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 --> 00:00:17,390 hundreds of MIT courses, visit MIT OpenCourseWare at 7 00:00:17,390 --> 00:00:18,640 ocw.mit.edu. 8 00:00:22,255 --> 00:00:24,940 PROFESSOR: Hi, and welcome back to the 14.01 problem 9 00:00:24,940 --> 00:00:26,370 solving videos. 10 00:00:26,370 --> 00:00:30,370 Today, we're going to do Fall 2010, Problem Set 3, 11 00:00:30,370 --> 00:00:31,950 Problem Number 5. 12 00:00:31,950 --> 00:00:33,210 And we're going to go ahead and we're going to work 13 00:00:33,210 --> 00:00:37,530 through parts A, B, C, D, and E, and then we're going to 14 00:00:37,530 --> 00:00:40,320 finish up parts F and G. 15 00:00:40,320 --> 00:00:43,480 Problem 5 says that Xiao spends all her income on 16 00:00:43,480 --> 00:00:46,380 statistical softwares and clothes. 17 00:00:46,380 --> 00:00:49,060 Her preferences can be represented by the utility 18 00:00:49,060 --> 00:00:53,190 function where her utility equals 4 times the natural log 19 00:00:53,190 --> 00:00:58,350 of S plus 6 times the natural log of C, where S is software 20 00:00:58,350 --> 00:01:00,540 and C is clothes. 21 00:01:00,540 --> 00:01:03,840 Part A asks us to compute the marginal rate of substitution 22 00:01:03,840 --> 00:01:08,330 of software for clothes, asks us if the MRS is increasing or 23 00:01:08,330 --> 00:01:14,330 decreasing in S, and also asks us how we interpret the MRS. 24 00:01:14,330 --> 00:01:16,610 So before we start with this, we should really think about, 25 00:01:16,610 --> 00:01:19,450 conceptually, what the marginal rate of substitution 26 00:01:19,450 --> 00:01:22,845 of software for clothes looks like on our graph. 27 00:01:22,845 --> 00:01:25,880 So on this graph, I have clothes on the y-axis-- 28 00:01:25,880 --> 00:01:27,250 the quantity of clothes-- 29 00:01:27,250 --> 00:01:32,150 and the quantity of software on the x-axis here. 30 00:01:32,150 --> 00:01:35,690 Looking at this graph, this line that I've drawn is one 31 00:01:35,690 --> 00:01:36,660 utility level. 32 00:01:36,660 --> 00:01:40,440 So at this place, she might have a utility equal to 1. 33 00:01:40,440 --> 00:01:43,840 So she's indifferent on this indifference curve between 34 00:01:43,840 --> 00:01:49,070 being at point here or at a point here. 35 00:01:49,070 --> 00:01:51,970 And what the marginal rate of substitution is really asking 36 00:01:51,970 --> 00:01:56,130 us, it's asking us how much clothing is she willing to 37 00:01:56,130 --> 00:01:59,530 give up to get one more unit of software? 38 00:01:59,530 --> 00:02:04,100 So she's going to have to give up a certain amount of clothes 39 00:02:04,100 --> 00:02:07,110 to get one more unit of software. 40 00:02:07,110 --> 00:02:10,660 And the marginal rate of substitution tells us exactly 41 00:02:10,660 --> 00:02:13,550 how much clothing she's willing to give up. 42 00:02:13,550 --> 00:02:15,740 To calculate this algebraically, all we're going 43 00:02:15,740 --> 00:02:18,660 to do is we're going to take the marginal utility of 44 00:02:18,660 --> 00:02:22,460 software and divide it by the marginal utility of clothes. 45 00:02:22,460 --> 00:02:24,530 So we're going to take the derivative with respect to 46 00:02:24,530 --> 00:02:26,820 software and the derivative with respect to 47 00:02:26,820 --> 00:02:28,070 clothing and divide. 48 00:02:31,470 --> 00:02:37,580 When we do this, we find that the MRS is going to be equal 49 00:02:37,580 --> 00:02:43,270 to 4 over S, which is our marginal utility of software, 50 00:02:43,270 --> 00:02:46,980 all over 6 divided by C, which is our 51 00:02:46,980 --> 00:02:51,710 marginal utility of clothes. 52 00:02:51,710 --> 00:02:56,780 Solving through, we find that our MRS is 4C over 6S. 53 00:02:59,840 --> 00:03:02,050 Now, we have to think about, conceptually, what happens 54 00:03:02,050 --> 00:03:04,450 when software increases? 55 00:03:04,450 --> 00:03:08,520 When we have S increase, since it's in the denominator, we're 56 00:03:08,520 --> 00:03:14,780 also going to have the MRS decrease. 57 00:03:14,780 --> 00:03:18,060 So what this means is as software is increasing, or as 58 00:03:18,060 --> 00:03:21,300 she has more software, she's going to be willing to give up 59 00:03:21,300 --> 00:03:24,830 fewer clothing, or less clothing, to get another unit 60 00:03:24,830 --> 00:03:25,520 of software. 61 00:03:25,520 --> 00:03:32,610 So looking at our graph, when she's at this point, she's 62 00:03:32,610 --> 00:03:35,760 more willing to give up clothing to get more software. 63 00:03:35,760 --> 00:03:39,490 But when she has more software down here, she's less willing 64 00:03:39,490 --> 00:03:42,510 to give up the clothing. 65 00:03:42,510 --> 00:03:51,710 Let's go ahead and move on to Part B. Part B, find Xiao's 66 00:03:51,710 --> 00:03:54,560 demand functions for software and clothes-- 67 00:03:54,560 --> 00:03:57,140 so we're going to call those QS and QC-- 68 00:03:57,140 --> 00:04:00,010 in terms of the price of software PS, the price of 69 00:04:00,010 --> 00:04:03,670 clothes PC, and Xiao's income. 70 00:04:03,670 --> 00:04:06,240 Now, before we move on with this, what we want to do is we 71 00:04:06,240 --> 00:04:11,350 want to solve for one of the variables C or S in terms of 72 00:04:11,350 --> 00:04:13,960 the prices and the other variable. 73 00:04:13,960 --> 00:04:21,079 So to do this, we're going to set the MRS equal to the price 74 00:04:21,079 --> 00:04:23,990 of the software over the price of the clothes. 75 00:04:33,920 --> 00:04:36,660 From here, we can solve through for C, and we find 76 00:04:36,660 --> 00:04:48,540 that C is going to be equal to 3/2 times PS over PC times S. 77 00:04:48,540 --> 00:04:49,810 Now, since we have two variables-- 78 00:04:49,810 --> 00:04:53,120 we have a variable for clothes and a variable for software-- 79 00:04:53,120 --> 00:04:55,280 we're going to have to introduce another constraint 80 00:04:55,280 --> 00:04:56,850 into this problem. 81 00:04:56,850 --> 00:04:58,810 And the constraint that we're going to introduce is going to 82 00:04:58,810 --> 00:05:02,330 be the income function. 83 00:05:02,330 --> 00:05:05,000 We know that Xiao has some sort of income that's going to 84 00:05:05,000 --> 00:05:07,440 be fixed, and she's going to spend all of this on either 85 00:05:07,440 --> 00:05:10,390 clothes or software. 86 00:05:10,390 --> 00:05:12,990 Now, the amount of money she spends on software is going to 87 00:05:12,990 --> 00:05:18,380 be equal to the price of software times how much 88 00:05:18,380 --> 00:05:21,060 software she's going to buy. 89 00:05:21,060 --> 00:05:23,780 The rest of her income is going to be spent on clothes, 90 00:05:23,780 --> 00:05:28,640 so the price of clothes times the quantity of clothing. 91 00:05:28,640 --> 00:05:33,560 Now, to solve for the demand function for software, all 92 00:05:33,560 --> 00:05:36,510 we're going to do is we're going to plug in for C in the 93 00:05:36,510 --> 00:05:39,800 income function here, and then we're going to solve through 94 00:05:39,800 --> 00:06:16,900 for S. 95 00:06:16,900 --> 00:06:19,690 I know it's a little bit messy, but this says PS times 96 00:06:19,690 --> 00:06:25,940 3/2PS over PC, what we solved for here, times S. Now, when 97 00:06:25,940 --> 00:06:28,460 we solve through for S from this equation, we're going to 98 00:06:28,460 --> 00:06:32,580 find that the demand function for software is going to be 99 00:06:32,580 --> 00:06:42,110 equal to 2/2 times income over the price of software. 100 00:06:42,110 --> 00:06:45,200 Now, we can go through the same process solving for the 101 00:06:45,200 --> 00:06:48,430 demand function for clothing. 102 00:06:48,430 --> 00:06:53,770 And all we'd have to do now is we can take this S right here 103 00:06:53,770 --> 00:06:59,960 that we just solved for, we can plug this back into our 104 00:06:59,960 --> 00:07:04,720 income function, and then we can solve for C. When we solve 105 00:07:04,720 --> 00:07:08,040 for C, we're going to find that the demand function for 106 00:07:08,040 --> 00:07:16,580 clothing is going to equal 3/5 times I over PC. 107 00:07:16,580 --> 00:07:20,050 Part C asks us to draw the Engel curve for software. 108 00:07:20,050 --> 00:07:22,715 Now, all an Engel curve is, it's a relationship between 109 00:07:22,715 --> 00:07:26,200 the income and the quantity that's demanded for a product. 110 00:07:26,200 --> 00:07:29,860 And it shows us that as income increases, it shows how the 111 00:07:29,860 --> 00:07:34,380 quantity demanded is going to change with changing income. 112 00:07:34,380 --> 00:07:36,280 So to start off our Engel curve, we're going to draw an 113 00:07:36,280 --> 00:07:40,140 axes, we're going to put software, or the quantity 114 00:07:40,140 --> 00:07:42,970 that's demanded, on the x-axis, and we're going to put 115 00:07:42,970 --> 00:07:47,430 the income on the y-axis. 116 00:07:47,430 --> 00:07:49,880 Now, the nice thing about the software demand function that 117 00:07:49,880 --> 00:07:54,880 we solved for is that it's linear with respect to income. 118 00:08:01,100 --> 00:08:03,640 Now, before we can graph this equation, however, we have to 119 00:08:03,640 --> 00:08:05,840 get it in terms of income. 120 00:08:05,840 --> 00:08:08,360 So when we solve for this, we're going to find that 121 00:08:08,360 --> 00:08:21,610 income equals 5/2 PS times S. So all our Engel curve is 122 00:08:21,610 --> 00:08:25,880 going to look like is it's going to be a straight line. 123 00:08:25,880 --> 00:08:30,200 And the slope of that straight line is going to be 5/2 PS. 124 00:08:39,679 --> 00:08:43,900 And the way to interpret this conceptually is to say that 125 00:08:43,900 --> 00:08:49,280 with each one unit increase in income, the amount that's 126 00:08:49,280 --> 00:08:55,900 demanded is going to increase by 2/5 divided by PS. 127 00:08:58,540 --> 00:09:02,810 Let's go ahead and move on to Part D. Part D says, suppose 128 00:09:02,810 --> 00:09:06,780 that the price of software is PS equals 2, and the price of 129 00:09:06,780 --> 00:09:11,050 clothing is going to equal PC equals 3. 130 00:09:16,850 --> 00:09:22,580 And Xiao's income is going to equal 10. 131 00:09:22,580 --> 00:09:24,280 What bundle of software and clothes 132 00:09:24,280 --> 00:09:27,670 maximize Xiao's utility? 133 00:09:27,670 --> 00:09:31,770 Now, we've already found the conditional demand curves for 134 00:09:31,770 --> 00:09:33,570 both software and clothes. 135 00:09:33,570 --> 00:09:37,160 So we can start off this problem by writing down those 136 00:09:37,160 --> 00:09:39,320 conditional demand curves. 137 00:09:39,320 --> 00:09:48,070 The conditional demand curve for software was given by 2/5 138 00:09:48,070 --> 00:09:50,320 I divided by PS. 139 00:09:50,320 --> 00:09:57,730 And the conditional demand for clothing was given by 3/5 I 140 00:09:57,730 --> 00:10:00,050 divided by PC. 141 00:10:00,050 --> 00:10:02,300 All we have to do now is we have to plug in these 142 00:10:02,300 --> 00:10:06,950 variables to solve for the software and the clothing 143 00:10:06,950 --> 00:10:08,290 that's going to be demanded. 144 00:10:08,290 --> 00:10:12,520 When we plug those in, we're going to find that she's going 145 00:10:12,520 --> 00:10:18,960 to demand two units of both software and clothes. 146 00:10:18,960 --> 00:10:23,760 So this is in the scenario for Part D. Part E gives us 147 00:10:23,760 --> 00:10:25,970 another scenario that we can solve for. 148 00:10:25,970 --> 00:10:29,060 And all that's going to happen now is that the price of 149 00:10:29,060 --> 00:10:31,710 software is going to change. 150 00:10:31,710 --> 00:10:34,420 And we're going to look at how that affects the bundle that 151 00:10:34,420 --> 00:10:36,990 maximizes her utility. 152 00:10:36,990 --> 00:10:39,950 For Part E, it says, suppose that the price of software 153 00:10:39,950 --> 00:10:50,220 increases from PS equal to 2, and now it's going to be PS is 154 00:10:50,220 --> 00:10:53,040 going to equal 4. 155 00:10:53,040 --> 00:10:56,770 What bundle of software and clothes does Xiao demand now? 156 00:11:00,080 --> 00:11:04,610 Again, we're just going to solve through. 157 00:11:04,610 --> 00:11:08,610 With our new PS equals 4, we're going to solve for the 158 00:11:08,610 --> 00:11:11,180 software and clothing that Xiao demands. 159 00:11:11,180 --> 00:11:16,650 We're going to find that S is going to equal 1 now, and that 160 00:11:16,650 --> 00:11:20,125 the amount of clothing is going to equal 2. 161 00:11:23,440 --> 00:11:24,800 So let's take a pause right here. 162 00:11:24,800 --> 00:11:26,580 And we're going to come back in just a minute. 163 00:11:26,580 --> 00:11:29,140 And we're going to look at the more interesting case, which 164 00:11:29,140 --> 00:11:33,340 is given the fact that she's consuming less-- she has one 165 00:11:33,340 --> 00:11:35,500 less unit of software to consume-- 166 00:11:35,500 --> 00:11:39,040 how do we get her back to the utility that she had before? 167 00:11:39,040 --> 00:11:41,780 What amount of money or income do we have to give her so that 168 00:11:41,780 --> 00:11:44,870 she can be as happy as she was in this initial scenario with 169 00:11:44,870 --> 00:11:46,660 two units of both software and clothes? 170 00:11:51,960 --> 00:11:53,160 Welcome back. 171 00:11:53,160 --> 00:11:56,550 So we're going to continue onto Part F. Part F says, 172 00:11:56,550 --> 00:12:00,150 given the price increase, how much income does Xiao need to 173 00:12:00,150 --> 00:12:01,440 remain as happy-- 174 00:12:01,440 --> 00:12:02,970 have the same utility-- 175 00:12:02,970 --> 00:12:05,120 as she was before the price change? 176 00:12:05,120 --> 00:12:08,590 What bundle of softwares and clothes would Xiao consume if 177 00:12:08,590 --> 00:12:13,060 she had the additional income given the new prices? 178 00:12:13,060 --> 00:12:16,410 So we want to find out, how can we give her as much income 179 00:12:16,410 --> 00:12:19,150 so she can be as happy as she was to start off with? 180 00:12:19,150 --> 00:12:21,430 To start this problem, the first thing that we're going 181 00:12:21,430 --> 00:12:24,240 to have to find out is we're going to have to find out 182 00:12:24,240 --> 00:12:26,920 exactly how happy Xiao was to begin with. 183 00:12:26,920 --> 00:12:29,560 So we need to know her initial utility. 184 00:12:29,560 --> 00:12:33,370 So let's start off with that calculation. 185 00:12:33,370 --> 00:12:36,410 To calculate her initial utility, we're just going to 186 00:12:36,410 --> 00:12:46,260 start off by saying that her utility is equal to 4 natural 187 00:12:46,260 --> 00:12:54,860 log of S plus 6 natural log of C. And we can plug in 2 and 2 188 00:12:54,860 --> 00:12:59,340 for S and C. In this case, when we solve through, we find 189 00:12:59,340 --> 00:13:05,980 that her initial utility is 6.931. 190 00:13:05,980 --> 00:13:10,660 So we're going to set her utility equal to 6.931. 191 00:13:10,660 --> 00:13:13,540 And what we want to find out is we want to find out what 192 00:13:13,540 --> 00:13:16,770 income we have to give her so that she can get up to this 193 00:13:16,770 --> 00:13:19,370 utility, given the new prices. 194 00:13:19,370 --> 00:13:24,090 So we're going to take this utility function, and we're 195 00:13:24,090 --> 00:13:26,680 going to plug in the conditional demand curves for 196 00:13:26,680 --> 00:13:31,050 S and C so that income is now a function, or one of the 197 00:13:31,050 --> 00:13:32,920 inputs for her utility. 198 00:13:32,920 --> 00:13:36,580 When we do that, we're going to get this function. 199 00:13:54,450 --> 00:13:58,690 And remember, we said that we want, given this input and the 200 00:13:58,690 --> 00:13:59,530 new prices-- 201 00:13:59,530 --> 00:14:04,050 so we're going to set this PS is going to be equal to the 202 00:14:04,050 --> 00:14:06,750 new price in the problem. 203 00:14:06,750 --> 00:14:11,030 And we're going to also set the PC equal to the price that 204 00:14:11,030 --> 00:14:12,740 was in Part E as well. 205 00:14:12,740 --> 00:14:16,900 And flipping back to the problem, we know that the 206 00:14:16,900 --> 00:14:22,400 price of clothing is going to be equal to 3, and the price 207 00:14:22,400 --> 00:14:28,880 of software for the second part was equal to 4. 208 00:14:28,880 --> 00:14:32,840 So we're going to plug in for PS and PC, we're going to set 209 00:14:32,840 --> 00:14:36,970 utility equal to 6.931, and we're going to solve through 210 00:14:36,970 --> 00:14:43,410 for I. When we do this, and when we solve through for I, 211 00:14:43,410 --> 00:14:48,940 what we're going to find is we're going to have 6.931 is 212 00:14:48,940 --> 00:14:57,230 going to be equal to 10 natural log of I minus 4 213 00:14:57,230 --> 00:15:05,320 natural log of 10 minus 6 natural log of 5. 214 00:15:05,320 --> 00:15:08,020 Solving through, doing the inverse natural log function 215 00:15:08,020 --> 00:15:11,100 for I after isolating this variable, we're going to find 216 00:15:11,100 --> 00:15:19,350 that the new income that she needs to be supplied is 13.19. 217 00:15:19,350 --> 00:15:21,930 So the income that she needs to be just as happy with these 218 00:15:21,930 --> 00:15:27,460 prices has increased by 3.19. 219 00:15:27,460 --> 00:15:30,130 Now, we can go back to our conditional demand curves that 220 00:15:30,130 --> 00:15:31,400 we had here. 221 00:15:31,400 --> 00:15:37,180 We can plug in PS equals 4, PC equals 3, and we can plug in 222 00:15:37,180 --> 00:15:40,190 for income 13.19. 223 00:15:40,190 --> 00:15:45,410 And we can solve S double prime, which is the new 224 00:15:45,410 --> 00:15:51,340 software that she's going to demand, which will be 1.32, 225 00:15:51,340 --> 00:15:54,850 and C double prime, the new amount of clothes that she's 226 00:15:54,850 --> 00:16:07,920 going to demand, which is 2.64. 227 00:16:07,920 --> 00:16:11,290 Now, the final part of the problem, which we're going to 228 00:16:11,290 --> 00:16:15,080 move on to now, which is Part G, is actually the most 229 00:16:15,080 --> 00:16:17,780 important part of the problem, because what we're going to do 230 00:16:17,780 --> 00:16:20,130 is we're going to tie together the three 231 00:16:20,130 --> 00:16:22,430 scenarios that we did. 232 00:16:22,430 --> 00:16:27,490 We did this scenario where we were giving her income so that 233 00:16:27,490 --> 00:16:29,320 she would be just as happy. 234 00:16:29,320 --> 00:16:33,860 We had our initial scenario before the price increase. 235 00:16:33,860 --> 00:16:37,010 And we had the scenario after the price increase. 236 00:16:37,010 --> 00:16:39,940 And we're going to look at this conceptually on a graph, 237 00:16:39,940 --> 00:16:43,470 and we're going to see, how do we relate these three bundles 238 00:16:43,470 --> 00:16:45,570 of consumption? 239 00:16:45,570 --> 00:16:49,660 Part G says, going back to the situation in Part E, where PS 240 00:16:49,660 --> 00:16:53,940 equals 4 and I equals 10, we need to decompose the total 241 00:16:53,940 --> 00:16:57,120 change of softwares and clothes demanded into 242 00:16:57,120 --> 00:16:59,570 substitution and income effects. 243 00:16:59,570 --> 00:17:02,320 In a clearly-labelled diagram, with softwares on the 244 00:17:02,320 --> 00:17:05,480 horizontal axis, show the income and substitution 245 00:17:05,480 --> 00:17:08,089 effects of the increase in the price of software. 246 00:17:10,750 --> 00:17:14,060 Now, we're going to go back to this graph that 247 00:17:14,060 --> 00:17:16,440 we started off with. 248 00:17:16,440 --> 00:17:21,680 And what we're going to do here, is we're going to 249 00:17:21,680 --> 00:17:25,240 illustrate the three bundles that she selected. 250 00:17:25,240 --> 00:17:29,580 I'll illustrate the first bundle where she consumes 2 251 00:17:29,580 --> 00:17:30,930 units of each. 252 00:17:30,930 --> 00:17:33,690 And we already have our utility curve, or indifference 253 00:17:33,690 --> 00:17:35,600 curve, drawn up here. 254 00:17:35,600 --> 00:17:38,980 Now we need to draw the budget constraint that shows how much 255 00:17:38,980 --> 00:17:41,390 she can spend on each product. 256 00:17:41,390 --> 00:17:45,730 If she were to spend all her money on clothes, she would be 257 00:17:45,730 --> 00:17:48,020 up here at this corner solution. 258 00:17:48,020 --> 00:17:51,490 If she were to spend all her money on software, she would 259 00:17:51,490 --> 00:17:52,340 be down here. 260 00:17:52,340 --> 00:17:55,270 When we connect a line through here, this is her budget 261 00:17:55,270 --> 00:18:01,270 constraint that shows all the possible bundles of goods 262 00:18:01,270 --> 00:18:04,380 where she could potentially spend her money. 263 00:18:04,380 --> 00:18:10,430 And this first bundle is the point 2,2. 264 00:18:10,430 --> 00:18:14,160 This is where she starts off to begin with. 265 00:18:14,160 --> 00:18:17,900 Now, when the price of software increases, she's not 266 00:18:17,900 --> 00:18:23,010 going to be able to buy as much software with her money. 267 00:18:23,010 --> 00:18:25,750 But she can still buy the same amount of clothing. 268 00:18:25,750 --> 00:18:31,780 So her new budget constraint in this scenario is going to 269 00:18:31,780 --> 00:18:34,620 look like this. 270 00:18:34,620 --> 00:18:38,710 So in this scenario, which is in our problem's Part E, her 271 00:18:38,710 --> 00:18:41,880 utility has moved in towards the origin. 272 00:18:41,880 --> 00:18:44,230 And she isn't going to be as happy. 273 00:18:44,230 --> 00:18:48,100 And we can represent this on a utility curve as well. 274 00:18:54,890 --> 00:18:59,640 And we can see from this point on the utility curve the way 275 00:18:59,640 --> 00:19:03,470 that I've drawn it, that at this point, she's still 276 00:19:03,470 --> 00:19:06,510 consuming the same amount of clothing. 277 00:19:06,510 --> 00:19:08,560 But the amount of software she's consumed 278 00:19:08,560 --> 00:19:09,810 has been cut in half. 279 00:19:13,800 --> 00:19:15,960 This is the total effect of the price change. 280 00:19:15,960 --> 00:19:18,750 It's the difference between where she started and where 281 00:19:18,750 --> 00:19:22,070 she's ending up without giving her any money to change where 282 00:19:22,070 --> 00:19:23,320 she actually is. 283 00:19:25,590 --> 00:19:36,770 So the total effect is just that she's 284 00:19:36,770 --> 00:19:41,860 losing one unit of software. 285 00:19:45,360 --> 00:19:52,000 Now, we can break down the total effect in the 286 00:19:52,000 --> 00:19:56,790 substitution effects and income effects. 287 00:19:56,790 --> 00:19:59,880 It's important that we really understand conceptually how to 288 00:19:59,880 --> 00:20:04,210 define substitution and income effects. 289 00:20:04,210 --> 00:20:06,140 And what we're going to think about is we're going to think 290 00:20:06,140 --> 00:20:11,520 about, on this graph, we're going to represent the 291 00:20:11,520 --> 00:20:16,270 substitution effect by the movement-- 292 00:20:16,270 --> 00:20:18,420 if we were to just have the price change, and we were to 293 00:20:18,420 --> 00:20:22,320 give her income so she could stay up at this utility level, 294 00:20:22,320 --> 00:20:24,360 the substitution effect is how her bundle 295 00:20:24,360 --> 00:20:26,370 changes with that movement. 296 00:20:26,370 --> 00:20:29,460 The income effect is going to be-- since she's poorer 297 00:20:29,460 --> 00:20:31,770 because the prices are higher, it's going to 298 00:20:31,770 --> 00:20:33,780 be the shift downward. 299 00:20:33,780 --> 00:20:38,710 So I'm going to draw in the scenario that we calculated in 300 00:20:38,710 --> 00:20:41,890 Part F right here. 301 00:20:41,890 --> 00:20:46,300 By drawing in this scenario with the higher income level 302 00:20:46,300 --> 00:20:51,890 and the price change, we can represent this bundle as the 303 00:20:51,890 --> 00:20:54,210 substitution effect. 304 00:20:54,210 --> 00:20:57,480 So what this looks like is she's going to have the same 305 00:20:57,480 --> 00:21:00,520 budget constraint, only it's going to be shifted back up. 306 00:21:06,090 --> 00:21:09,480 This is going to be the bundle in Part F. And we can label 307 00:21:09,480 --> 00:21:20,330 the bundle 1.32, 2.64. 308 00:21:20,330 --> 00:21:23,610 And this is where it's going to get a little bit tricky. 309 00:21:23,610 --> 00:21:36,040 The substitution effect is just the movement from 2.2 to 310 00:21:36,040 --> 00:21:38,940 the same utility curve but at a different point with a 311 00:21:38,940 --> 00:21:39,620 different bundle. 312 00:21:39,620 --> 00:21:42,250 So it's when we've given her income to keep her at the same 313 00:21:42,250 --> 00:21:46,090 utility level, but we've had the price change. 314 00:21:46,090 --> 00:21:47,910 This is going to be the substitution effect. 315 00:21:47,910 --> 00:21:50,730 I'm going to label it 1. 316 00:21:50,730 --> 00:21:54,460 Now, the income effect is the next movement. 317 00:21:54,460 --> 00:21:57,980 It's the movement that says, well, we don't really give her 318 00:21:57,980 --> 00:21:58,580 more income. 319 00:21:58,580 --> 00:22:00,240 She's actually poorer. 320 00:22:00,240 --> 00:22:07,910 It's the movement down from 1.32, 2.64, down to 1, 2. 321 00:22:07,910 --> 00:22:11,430 And then the total effect is just this 322 00:22:11,430 --> 00:22:15,970 movement from 2.2 to 1.2. 323 00:22:15,970 --> 00:22:21,870 So I can label the substitution effect 1, the 324 00:22:21,870 --> 00:22:27,360 income effect 2, and the total effect 3. 325 00:22:27,360 --> 00:22:30,500 So to calculate the substitution effect, all it's 326 00:22:30,500 --> 00:22:33,810 going to be is it's going to be the difference between 2.2 327 00:22:33,810 --> 00:22:37,640 and 1.32 and 2.64. 328 00:22:37,640 --> 00:22:42,660 So in this case, our substitution effect is going 329 00:22:42,660 --> 00:22:55,020 to be equal to 0.68, negative 0.64. 330 00:22:55,020 --> 00:22:58,080 And you can see that we actually had an increase in 331 00:22:58,080 --> 00:23:03,710 the consumption of clothes for the substitution effect. 332 00:23:03,710 --> 00:23:11,970 And then the income effect, using this equation and what 333 00:23:11,970 --> 00:23:14,772 we calculated the substitution effect and the total effect to 334 00:23:14,772 --> 00:23:31,610 be, we find that the income effect is equal to 0.32, 0.64. 335 00:23:31,610 --> 00:23:35,440 So what this problem basically had us do is it made us look 336 00:23:35,440 --> 00:23:38,400 at the effect of a price change on the consumption 337 00:23:38,400 --> 00:23:40,210 decisions of a consumer. 338 00:23:40,210 --> 00:23:41,970 So when a price increases, two things 339 00:23:41,970 --> 00:23:43,410 are basically happening. 340 00:23:43,410 --> 00:23:46,440 The first thing that's happening is the price of that 341 00:23:46,440 --> 00:23:49,950 product is more, so the person, in most cases, shifts 342 00:23:49,950 --> 00:23:53,320 their buying away from that product and towards the less 343 00:23:53,320 --> 00:23:54,790 expensive product. 344 00:23:54,790 --> 00:23:58,300 That's what this substitution effect shows us. 345 00:23:58,300 --> 00:24:00,260 The other effect that the person feels is since the 346 00:24:00,260 --> 00:24:05,480 price is higher, they can't buy as much stuff with the 347 00:24:05,480 --> 00:24:09,000 money that they have. So they feel poorer, even though they 348 00:24:09,000 --> 00:24:11,880 have the same amount of money, because the prices are higher. 349 00:24:11,880 --> 00:24:14,670 That's what this income effect represents. 350 00:24:14,670 --> 00:24:18,600 And the total effect is just the summation of the fact that 351 00:24:18,600 --> 00:24:20,340 the price is higher for one good and 352 00:24:20,340 --> 00:24:21,910 that they feel poorer. 353 00:24:21,910 --> 00:24:24,340 And so we looked at the total effect broken down into 354 00:24:24,340 --> 00:24:26,300 substitution and income effect.