WEBVTT 00:00:00.040 --> 00:00:02.460 The following content is provided under a Creative 00:00:02.460 --> 00:00:03.870 Commons license. 00:00:03.870 --> 00:00:06.910 Your support will help MIT OpenCourseWare continue to 00:00:06.910 --> 00:00:10.560 offer high-quality educational resources for free. 00:00:10.560 --> 00:00:13.460 To make a donation or view additional materials from 00:00:13.460 --> 00:00:17.390 hundreds of MIT courses, visit MIT OpenCourseWare at 00:00:17.390 --> 00:00:18.640 ocw.mit.edu. 00:00:22.255 --> 00:00:24.940 PROFESSOR: Hi, and welcome back to the 14.01 problem 00:00:24.940 --> 00:00:26.370 solving videos. 00:00:26.370 --> 00:00:30.370 Today, we're going to do Fall 2010, Problem Set 3, 00:00:30.370 --> 00:00:31.950 Problem Number 5. 00:00:31.950 --> 00:00:33.210 And we're going to go ahead and we're going to work 00:00:33.210 --> 00:00:37.530 through parts A, B, C, D, and E, and then we're going to 00:00:37.530 --> 00:00:40.320 finish up parts F and G. 00:00:40.320 --> 00:00:43.480 Problem 5 says that Xiao spends all her income on 00:00:43.480 --> 00:00:46.380 statistical softwares and clothes. 00:00:46.380 --> 00:00:49.060 Her preferences can be represented by the utility 00:00:49.060 --> 00:00:53.190 function where her utility equals 4 times the natural log 00:00:53.190 --> 00:00:58.350 of S plus 6 times the natural log of C, where S is software 00:00:58.350 --> 00:01:00.540 and C is clothes. 00:01:00.540 --> 00:01:03.840 Part A asks us to compute the marginal rate of substitution 00:01:03.840 --> 00:01:08.330 of software for clothes, asks us if the MRS is increasing or 00:01:08.330 --> 00:01:14.330 decreasing in S, and also asks us how we interpret the MRS. 00:01:14.330 --> 00:01:16.610 So before we start with this, we should really think about, 00:01:16.610 --> 00:01:19.450 conceptually, what the marginal rate of substitution 00:01:19.450 --> 00:01:22.845 of software for clothes looks like on our graph. 00:01:22.845 --> 00:01:25.880 So on this graph, I have clothes on the y-axis-- 00:01:25.880 --> 00:01:27.250 the quantity of clothes-- 00:01:27.250 --> 00:01:32.150 and the quantity of software on the x-axis here. 00:01:32.150 --> 00:01:35.690 Looking at this graph, this line that I've drawn is one 00:01:35.690 --> 00:01:36.660 utility level. 00:01:36.660 --> 00:01:40.440 So at this place, she might have a utility equal to 1. 00:01:40.440 --> 00:01:43.840 So she's indifferent on this indifference curve between 00:01:43.840 --> 00:01:49.070 being at point here or at a point here. 00:01:49.070 --> 00:01:51.970 And what the marginal rate of substitution is really asking 00:01:51.970 --> 00:01:56.130 us, it's asking us how much clothing is she willing to 00:01:56.130 --> 00:01:59.530 give up to get one more unit of software? 00:01:59.530 --> 00:02:04.100 So she's going to have to give up a certain amount of clothes 00:02:04.100 --> 00:02:07.110 to get one more unit of software. 00:02:07.110 --> 00:02:10.660 And the marginal rate of substitution tells us exactly 00:02:10.660 --> 00:02:13.550 how much clothing she's willing to give up. 00:02:13.550 --> 00:02:15.740 To calculate this algebraically, all we're going 00:02:15.740 --> 00:02:18.660 to do is we're going to take the marginal utility of 00:02:18.660 --> 00:02:22.460 software and divide it by the marginal utility of clothes. 00:02:22.460 --> 00:02:24.530 So we're going to take the derivative with respect to 00:02:24.530 --> 00:02:26.820 software and the derivative with respect to 00:02:26.820 --> 00:02:28.070 clothing and divide. 00:02:31.470 --> 00:02:37.580 When we do this, we find that the MRS is going to be equal 00:02:37.580 --> 00:02:43.270 to 4 over S, which is our marginal utility of software, 00:02:43.270 --> 00:02:46.980 all over 6 divided by C, which is our 00:02:46.980 --> 00:02:51.710 marginal utility of clothes. 00:02:51.710 --> 00:02:56.780 Solving through, we find that our MRS is 4C over 6S. 00:02:59.840 --> 00:03:02.050 Now, we have to think about, conceptually, what happens 00:03:02.050 --> 00:03:04.450 when software increases? 00:03:04.450 --> 00:03:08.520 When we have S increase, since it's in the denominator, we're 00:03:08.520 --> 00:03:14.780 also going to have the MRS decrease. 00:03:14.780 --> 00:03:18.060 So what this means is as software is increasing, or as 00:03:18.060 --> 00:03:21.300 she has more software, she's going to be willing to give up 00:03:21.300 --> 00:03:24.830 fewer clothing, or less clothing, to get another unit 00:03:24.830 --> 00:03:25.520 of software. 00:03:25.520 --> 00:03:32.610 So looking at our graph, when she's at this point, she's 00:03:32.610 --> 00:03:35.760 more willing to give up clothing to get more software. 00:03:35.760 --> 00:03:39.490 But when she has more software down here, she's less willing 00:03:39.490 --> 00:03:42.510 to give up the clothing. 00:03:42.510 --> 00:03:51.710 Let's go ahead and move on to Part B. Part B, find Xiao's 00:03:51.710 --> 00:03:54.560 demand functions for software and clothes-- 00:03:54.560 --> 00:03:57.140 so we're going to call those QS and QC-- 00:03:57.140 --> 00:04:00.010 in terms of the price of software PS, the price of 00:04:00.010 --> 00:04:03.670 clothes PC, and Xiao's income. 00:04:03.670 --> 00:04:06.240 Now, before we move on with this, what we want to do is we 00:04:06.240 --> 00:04:11.350 want to solve for one of the variables C or S in terms of 00:04:11.350 --> 00:04:13.960 the prices and the other variable. 00:04:13.960 --> 00:04:21.079 So to do this, we're going to set the MRS equal to the price 00:04:21.079 --> 00:04:23.990 of the software over the price of the clothes. 00:04:33.920 --> 00:04:36.660 From here, we can solve through for C, and we find 00:04:36.660 --> 00:04:48.540 that C is going to be equal to 3/2 times PS over PC times S. 00:04:48.540 --> 00:04:49.810 Now, since we have two variables-- 00:04:49.810 --> 00:04:53.120 we have a variable for clothes and a variable for software-- 00:04:53.120 --> 00:04:55.280 we're going to have to introduce another constraint 00:04:55.280 --> 00:04:56.850 into this problem. 00:04:56.850 --> 00:04:58.810 And the constraint that we're going to introduce is going to 00:04:58.810 --> 00:05:02.330 be the income function. 00:05:02.330 --> 00:05:05.000 We know that Xiao has some sort of income that's going to 00:05:05.000 --> 00:05:07.440 be fixed, and she's going to spend all of this on either 00:05:07.440 --> 00:05:10.390 clothes or software. 00:05:10.390 --> 00:05:12.990 Now, the amount of money she spends on software is going to 00:05:12.990 --> 00:05:18.380 be equal to the price of software times how much 00:05:18.380 --> 00:05:21.060 software she's going to buy. 00:05:21.060 --> 00:05:23.780 The rest of her income is going to be spent on clothes, 00:05:23.780 --> 00:05:28.640 so the price of clothes times the quantity of clothing. 00:05:28.640 --> 00:05:33.560 Now, to solve for the demand function for software, all 00:05:33.560 --> 00:05:36.510 we're going to do is we're going to plug in for C in the 00:05:36.510 --> 00:05:39.800 income function here, and then we're going to solve through 00:05:39.800 --> 00:06:16.900 for S. 00:06:16.900 --> 00:06:19.690 I know it's a little bit messy, but this says PS times 00:06:19.690 --> 00:06:25.940 3/2PS over PC, what we solved for here, times S. Now, when 00:06:25.940 --> 00:06:28.460 we solve through for S from this equation, we're going to 00:06:28.460 --> 00:06:32.580 find that the demand function for software is going to be 00:06:32.580 --> 00:06:42.110 equal to 2/2 times income over the price of software. 00:06:42.110 --> 00:06:45.200 Now, we can go through the same process solving for the 00:06:45.200 --> 00:06:48.430 demand function for clothing. 00:06:48.430 --> 00:06:53.770 And all we'd have to do now is we can take this S right here 00:06:53.770 --> 00:06:59.960 that we just solved for, we can plug this back into our 00:06:59.960 --> 00:07:04.720 income function, and then we can solve for C. When we solve 00:07:04.720 --> 00:07:08.040 for C, we're going to find that the demand function for 00:07:08.040 --> 00:07:16.580 clothing is going to equal 3/5 times I over PC. 00:07:16.580 --> 00:07:20.050 Part C asks us to draw the Engel curve for software. 00:07:20.050 --> 00:07:22.715 Now, all an Engel curve is, it's a relationship between 00:07:22.715 --> 00:07:26.200 the income and the quantity that's demanded for a product. 00:07:26.200 --> 00:07:29.860 And it shows us that as income increases, it shows how the 00:07:29.860 --> 00:07:34.380 quantity demanded is going to change with changing income. 00:07:34.380 --> 00:07:36.280 So to start off our Engel curve, we're going to draw an 00:07:36.280 --> 00:07:40.140 axes, we're going to put software, or the quantity 00:07:40.140 --> 00:07:42.970 that's demanded, on the x-axis, and we're going to put 00:07:42.970 --> 00:07:47.430 the income on the y-axis. 00:07:47.430 --> 00:07:49.880 Now, the nice thing about the software demand function that 00:07:49.880 --> 00:07:54.880 we solved for is that it's linear with respect to income. 00:08:01.100 --> 00:08:03.640 Now, before we can graph this equation, however, we have to 00:08:03.640 --> 00:08:05.840 get it in terms of income. 00:08:05.840 --> 00:08:08.360 So when we solve for this, we're going to find that 00:08:08.360 --> 00:08:21.610 income equals 5/2 PS times S. So all our Engel curve is 00:08:21.610 --> 00:08:25.880 going to look like is it's going to be a straight line. 00:08:25.880 --> 00:08:30.200 And the slope of that straight line is going to be 5/2 PS. 00:08:39.679 --> 00:08:43.900 And the way to interpret this conceptually is to say that 00:08:43.900 --> 00:08:49.280 with each one unit increase in income, the amount that's 00:08:49.280 --> 00:08:55.900 demanded is going to increase by 2/5 divided by PS. 00:08:58.540 --> 00:09:02.810 Let's go ahead and move on to Part D. Part D says, suppose 00:09:02.810 --> 00:09:06.780 that the price of software is PS equals 2, and the price of 00:09:06.780 --> 00:09:11.050 clothing is going to equal PC equals 3. 00:09:16.850 --> 00:09:22.580 And Xiao's income is going to equal 10. 00:09:22.580 --> 00:09:24.280 What bundle of software and clothes 00:09:24.280 --> 00:09:27.670 maximize Xiao's utility? 00:09:27.670 --> 00:09:31.770 Now, we've already found the conditional demand curves for 00:09:31.770 --> 00:09:33.570 both software and clothes. 00:09:33.570 --> 00:09:37.160 So we can start off this problem by writing down those 00:09:37.160 --> 00:09:39.320 conditional demand curves. 00:09:39.320 --> 00:09:48.070 The conditional demand curve for software was given by 2/5 00:09:48.070 --> 00:09:50.320 I divided by PS. 00:09:50.320 --> 00:09:57.730 And the conditional demand for clothing was given by 3/5 I 00:09:57.730 --> 00:10:00.050 divided by PC. 00:10:00.050 --> 00:10:02.300 All we have to do now is we have to plug in these 00:10:02.300 --> 00:10:06.950 variables to solve for the software and the clothing 00:10:06.950 --> 00:10:08.290 that's going to be demanded. 00:10:08.290 --> 00:10:12.520 When we plug those in, we're going to find that she's going 00:10:12.520 --> 00:10:18.960 to demand two units of both software and clothes. 00:10:18.960 --> 00:10:23.760 So this is in the scenario for Part D. Part E gives us 00:10:23.760 --> 00:10:25.970 another scenario that we can solve for. 00:10:25.970 --> 00:10:29.060 And all that's going to happen now is that the price of 00:10:29.060 --> 00:10:31.710 software is going to change. 00:10:31.710 --> 00:10:34.420 And we're going to look at how that affects the bundle that 00:10:34.420 --> 00:10:36.990 maximizes her utility. 00:10:36.990 --> 00:10:39.950 For Part E, it says, suppose that the price of software 00:10:39.950 --> 00:10:50.220 increases from PS equal to 2, and now it's going to be PS is 00:10:50.220 --> 00:10:53.040 going to equal 4. 00:10:53.040 --> 00:10:56.770 What bundle of software and clothes does Xiao demand now? 00:11:00.080 --> 00:11:04.610 Again, we're just going to solve through. 00:11:04.610 --> 00:11:08.610 With our new PS equals 4, we're going to solve for the 00:11:08.610 --> 00:11:11.180 software and clothing that Xiao demands. 00:11:11.180 --> 00:11:16.650 We're going to find that S is going to equal 1 now, and that 00:11:16.650 --> 00:11:20.125 the amount of clothing is going to equal 2. 00:11:23.440 --> 00:11:24.800 So let's take a pause right here. 00:11:24.800 --> 00:11:26.580 And we're going to come back in just a minute. 00:11:26.580 --> 00:11:29.140 And we're going to look at the more interesting case, which 00:11:29.140 --> 00:11:33.340 is given the fact that she's consuming less-- she has one 00:11:33.340 --> 00:11:35.500 less unit of software to consume-- 00:11:35.500 --> 00:11:39.040 how do we get her back to the utility that she had before? 00:11:39.040 --> 00:11:41.780 What amount of money or income do we have to give her so that 00:11:41.780 --> 00:11:44.870 she can be as happy as she was in this initial scenario with 00:11:44.870 --> 00:11:46.660 two units of both software and clothes? 00:11:51.960 --> 00:11:53.160 Welcome back. 00:11:53.160 --> 00:11:56.550 So we're going to continue onto Part F. Part F says, 00:11:56.550 --> 00:12:00.150 given the price increase, how much income does Xiao need to 00:12:00.150 --> 00:12:01.440 remain as happy-- 00:12:01.440 --> 00:12:02.970 have the same utility-- 00:12:02.970 --> 00:12:05.120 as she was before the price change? 00:12:05.120 --> 00:12:08.590 What bundle of softwares and clothes would Xiao consume if 00:12:08.590 --> 00:12:13.060 she had the additional income given the new prices? 00:12:13.060 --> 00:12:16.410 So we want to find out, how can we give her as much income 00:12:16.410 --> 00:12:19.150 so she can be as happy as she was to start off with? 00:12:19.150 --> 00:12:21.430 To start this problem, the first thing that we're going 00:12:21.430 --> 00:12:24.240 to have to find out is we're going to have to find out 00:12:24.240 --> 00:12:26.920 exactly how happy Xiao was to begin with. 00:12:26.920 --> 00:12:29.560 So we need to know her initial utility. 00:12:29.560 --> 00:12:33.370 So let's start off with that calculation. 00:12:33.370 --> 00:12:36.410 To calculate her initial utility, we're just going to 00:12:36.410 --> 00:12:46.260 start off by saying that her utility is equal to 4 natural 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 00:12:54.860 --> 00:12:59.340 for S and C. In this case, when we solve through, we find 00:12:59.340 --> 00:13:05.980 that her initial utility is 6.931. 00:13:05.980 --> 00:13:10.660 So we're going to set her utility equal to 6.931. 00:13:10.660 --> 00:13:13.540 And what we want to find out is we want to find out what 00:13:13.540 --> 00:13:16.770 income we have to give her so that she can get up to this 00:13:16.770 --> 00:13:19.370 utility, given the new prices. 00:13:19.370 --> 00:13:24.090 So we're going to take this utility function, and we're 00:13:24.090 --> 00:13:26.680 going to plug in the conditional demand curves for 00:13:26.680 --> 00:13:31.050 S and C so that income is now a function, or one of the 00:13:31.050 --> 00:13:32.920 inputs for her utility. 00:13:32.920 --> 00:13:36.580 When we do that, we're going to get this function. 00:13:54.450 --> 00:13:58.690 And remember, we said that we want, given this input and the 00:13:58.690 --> 00:13:59.530 new prices-- 00:13:59.530 --> 00:14:04.050 so we're going to set this PS is going to be equal to the 00:14:04.050 --> 00:14:06.750 new price in the problem. 00:14:06.750 --> 00:14:11.030 And we're going to also set the PC equal to the price that 00:14:11.030 --> 00:14:12.740 was in Part E as well. 00:14:12.740 --> 00:14:16.900 And flipping back to the problem, we know that the 00:14:16.900 --> 00:14:22.400 price of clothing is going to be equal to 3, and the price 00:14:22.400 --> 00:14:28.880 of software for the second part was equal to 4. 00:14:28.880 --> 00:14:32.840 So we're going to plug in for PS and PC, we're going to set 00:14:32.840 --> 00:14:36.970 utility equal to 6.931, and we're going to solve through 00:14:36.970 --> 00:14:43.410 for I. When we do this, and when we solve through for I, 00:14:43.410 --> 00:14:48.940 what we're going to find is we're going to have 6.931 is 00:14:48.940 --> 00:14:57.230 going to be equal to 10 natural log of I minus 4 00:14:57.230 --> 00:15:05.320 natural log of 10 minus 6 natural log of 5. 00:15:05.320 --> 00:15:08.020 Solving through, doing the inverse natural log function 00:15:08.020 --> 00:15:11.100 for I after isolating this variable, we're going to find 00:15:11.100 --> 00:15:19.350 that the new income that she needs to be supplied is 13.19. 00:15:19.350 --> 00:15:21.930 So the income that she needs to be just as happy with these 00:15:21.930 --> 00:15:27.460 prices has increased by 3.19. 00:15:27.460 --> 00:15:30.130 Now, we can go back to our conditional demand curves that 00:15:30.130 --> 00:15:31.400 we had here. 00:15:31.400 --> 00:15:37.180 We can plug in PS equals 4, PC equals 3, and we can plug in 00:15:37.180 --> 00:15:40.190 for income 13.19. 00:15:40.190 --> 00:15:45.410 And we can solve S double prime, which is the new 00:15:45.410 --> 00:15:51.340 software that she's going to demand, which will be 1.32, 00:15:51.340 --> 00:15:54.850 and C double prime, the new amount of clothes that she's 00:15:54.850 --> 00:16:07.920 going to demand, which is 2.64. 00:16:07.920 --> 00:16:11.290 Now, the final part of the problem, which we're going to 00:16:11.290 --> 00:16:15.080 move on to now, which is Part G, is actually the most 00:16:15.080 --> 00:16:17.780 important part of the problem, because what we're going to do 00:16:17.780 --> 00:16:20.130 is we're going to tie together the three 00:16:20.130 --> 00:16:22.430 scenarios that we did. 00:16:22.430 --> 00:16:27.490 We did this scenario where we were giving her income so that 00:16:27.490 --> 00:16:29.320 she would be just as happy. 00:16:29.320 --> 00:16:33.860 We had our initial scenario before the price increase. 00:16:33.860 --> 00:16:37.010 And we had the scenario after the price increase. 00:16:37.010 --> 00:16:39.940 And we're going to look at this conceptually on a graph, 00:16:39.940 --> 00:16:43.470 and we're going to see, how do we relate these three bundles 00:16:43.470 --> 00:16:45.570 of consumption? 00:16:45.570 --> 00:16:49.660 Part G says, going back to the situation in Part E, where PS 00:16:49.660 --> 00:16:53.940 equals 4 and I equals 10, we need to decompose the total 00:16:53.940 --> 00:16:57.120 change of softwares and clothes demanded into 00:16:57.120 --> 00:16:59.570 substitution and income effects. 00:16:59.570 --> 00:17:02.320 In a clearly-labelled diagram, with softwares on the 00:17:02.320 --> 00:17:05.480 horizontal axis, show the income and substitution 00:17:05.480 --> 00:17:08.089 effects of the increase in the price of software. 00:17:10.750 --> 00:17:14.060 Now, we're going to go back to this graph that 00:17:14.060 --> 00:17:16.440 we started off with. 00:17:16.440 --> 00:17:21.680 And what we're going to do here, is we're going to 00:17:21.680 --> 00:17:25.240 illustrate the three bundles that she selected. 00:17:25.240 --> 00:17:29.580 I'll illustrate the first bundle where she consumes 2 00:17:29.580 --> 00:17:30.930 units of each. 00:17:30.930 --> 00:17:33.690 And we already have our utility curve, or indifference 00:17:33.690 --> 00:17:35.600 curve, drawn up here. 00:17:35.600 --> 00:17:38.980 Now we need to draw the budget constraint that shows how much 00:17:38.980 --> 00:17:41.390 she can spend on each product. 00:17:41.390 --> 00:17:45.730 If she were to spend all her money on clothes, she would be 00:17:45.730 --> 00:17:48.020 up here at this corner solution. 00:17:48.020 --> 00:17:51.490 If she were to spend all her money on software, she would 00:17:51.490 --> 00:17:52.340 be down here. 00:17:52.340 --> 00:17:55.270 When we connect a line through here, this is her budget 00:17:55.270 --> 00:18:01.270 constraint that shows all the possible bundles of goods 00:18:01.270 --> 00:18:04.380 where she could potentially spend her money. 00:18:04.380 --> 00:18:10.430 And this first bundle is the point 2,2. 00:18:10.430 --> 00:18:14.160 This is where she starts off to begin with. 00:18:14.160 --> 00:18:17.900 Now, when the price of software increases, she's not 00:18:17.900 --> 00:18:23.010 going to be able to buy as much software with her money. 00:18:23.010 --> 00:18:25.750 But she can still buy the same amount of clothing. 00:18:25.750 --> 00:18:31.780 So her new budget constraint in this scenario is going to 00:18:31.780 --> 00:18:34.620 look like this. 00:18:34.620 --> 00:18:38.710 So in this scenario, which is in our problem's Part E, her 00:18:38.710 --> 00:18:41.880 utility has moved in towards the origin. 00:18:41.880 --> 00:18:44.230 And she isn't going to be as happy. 00:18:44.230 --> 00:18:48.100 And we can represent this on a utility curve as well. 00:18:54.890 --> 00:18:59.640 And we can see from this point on the utility curve the way 00:18:59.640 --> 00:19:03.470 that I've drawn it, that at this point, she's still 00:19:03.470 --> 00:19:06.510 consuming the same amount of clothing. 00:19:06.510 --> 00:19:08.560 But the amount of software she's consumed 00:19:08.560 --> 00:19:09.810 has been cut in half. 00:19:13.800 --> 00:19:15.960 This is the total effect of the price change. 00:19:15.960 --> 00:19:18.750 It's the difference between where she started and where 00:19:18.750 --> 00:19:22.070 she's ending up without giving her any money to change where 00:19:22.070 --> 00:19:23.320 she actually is. 00:19:25.590 --> 00:19:36.770 So the total effect is just that she's 00:19:36.770 --> 00:19:41.860 losing one unit of software. 00:19:45.360 --> 00:19:52.000 Now, we can break down the total effect in the 00:19:52.000 --> 00:19:56.790 substitution effects and income effects. 00:19:56.790 --> 00:19:59.880 It's important that we really understand conceptually how to 00:19:59.880 --> 00:20:04.210 define substitution and income effects. 00:20:04.210 --> 00:20:06.140 And what we're going to think about is we're going to think 00:20:06.140 --> 00:20:11.520 about, on this graph, we're going to represent the 00:20:11.520 --> 00:20:16.270 substitution effect by the movement-- 00:20:16.270 --> 00:20:18.420 if we were to just have the price change, and we were to 00:20:18.420 --> 00:20:22.320 give her income so she could stay up at this utility level, 00:20:22.320 --> 00:20:24.360 the substitution effect is how her bundle 00:20:24.360 --> 00:20:26.370 changes with that movement. 00:20:26.370 --> 00:20:29.460 The income effect is going to be-- since she's poorer 00:20:29.460 --> 00:20:31.770 because the prices are higher, it's going to 00:20:31.770 --> 00:20:33.780 be the shift downward. 00:20:33.780 --> 00:20:38.710 So I'm going to draw in the scenario that we calculated in 00:20:38.710 --> 00:20:41.890 Part F right here. 00:20:41.890 --> 00:20:46.300 By drawing in this scenario with the higher income level 00:20:46.300 --> 00:20:51.890 and the price change, we can represent this bundle as the 00:20:51.890 --> 00:20:54.210 substitution effect. 00:20:54.210 --> 00:20:57.480 So what this looks like is she's going to have the same 00:20:57.480 --> 00:21:00.520 budget constraint, only it's going to be shifted back up. 00:21:06.090 --> 00:21:09.480 This is going to be the bundle in Part F. And we can label 00:21:09.480 --> 00:21:20.330 the bundle 1.32, 2.64. 00:21:20.330 --> 00:21:23.610 And this is where it's going to get a little bit tricky. 00:21:23.610 --> 00:21:36.040 The substitution effect is just the movement from 2.2 to 00:21:36.040 --> 00:21:38.940 the same utility curve but at a different point with a 00:21:38.940 --> 00:21:39.620 different bundle. 00:21:39.620 --> 00:21:42.250 So it's when we've given her income to keep her at the same 00:21:42.250 --> 00:21:46.090 utility level, but we've had the price change. 00:21:46.090 --> 00:21:47.910 This is going to be the substitution effect. 00:21:47.910 --> 00:21:50.730 I'm going to label it 1. 00:21:50.730 --> 00:21:54.460 Now, the income effect is the next movement. 00:21:54.460 --> 00:21:57.980 It's the movement that says, well, we don't really give her 00:21:57.980 --> 00:21:58.580 more income. 00:21:58.580 --> 00:22:00.240 She's actually poorer. 00:22:00.240 --> 00:22:07.910 It's the movement down from 1.32, 2.64, down to 1, 2. 00:22:07.910 --> 00:22:11.430 And then the total effect is just this 00:22:11.430 --> 00:22:15.970 movement from 2.2 to 1.2. 00:22:15.970 --> 00:22:21.870 So I can label the substitution effect 1, the 00:22:21.870 --> 00:22:27.360 income effect 2, and the total effect 3. 00:22:27.360 --> 00:22:30.500 So to calculate the substitution effect, all it's 00:22:30.500 --> 00:22:33.810 going to be is it's going to be the difference between 2.2 00:22:33.810 --> 00:22:37.640 and 1.32 and 2.64. 00:22:37.640 --> 00:22:42.660 So in this case, our substitution effect is going 00:22:42.660 --> 00:22:55.020 to be equal to 0.68, negative 0.64. 00:22:55.020 --> 00:22:58.080 And you can see that we actually had an increase in 00:22:58.080 --> 00:23:03.710 the consumption of clothes for the substitution effect. 00:23:03.710 --> 00:23:11.970 And then the income effect, using this equation and what 00:23:11.970 --> 00:23:14.772 we calculated the substitution effect and the total effect to 00:23:14.772 --> 00:23:31.610 be, we find that the income effect is equal to 0.32, 0.64. 00:23:31.610 --> 00:23:35.440 So what this problem basically had us do is it made us look 00:23:35.440 --> 00:23:38.400 at the effect of a price change on the consumption 00:23:38.400 --> 00:23:40.210 decisions of a consumer. 00:23:40.210 --> 00:23:41.970 So when a price increases, two things 00:23:41.970 --> 00:23:43.410 are basically happening. 00:23:43.410 --> 00:23:46.440 The first thing that's happening is the price of that 00:23:46.440 --> 00:23:49.950 product is more, so the person, in most cases, shifts 00:23:49.950 --> 00:23:53.320 their buying away from that product and towards the less 00:23:53.320 --> 00:23:54.790 expensive product. 00:23:54.790 --> 00:23:58.300 That's what this substitution effect shows us. 00:23:58.300 --> 00:24:00.260 The other effect that the person feels is since the 00:24:00.260 --> 00:24:05.480 price is higher, they can't buy as much stuff with the 00:24:05.480 --> 00:24:09.000 money that they have. So they feel poorer, even though they 00:24:09.000 --> 00:24:11.880 have the same amount of money, because the prices are higher. 00:24:11.880 --> 00:24:14.670 That's what this income effect represents. 00:24:14.670 --> 00:24:18.600 And the total effect is just the summation of the fact that 00:24:18.600 --> 00:24:20.340 the price is higher for one good and 00:24:20.340 --> 00:24:21.910 that they feel poorer. 00:24:21.910 --> 00:24:24.340 And so we looked at the total effect broken down into 00:24:24.340 --> 00:24:26.300 substitution and income effect.