of a pizza. 506 00:23:40,970 --> 00:23:42,400 So that's the marginal rate of substitution. 507 00:23:42,400 --> 00:23:44,370 That's about preferences only. 508 00:23:44,370 --> 00:23:48,170 At the same time, we're saying that that marginal rate of 509 00:23:48,170 --> 00:23:53,060 substitution is equal to-- 510 00:23:53,060 --> 00:23:56,610 this slope is equal to the slope of the budget 511 00:23:56,610 --> 00:23:57,570 constraint. 512 00:23:57,570 --> 00:24:00,200 Well, the slope of the budget constraint we call the 513 00:24:00,200 --> 00:24:02,630 marginal rate of transformation, which is the 514 00:24:02,630 --> 00:24:03,880 price ratio. 515 00:24:08,960 --> 00:24:11,940 The slope of the budget constraint is the negative of 516 00:24:11,940 --> 00:24:12,610 the price ratio. 517 00:24:12,610 --> 00:24:15,900 That's where you were sort of one step ahead of us here. 518 00:24:15,900 --> 00:24:20,320 So preferences give us this, the marginal rate of 519 00:24:20,320 --> 00:24:21,410 substitution. 520 00:24:21,410 --> 00:24:23,810 The mechanics of the market give us the marginal rate of 521 00:24:23,810 --> 00:24:25,310 transformation. 522 00:24:25,310 --> 00:24:31,390 And utility maximization gives us that those are equal, 523 00:24:31,390 --> 00:24:33,100 because they're equal at that tangency. 524 00:24:40,180 --> 00:24:43,910 At that tangency is where you get to the highest possible 525 00:24:43,910 --> 00:24:46,490 indifference curve. 526 00:24:46,490 --> 00:24:52,790 So at the optimum, you get that the ratio of marginal 527 00:24:52,790 --> 00:24:54,400 utility equals the ratio of prices. 528 00:24:54,400 --> 00:24:57,360 Now, I want to try to see you understand this a bit more 529 00:24:57,360 --> 00:25:00,170 intuitively, given this mathematics. 530 00:25:00,170 --> 00:25:02,590 The way I like to think about this is, think about the ratio 531 00:25:02,590 --> 00:25:07,170 of the marginal utilities as the marginal benefit. 532 00:25:07,170 --> 00:25:13,630 So it's the benefit of another movie in terms of pizza. 533 00:25:13,630 --> 00:25:15,560 The marginal rate of substitution is the benefit of 534 00:25:15,560 --> 00:25:16,840 another movie in terms of pizza. 535 00:25:16,840 --> 00:25:19,340 It's how much you like that next movie relative to how 536 00:25:19,340 --> 00:25:20,590 much you like that next pizza. 537 00:25:23,605 --> 00:25:26,020 The marginal rate of transformation, the cost, is 538 00:25:26,020 --> 00:25:28,710 the price of that next movie relative to the price of that 539 00:25:28,710 --> 00:25:30,350 next pizza. 540 00:25:30,350 --> 00:25:34,500 So what we're saying here is we're setting benefits equal 541 00:25:34,500 --> 00:25:37,260 to the costs. 542 00:25:37,260 --> 00:25:40,410 In particular, we're setting marginal benefits equal to 543 00:25:40,410 --> 00:25:41,740 marginal cost. 544 00:25:41,740 --> 00:25:45,690 The marginal benefit, the benefit to that next movie in 545 00:25:45,690 --> 00:25:50,540 terms of pizza, has got to be equal to the marginal cost, 546 00:25:50,540 --> 00:25:51,820 the cost to you in terms of that next 547 00:25:51,820 --> 00:25:53,230 movie in terms of pizza. 548 00:25:53,230 --> 00:25:56,415 And this notion that the optimum will be where marginal 549 00:25:56,415 --> 00:25:58,610 benefit equals marginal cost will pervade 550 00:25:58,610 --> 00:25:59,910 through the whole course. 551 00:25:59,910 --> 00:26:02,670 When we do firm maximization, it'll be the same thing. 552 00:26:02,670 --> 00:26:07,690 Any maximization we'll do in this course, any optimization, 553 00:26:07,690 --> 00:26:10,460 will be about equating these margins. 554 00:26:10,460 --> 00:26:14,180 Setting the marginal benefits equal to marginal costs. 555 00:26:14,180 --> 00:26:16,500 Now, this is different than benefits equals cost, because 556 00:26:16,500 --> 00:26:18,850 it's about the next unit. 557 00:26:18,850 --> 00:26:22,205 It's saying, how do we feel about that next movie compared 558 00:26:22,205 --> 00:26:24,150 to the price of that next movie. 559 00:26:24,150 --> 00:26:26,100 Now, prices here we have being constant. 560 00:26:26,100 --> 00:26:28,310 You could imagine prices of movies changing as you see 561 00:26:28,310 --> 00:26:29,710 more, but that gets complicated. 562 00:26:29,710 --> 00:26:30,600 We'll worry about that later. 563 00:26:30,600 --> 00:26:32,030 For now, the price is constant. 564 00:26:32,030 --> 00:26:34,300 But the marginal utilities are not constant. 565 00:26:34,300 --> 00:26:37,980 Marginal utilities are obviously changing the more 566 00:26:37,980 --> 00:26:41,130 moves you see. 567 00:26:41,130 --> 00:26:42,830 Once again, with intuition, you have to 568 00:26:42,830 --> 00:26:44,240 develop your own intuition. 569 00:26:44,240 --> 00:26:46,220 The way that I like to think about this intuitively is to 570 00:26:46,220 --> 00:26:49,590 actually rewrite this a little bit, and rewrite it as saying 571 00:26:49,590 --> 00:26:52,560 that the marginal utility of movies over the price of 572 00:26:52,560 --> 00:26:56,390 movies equals the marginal utility of pizza over the 573 00:26:56,390 --> 00:26:57,640 price of pizza. 574 00:27:00,390 --> 00:27:03,470 At the optimum, this'll be true. 575 00:27:03,470 --> 00:27:06,340 I like this because to me this term sort of says, look, the 576 00:27:06,340 --> 00:27:09,845 bang for the buck has to be the same across all goods. 577 00:27:12,470 --> 00:27:16,110 For each dollar of movie expenditure, what's it buying? 578 00:27:16,110 --> 00:27:18,870 What's that next dollar of movie expenditure buying you? 579 00:27:18,870 --> 00:27:20,780 This is saying, what's that next dollar of pizza 580 00:27:20,780 --> 00:27:22,230 expenditure buying you? 581 00:27:22,230 --> 00:27:23,720 And they've got to be equal. 582 00:27:23,720 --> 00:27:26,120 If the next dollar of movie expenditure buys you a lot 583 00:27:26,120 --> 00:27:29,720 more happiness than the next dollar of pizza expenditure, 584 00:27:29,720 --> 00:27:31,180 then you're not at the right place. 585 00:27:31,180 --> 00:27:32,985 You should shift your money and spend more on movies and 586 00:27:32,985 --> 00:27:34,830 less on pizza. 587 00:27:34,830 --> 00:27:38,080 If the next dollar of pizza expenditure buys you a lot 588 00:27:38,080 --> 00:27:39,610 more happiness than the next dollar of movie expenditure, 589 00:27:39,610 --> 00:27:41,000 then you're not in the right place either. 590 00:27:41,000 --> 00:27:45,200 You should see fewer movies and buy more pizza. 591 00:27:45,200 --> 00:27:50,720 So basically, it's where the marginal benefit to you-- 592 00:27:50,720 --> 00:27:53,600 the bang for the buck of that next movie is the same as the 593 00:27:53,600 --> 00:27:57,830 bang for the buck of that next pizza. 594 00:27:57,830 --> 00:28:01,580 So to see this, let's go back to figure 5-4 and let's 595 00:28:01,580 --> 00:28:04,230 actually think through the mathematics of a couple of 596 00:28:04,230 --> 00:28:07,110 these points. 597 00:28:07,110 --> 00:28:20,550 Let's take point A. At point A, you have two pizzas and 598 00:28:20,550 --> 00:28:21,820 five movies. 599 00:28:21,820 --> 00:28:28,990 So pizza equals two, movies equals five at point A. So 600 00:28:28,990 --> 00:28:35,230 utility is equal to square root of 10 at point A. 601 00:28:35,230 --> 00:28:39,390 Now, in particular, your marginal utility for pizzas at 602 00:28:39,390 --> 00:28:40,360 that point-- 603 00:28:40,360 --> 00:28:41,680 what's the marginal utility for pizzas? 604 00:28:41,680 --> 00:28:42,760 Well, we can differentiate. 605 00:28:42,760 --> 00:28:46,630 That's the derivative of the utility function with respect 606 00:28:46,630 --> 00:28:50,230 to prices, du/dp. 607 00:28:50,230 --> 00:28:56,710 Which is going to be 0.5 times movies over the square root of 608 00:28:56,710 --> 00:29:02,540 p times m, which at these values is going to be one over 609 00:29:02,540 --> 00:29:05,650 the square root of 10. 610 00:29:05,650 --> 00:29:08,740 That's your marginal utility of pizzas. 611 00:29:08,740 --> 00:29:14,350 Your marginal utility of movies is going to be du/dm, 612 00:29:14,350 --> 00:29:21,020 which is going to be 0.5 times p over square root of p times 613 00:29:21,020 --> 00:29:31,740 m, which is going to be 2.5 over square root of 10. 614 00:29:31,740 --> 00:29:35,990 So the marginal rate of substitution between 615 00:29:35,990 --> 00:29:40,350 these two is 2.5. 616 00:29:40,350 --> 00:29:47,130 The marginal rate of substitution, 2.5. 617 00:29:47,130 --> 00:29:49,570 What does that mean intuitively? 618 00:29:49,570 --> 00:29:51,040 Can someone tell me what that means intuitively, the 619 00:29:51,040 --> 00:29:53,070 marginal rate of substitution is 2.5? 620 00:29:53,070 --> 00:29:54,680 What does that mean? 621 00:29:54,680 --> 00:29:56,580 Someone explain that like you'd explain it to someone 622 00:29:56,580 --> 00:29:58,330 who's speaking English. 623 00:29:58,330 --> 00:29:59,220 What does it mean that the marginal rate of 624 00:29:59,220 --> 00:30:02,350 substitution is 2.5? 625 00:30:02,350 --> 00:30:02,890 Yeah? 626 00:30:02,890 --> 00:30:06,260 AUDIENCE: You'd give up one pizza for 2.5 movies. 627 00:30:06,260 --> 00:30:06,640 Yes. 628 00:30:06,640 --> 00:30:07,820 No, actually, the opposite. 629 00:30:07,820 --> 00:30:11,420 You'd give up two and 1/2 pizzas-- 630 00:30:11,420 --> 00:30:14,746 the marginal rate of substitution is 2.5-- 631 00:30:17,662 --> 00:30:19,620 no, that's right. 632 00:30:19,620 --> 00:30:23,320 You would give up 2.5-- 633 00:30:23,320 --> 00:30:25,440 one second, let's make sure I have this right. 634 00:30:29,510 --> 00:30:36,305 Right, so you would give up one pizza to see 2 and 1/2-- 635 00:30:36,305 --> 00:30:37,580 no, it's the other way around. 636 00:30:43,040 --> 00:30:45,060 You're getting a lot of pizza and not enough movies. 637 00:30:45,060 --> 00:30:47,640 So you would give up two and 1/2 pizzas to 638 00:30:47,640 --> 00:30:50,890 get one more movie. 639 00:30:50,890 --> 00:30:52,310 This is confusing, OK? 640 00:30:52,310 --> 00:30:55,000 You'd give up two and 1/2 pizzas to get one more movie. 641 00:30:55,000 --> 00:30:57,070 That's what it means. 642 00:30:57,070 --> 00:30:59,700 You would give up two and 1/2 pizzas to see one more movie, 643 00:30:59,700 --> 00:31:01,100 and why is that? 644 00:31:01,100 --> 00:31:03,150 Why at a point like A would you give up two and 1/2 pizzas 645 00:31:03,150 --> 00:31:04,120 to see one more movie? 646 00:31:04,120 --> 00:31:04,597 Yeah? 647 00:31:04,597 --> 00:31:06,982 AUDIENCE: Well, if you just look at the line tangent to 648 00:31:06,982 --> 00:31:09,844 the indifference curve at A, it's really 649 00:31:09,844 --> 00:31:11,280 not a downward slope. 650 00:31:11,280 --> 00:31:12,970 PROFESSOR: It's really steep, which means what? 651 00:31:12,970 --> 00:31:15,850 AUDIENCE: Which means you get a lot more benefit--like you 652 00:31:15,850 --> 00:31:17,530 don't care if you give up a lot of 653 00:31:17,530 --> 00:31:19,700 pizzas to see more movies. 654 00:31:19,700 --> 00:31:20,820 PROFESSOR: Exactly. 655 00:31:20,820 --> 00:31:22,470 Actually, that's a great way to bring the graphics and the 656 00:31:22,470 --> 00:31:23,830 intuition together. 657 00:31:23,830 --> 00:31:26,990 Here's thinking of it intuitively. 658 00:31:26,990 --> 00:31:29,670 I'm getting a lot of pizza at point A. I'm not 659 00:31:29,670 --> 00:31:31,970 getting a lot of movies. 660 00:31:31,970 --> 00:31:34,990 So I would happily give up a lot of pizza 661 00:31:34,990 --> 00:31:36,790 to get my next movie. 662 00:31:36,790 --> 00:31:39,210 What you pointed out is the tie to the graphics here. 663 00:31:39,210 --> 00:31:43,940 The indifference curve is very steep at that point through A. 664 00:31:43,940 --> 00:31:48,310 A steep indifference curve in that way means I don't really 665 00:31:48,310 --> 00:31:53,150 care a whole lot at this point about how many pizzas I get, 666 00:31:53,150 --> 00:31:56,650 but I care a lot about getting more movies. 667 00:31:56,650 --> 00:32:02,010 So at a point like A where it's very steep, you are 668 00:32:02,010 --> 00:32:05,960 willing to give up two and 1/2 pizzas to see a movie. 669 00:32:05,960 --> 00:32:07,050 But what do you have to give up? 670 00:32:07,050 --> 00:32:08,250 What's the market telling you you have to 671 00:32:08,250 --> 00:32:11,370 give up to see a movie? 672 00:32:11,370 --> 00:32:12,910 How much pizza do you actually have to give up to see a movie 673 00:32:12,910 --> 00:32:14,340 in practice? 674 00:32:14,340 --> 00:32:16,720 You're willing to give up two and 1/2 pizzas to see a movie, 675 00:32:16,720 --> 00:32:18,420 but how many pizzas do you actually have to give up? 676 00:32:18,420 --> 00:32:19,350 AUDIENCE: 1/2. 677 00:32:19,350 --> 00:32:21,330 PROFESSOR: 1/2 a pizza to see a movie. 678 00:32:21,330 --> 00:32:23,140 So that can't be the optimum. 679 00:32:23,140 --> 00:32:25,160 You're willing to give up two and 1/2 pizzas to see a movie, 680 00:32:25,160 --> 00:32:27,710 but you only have to give up 1/2 a pizza to see a movie. 681 00:32:27,710 --> 00:32:29,890 So you can't be at the right place. 682 00:32:29,890 --> 00:32:33,260 You should be changing your consumption bundle. 683 00:32:33,260 --> 00:32:35,500 You should be changing your consumption bundle, because 684 00:32:35,500 --> 00:32:38,530 the market is only asking for 1/2 a pizza to see a movie, 685 00:32:38,530 --> 00:32:39,846 but you're willing to give up two and 1/2 686 00:32:39,846 --> 00:32:41,090 pizzas to see a movie. 687 00:32:41,090 --> 00:32:45,470 So at a point like A, you're clearly not at the optimum. 688 00:32:45,470 --> 00:32:48,550 Because you are willing to make a trade. 689 00:32:48,550 --> 00:32:50,980 Remember, we talked about-- we can go all the way back to the 690 00:32:50,980 --> 00:32:52,170 first lecture. 691 00:32:52,170 --> 00:32:55,690 The key point was-- the first or second lecture-- 692 00:32:55,690 --> 00:32:58,390 inefficiency happens when trades aren't 693 00:32:58,390 --> 00:33:01,020 made that people value. 694 00:33:01,020 --> 00:33:03,300 Here's a trade that you value. 695 00:33:03,300 --> 00:33:06,030 You're willing to give up two and 1/2 pizzas to see a movie. 696 00:33:06,030 --> 00:33:08,590 The market only wants 1/2 a pizza to see a movie. 697 00:33:08,590 --> 00:33:10,550 You're not making a trade you value, so that's not the 698 00:33:10,550 --> 00:33:12,200 efficient outcome. 699 00:33:12,200 --> 00:33:15,740 Likewise, let's do the same mathematics at point B. Well, 700 00:33:15,740 --> 00:33:19,390 at point B, if you do the math and work it out, you see that 701 00:33:19,390 --> 00:33:22,190 the marginal utility of pizza is five over 702 00:33:22,190 --> 00:33:24,340 square root of ten. 703 00:33:24,340 --> 00:33:26,160 The marginal utility of movies is 0.5 over the 704 00:33:26,160 --> 00:33:27,360 square root of 10. 705 00:33:27,360 --> 00:33:30,250 So the MRS is 0.1. 706 00:33:30,250 --> 00:33:33,960 At this point, you'd only be willing to give up 0.1 pizzas 707 00:33:33,960 --> 00:33:34,730 to see a movie. 708 00:33:34,730 --> 00:33:36,835 At a point like B, the indifference 709 00:33:36,835 --> 00:33:38,720 curve is very flat. 710 00:33:38,720 --> 00:33:41,340 You're only willing to give up 0.1 pizzas to see a movie. 711 00:33:44,590 --> 00:33:49,170 But remember, the market is willing to say, look-- 712 00:33:49,170 --> 00:33:51,810 you can flip it around, the market's willing to say, look, 713 00:33:51,810 --> 00:33:53,060 you can get a movie. 714 00:33:57,235 --> 00:33:59,670 You're only willing to give up 0.1 pizzas to see a movie. 715 00:33:59,670 --> 00:34:02,720 Well, that means clearly that you have too many movies and 716 00:34:02,720 --> 00:34:04,190 not enough pizza. 717 00:34:04,190 --> 00:34:12,010 You're clearly at that point happy to say, wow, you mean 718 00:34:12,010 --> 00:34:15,730 that I can gain a whole pizza by just giving up two movies? 719 00:34:15,730 --> 00:34:19,850 Heck, I'd be willing to give up 10 movies to get a pizza. 720 00:34:19,850 --> 00:34:21,650 At the point I'm at right there, I'd be willing to give 721 00:34:21,650 --> 00:34:23,520 up 10 movies to get a pizza. 722 00:34:23,520 --> 00:34:25,590 You're telling me we only have to give up two 723 00:34:25,590 --> 00:34:26,239 movies to get a pizza? 724 00:34:26,239 --> 00:34:26,960 Great. 725 00:34:26,960 --> 00:34:28,280 I'm going to do that trade. 726 00:34:28,280 --> 00:34:32,380 I'm going to move back towards point D. So that's why this 727 00:34:32,380 --> 00:34:36,719 idea of what you're willing to do, which is the MRS, and what 728 00:34:36,719 --> 00:34:41,170 the market's making you do, you want to equilibrate those 729 00:34:41,170 --> 00:34:44,489 to decide how much you want to consume. 730 00:34:44,489 --> 00:34:47,570 Now, obviously a point like-- 731 00:34:47,570 --> 00:34:51,710 let's talk about point C. Point C is interesting, 732 00:34:51,710 --> 00:34:55,070 because at point C, what's true? 733 00:34:55,070 --> 00:34:57,139 The marginal rate of substitution is equal to the 734 00:34:57,139 --> 00:35:00,460 marginal rate of transformation at point C. The 735 00:35:00,460 --> 00:35:02,630 slope of the indifference curve and the budget 736 00:35:02,630 --> 00:35:05,980 constraint are equal. 737 00:35:05,980 --> 00:35:08,160 That's why you have to check two conditions for 738 00:35:08,160 --> 00:35:09,330 optimization. 739 00:35:09,330 --> 00:35:11,620 First of all, those slopes have to be equal. 740 00:35:11,620 --> 00:35:14,660 Second of all, you've got to spend all your money. 741 00:35:14,660 --> 00:35:17,040 So it's true there's a whole host of points-- in fact, 742 00:35:17,040 --> 00:35:21,330 there's a vector running through CDE, all which are 743 00:35:21,330 --> 00:35:25,520 points where the margin rate of substitution equals the 744 00:35:25,520 --> 00:35:26,880 margin rate of transformation. 745 00:35:26,880 --> 00:35:30,630 But only D is optimal, because you also have to 746 00:35:30,630 --> 00:35:31,770 remember more is better. 747 00:35:31,770 --> 00:35:33,700 You never want to leave money on the table. 748 00:35:33,700 --> 00:35:37,770 So the two conditions you have to meet is that you're at the 749 00:35:37,770 --> 00:35:42,190 point where your desired trade-off between pizzas and 750 00:35:42,190 --> 00:35:46,460 movies is the same as the market's, and where you're 751 00:35:46,460 --> 00:35:48,050 spending all your budget. 752 00:35:48,050 --> 00:35:49,890 And that's the optimum. 753 00:35:49,890 --> 00:35:51,140 OK, questions about that? 754 00:35:53,830 --> 00:35:56,820 So that's basically how we think about optimization. 755 00:35:56,820 --> 00:35:58,980 That's how we think about consumers making their 756 00:35:58,980 --> 00:36:02,940 decisions deciding between consuming pizzas and movies. 757 00:36:02,940 --> 00:36:05,490 Now, let's come back-- however, this is a particular 758 00:36:05,490 --> 00:36:07,190 case we've looked at. 759 00:36:07,190 --> 00:36:09,530 This is a case in particular where we've imposed that 760 00:36:09,530 --> 00:36:12,120 there's an interior solution. 761 00:36:12,120 --> 00:36:15,910 In fact, in practice you could end up in these kinds of 762 00:36:15,910 --> 00:36:18,560 choices with corner solutions. 763 00:36:18,560 --> 00:36:25,600 So let's take a look at the last figure, figure 5-5. 764 00:36:25,600 --> 00:36:31,480 We've chosen a case where your optimal bundle includes both 765 00:36:31,480 --> 00:36:32,730 pizza and movies. 766 00:36:37,080 --> 00:36:38,920 But you could imagine a situation where 767 00:36:38,920 --> 00:36:40,370 your optimal bundle-- 768 00:36:40,370 --> 00:36:43,945 and once again, that should be a p, not a c in figure 5-5, 769 00:36:43,945 --> 00:36:46,420 that should be p on the y-axis-- 770 00:36:46,420 --> 00:36:49,960 where your optimal bundle includes 771 00:36:49,960 --> 00:36:51,470 only one or the other. 772 00:36:51,470 --> 00:36:54,300 So this is a particular case-- we have the same budget line 773 00:36:54,300 --> 00:36:59,560 as before, which is you're trading off pizza and movies. 774 00:36:59,560 --> 00:37:02,860 You have an income of 96, the price of pizzas is 16, the 775 00:37:02,860 --> 00:37:04,460 price of movies is 8. 776 00:37:04,460 --> 00:37:06,400 So same budget line as before. 777 00:37:06,400 --> 00:37:09,040 But now your indifference curves look very different. 778 00:37:09,040 --> 00:37:12,750 Now your preferences are such that you've got these linear 779 00:37:12,750 --> 00:37:15,180 difference curves of the form I1, I2, I3. 780 00:37:17,720 --> 00:37:19,030 You've got these linear indifference curves. 781 00:37:19,030 --> 00:37:21,780 What that means is you've got-- 782 00:37:21,780 --> 00:37:25,930 these indifference curves mean that you have a constant rate 783 00:37:25,930 --> 00:37:28,580 at which you're willing to trade off pizza for movies. 784 00:37:28,580 --> 00:37:31,245 If we go back to figure 5.4, the rate at which you're 785 00:37:31,245 --> 00:37:33,450 willing to trade off pizza for movies changes. 786 00:37:33,450 --> 00:37:35,390 Your preferences are such that-- 787 00:37:35,390 --> 00:37:37,790 because the square root function as pointed out-- 788 00:37:37,790 --> 00:37:41,960 your preferences are such that you are willing to make 789 00:37:41,960 --> 00:37:44,040 different rates of trade at different amounts. 790 00:37:44,040 --> 00:37:47,430 In figure 5-5, your preferences are constant, no 791 00:37:47,430 --> 00:37:50,000 matter how many movies or pizzas you have. You're always 792 00:37:50,000 --> 00:37:56,850 willing to make that trade-off at the same rate. 793 00:37:56,850 --> 00:38:00,230 Well, in that case you can end up with a corner solution, 794 00:38:00,230 --> 00:38:10,370 where in fact, you're going to consume only six 795 00:38:10,370 --> 00:38:12,540 pizzas and no movies. 796 00:38:12,540 --> 00:38:13,580 And why is that? 797 00:38:13,580 --> 00:38:17,930 That's because this is a person who loves pizza 798 00:38:17,930 --> 00:38:18,630 relative to movies. 799 00:38:18,630 --> 00:38:21,460 It's a very flat indifference curve. 800 00:38:21,460 --> 00:38:24,520 They love pizza relative to movies. 801 00:38:24,520 --> 00:38:29,140 And they love pizza so much relative to movies that given 802 00:38:29,140 --> 00:38:31,950 the prices they face, they'll just go ahead and choose six 803 00:38:31,950 --> 00:38:35,380 pizzas and no movies. 804 00:38:35,380 --> 00:38:37,330 So that's a corner solution. 805 00:38:37,330 --> 00:38:39,330 So mathematically, as you'll go through a section on 806 00:38:39,330 --> 00:38:44,360 Friday, you're going to have to check for corner solutions. 807 00:38:44,360 --> 00:38:46,520 You may solve these problems and end up with negative 808 00:38:46,520 --> 00:38:49,640 quantities and be befuddled about what happens. 809 00:38:49,640 --> 00:38:52,030 Well, if an answer looks wrong, it is wrong. 810 00:38:52,030 --> 00:38:53,460 If you solve problems with negative quantities, that's 811 00:38:53,460 --> 00:38:55,670 probably because there's a corner solution to the 812 00:38:55,670 --> 00:38:59,330 problem, and actually the optimal quantity is to have 813 00:38:59,330 --> 00:39:01,230 zero of one thing and spend your entire budget on 814 00:39:01,230 --> 00:39:04,240 something else. 815 00:39:04,240 --> 00:39:05,490 Questions about that? 816 00:39:07,870 --> 00:39:15,700 So now let's think about applying this to the kinds of 817 00:39:15,700 --> 00:39:18,680 decisions that you all have to make. 818 00:39:18,680 --> 00:39:21,340 So I talked about this particular example of pizza 819 00:39:21,340 --> 00:39:23,270 and movies. 820 00:39:23,270 --> 00:39:27,500 And in fact, you might say, well, that's sort of 821 00:39:27,500 --> 00:39:29,150 unrealistic. 822 00:39:29,150 --> 00:39:33,120 Gee, I spend my budget on lots of things, 823 00:39:33,120 --> 00:39:33,960 and how do I do this? 824 00:39:33,960 --> 00:39:35,460 Well, in practice, what you'd have to do is you'd have to 825 00:39:35,460 --> 00:39:37,060 draw a multi-dimensional graph and solve a 826 00:39:37,060 --> 00:39:38,840 multi-dimensional problem. 827 00:39:38,840 --> 00:39:41,270 And that's a bear. 828 00:39:41,270 --> 00:39:44,080 But in practice, in fact, we can often think about breaking 829 00:39:44,080 --> 00:39:47,220 down the choices we make into pairs of choices. 830 00:39:47,220 --> 00:39:50,920 In practice, you could think about saying, look-- 831 00:39:50,920 --> 00:39:56,440 many people do what a lot of psychologists call mental 832 00:39:56,440 --> 00:40:06,400 accounting, where basically they say, look, yes, I have a 833 00:40:06,400 --> 00:40:08,550 whole budget and lots of things I can buy. 834 00:40:08,550 --> 00:40:10,810 But in fact, I like to think of my budget in sort of 835 00:40:10,810 --> 00:40:11,360 subcategories. 836 00:40:11,360 --> 00:40:12,790 I think of a certain amount I'm willing to spend on 837 00:40:12,790 --> 00:40:14,720 entertainment and a certain amount I'm 838 00:40:14,720 --> 00:40:16,200 willing to spend on food. 839 00:40:16,200 --> 00:40:20,610 And I take my budget and I mentally put it 840 00:40:20,610 --> 00:40:22,710 in different buckets. 841 00:40:22,710 --> 00:40:25,030 And within each of those buckets, you can then do the 842 00:40:25,030 --> 00:40:29,240 same kind of optimization problem that we've done here. 843 00:40:29,240 --> 00:40:33,120 So even though in reality we choose across a whole host of 844 00:40:33,120 --> 00:40:38,200 goods, in practice what you're going to see is that people 845 00:40:38,200 --> 00:40:44,290 will do this kind of mental accounting, where they sort of 846 00:40:44,290 --> 00:40:48,150 divide their goods into different buckets and optimize 847 00:40:48,150 --> 00:40:49,400 within each of those buckets. 848 00:40:51,700 --> 00:40:57,100 What this means in practice is that in fact, if we now stop 849 00:40:57,100 --> 00:40:58,640 for a second and think about the government, and how it 850 00:40:58,640 --> 00:41:01,370 affects our consumption decisions, what this means is 851 00:41:01,370 --> 00:41:03,870 that in practice, the government-- 852 00:41:03,870 --> 00:41:06,100 so, one way we typically of the government affecting 853 00:41:06,100 --> 00:41:09,810 consumption decisions is through the power of taxation. 854 00:41:09,810 --> 00:41:13,120 So let's say for example, the government decided 855 00:41:13,120 --> 00:41:14,790 that pizzas were bad. 856 00:41:14,790 --> 00:41:17,190 They caused obesity. 857 00:41:17,190 --> 00:41:18,840 That there's too much obesity because people are eating too 858 00:41:18,840 --> 00:41:24,660 much pizza, and we need to deal with that through a 859 00:41:24,660 --> 00:41:28,550 government policy that involves taxation. 860 00:41:28,550 --> 00:41:31,130 Somebody talk me through the analysis of how we'd think 861 00:41:31,130 --> 00:41:36,460 about analyzing a tax on pizza given these diagrams. 862 00:41:36,460 --> 00:41:40,970 Let's go to figure 5-4. 863 00:41:43,480 --> 00:41:49,780 And imagine I said that we're going to place 864 00:41:49,780 --> 00:41:51,920 a 50% tax on pizza. 865 00:41:51,920 --> 00:42:00,040 So we're going to say that every dollar you pay on pizza, 866 00:42:00,040 --> 00:42:03,150 you're going to have to pay $0.50 to the government. 867 00:42:03,150 --> 00:42:04,256 Because we're really worried people are 868 00:42:04,256 --> 00:42:06,180 eating too much pizza. 869 00:42:06,180 --> 00:42:09,210 What would that do the budget constraint? 870 00:42:09,210 --> 00:42:09,640 Yeah. 871 00:42:09,640 --> 00:42:10,464 AUDIENCE: Well, effectively you're increasing 872 00:42:10,464 --> 00:42:12,540 the price of pizza. 873 00:42:12,540 --> 00:42:13,604 PROFESSOR: Effectively you're increasing the price of pizza 874 00:42:13,604 --> 00:42:14,260 to the consumer. 875 00:42:14,260 --> 00:42:15,484 AUDIENCE: The budget constraint would 876 00:42:15,484 --> 00:42:17,260 shift down like this. 877 00:42:17,260 --> 00:42:19,350 PROFESSOR: It's actually going to have the same effect as we 878 00:42:19,350 --> 00:42:20,920 saw in figure 5-2. 879 00:42:20,920 --> 00:42:23,620 In fact, I've just replicated figure 5-2. 880 00:42:23,620 --> 00:42:32,640 Because in figure 5-2, the price of pizza went up by 50%, 881 00:42:32,640 --> 00:42:40,350 from $16 to $24. 882 00:42:40,350 --> 00:42:43,020 That's the same thing that the government's just done. 883 00:42:43,020 --> 00:42:45,460 It's raised the price of pizza effectively from $16 a pizza 884 00:42:45,460 --> 00:42:49,140 to $24 because instead of paying your $16, you're also 885 00:42:49,140 --> 00:42:52,060 going to pay $8 to the government in tax. 886 00:42:52,060 --> 00:42:54,070 So what's that going to do? 887 00:42:54,070 --> 00:42:58,440 That is going to, in general, lower consumption of pizza. 888 00:42:58,440 --> 00:43:01,260 So that kind of price increase is going to, in general, lower 889 00:43:01,260 --> 00:43:02,510 the consumption of pizza. 890 00:43:02,510 --> 00:43:05,440 So the government has tried to accomplish its goal by 891 00:43:05,440 --> 00:43:08,750 shifting people away from pizza towards movies, away 892 00:43:08,750 --> 00:43:11,340 from pizza toward other things. 893 00:43:11,340 --> 00:43:13,240 Yeah? 894 00:43:13,240 --> 00:43:14,520 AUDIENCE: Would it be meaningful to say that it also 895 00:43:14,520 --> 00:43:18,040 affects the utility curves? 896 00:43:18,040 --> 00:43:20,870 PROFESSOR: It would not be meaningful, actually-- 897 00:43:20,870 --> 00:43:24,830 it will affect your optimal choice. 898 00:43:24,830 --> 00:43:26,980 In general, you will choose a different amount 899 00:43:26,980 --> 00:43:27,570 of pizza and movies. 900 00:43:27,570 --> 00:43:28,920 We'll talk about that next time. 901 00:43:28,920 --> 00:43:31,440 But it's very important, it would not be right to say it 902 00:43:31,440 --> 00:43:32,800 affects utility. 903 00:43:32,800 --> 00:43:35,900 Utility is like what you're born with, it's an innate 904 00:43:35,900 --> 00:43:39,350 concept about your underlying preferences. 905 00:43:39,350 --> 00:43:41,730 However, you're actually getting to my point, which is 906 00:43:41,730 --> 00:43:44,880 in fact, the way economists typically think about this is 907 00:43:44,880 --> 00:43:46,230 the government can't affect your preferences. 908 00:43:46,230 --> 00:43:48,700 But in fact, if people do mental accounting, the 909 00:43:48,700 --> 00:43:51,040 government maybe can affect your preferences. 910 00:43:51,040 --> 00:43:53,410 So let's say that basically the way I think about it is, 911 00:43:53,410 --> 00:43:56,600 let's say I think I have a budget for food and I have a 912 00:43:56,600 --> 00:43:58,430 budget for entertainment. 913 00:43:58,430 --> 00:43:59,770 And let's say I think my budget for entertainment's 914 00:43:59,770 --> 00:44:00,870 pretty small because I'm low income. 915 00:44:00,870 --> 00:44:03,100 I've gotta have a budget for food. 916 00:44:03,100 --> 00:44:05,490 And so let's say I put pizza in my budget for food, so I 917 00:44:05,490 --> 00:44:09,000 allocate some of my budget for food to pizza. 918 00:44:09,000 --> 00:44:10,690 And the government can then cause me to eat less 919 00:44:10,690 --> 00:44:13,110 pizza by taxing it. 920 00:44:13,110 --> 00:44:14,960 But what if somehow the government could get me to 921 00:44:14,960 --> 00:44:17,110 think of pizza differently? 922 00:44:17,110 --> 00:44:18,670 What if somehow the government could get me to think of pizza 923 00:44:18,670 --> 00:44:20,590 as entertainment? 924 00:44:20,590 --> 00:44:23,300 And suddenly I put it in that bucket, where I'm trading it 925 00:44:23,300 --> 00:44:25,050 off not against other food, but against the fact that I 926 00:44:25,050 --> 00:44:27,180 want to see a movie and I want to download stuff 927 00:44:27,180 --> 00:44:28,600 from iTunes, et cetera. 928 00:44:28,600 --> 00:44:31,460 Maybe then I'd buy less pizza at the same price because I'm 929 00:44:31,460 --> 00:44:34,610 putting it in the bucket where I have less money. 930 00:44:34,610 --> 00:44:35,970 So in other words, we've imagined a 931 00:44:35,970 --> 00:44:38,750 world with two goods. 932 00:44:38,750 --> 00:44:41,083 And the only way you can affect the choice across those 933 00:44:41,083 --> 00:44:42,880 two goods is to lower your income or your price. 934 00:44:42,880 --> 00:44:48,030 But in fact, if people have lots of different bundles of 935 00:44:48,030 --> 00:44:50,340 goods, somehow I could shift you mentally from considering 936 00:44:50,340 --> 00:44:52,820 pizza in a bucket where you have a lot of money to putting 937 00:44:52,820 --> 00:44:55,090 pizza in a bucket where you don't have as much money. 938 00:44:55,090 --> 00:44:57,490 I can lower your consumption of pizza without affecting 939 00:44:57,490 --> 00:45:02,240 prices, without an obtrusive government tax policy. 940 00:45:02,240 --> 00:45:04,020 This is the kind of thing that we call in 941 00:45:04,020 --> 00:45:06,340 economic policy a nudge. 942 00:45:08,990 --> 00:45:13,660 And there's a new book called Nudge by Richard Thaler, who's 943 00:45:13,660 --> 00:45:16,440 a famous behavioral economist, basically bringing psychology 944 00:45:16,440 --> 00:45:17,610 into economics. 945 00:45:17,610 --> 00:45:20,110 There's this very important field now in economics called 946 00:45:20,110 --> 00:45:27,770 behavioral economics, which is all about, how can we bring 947 00:45:27,770 --> 00:45:30,480 the lessons of psychology into economics? 948 00:45:30,480 --> 00:45:32,090 We don't do that in 14.01. 949 00:45:32,090 --> 00:45:34,310 14.01's all about, we assume everybody's these perfectly 950 00:45:34,310 --> 00:45:37,630 rational people who would never really be fooled into 951 00:45:37,630 --> 00:45:38,800 thinking about pizza differently just because of 952 00:45:38,800 --> 00:45:40,220 what the government told them. 953 00:45:40,220 --> 00:45:42,610 But in fact, in reality people think about things differently 954 00:45:42,610 --> 00:45:46,070 based on the kinds of information they have. And 955 00:45:46,070 --> 00:45:49,510 given that tax policies can feel very intrusive-- imagine 956 00:45:49,510 --> 00:45:51,820 some of you are like, wow, they're raising my pizza to 957 00:45:51,820 --> 00:45:53,670 $24, that seems very intrusive. 958 00:45:53,670 --> 00:45:55,680 If the government could somehow through nudging you to 959 00:45:55,680 --> 00:45:58,220 think about pizza differently change your pizza consumption, 960 00:45:58,220 --> 00:46:00,940 that might be a much more acceptable and palatable 961 00:46:00,940 --> 00:46:02,480 policy to many people. 962 00:46:02,480 --> 00:46:06,110 And that's the kind of role the government can play, or 963 00:46:06,110 --> 00:46:08,340 policy-makers can play, is not just by changing your prices 964 00:46:08,340 --> 00:46:10,880 or income, but by actually changing how you categorize 965 00:46:10,880 --> 00:46:13,160 things mentally, they can change the choices you make.