0:00:00.220,0:00:02.737 Male: In the last video,[br]we began our exploration 0:00:02.737,0:00:04.736 of what a consumption function is. 0:00:04.736,0:00:06.331 It's a fairly straightforward idea. 0:00:06.331,0:00:08.234 It's a function that describes how 0:00:08.234,0:00:12.138 aggregate income can drive[br]aggregate consumption. 0:00:12.138,0:00:14.479 We started with a fairly[br]simple model of this, 0:00:14.479,0:00:16.233 a fairly simple consumption function. 0:00:16.233,0:00:17.536 It was a linear one. 0:00:17.536,0:00:19.313 You had some base level of consumption, 0:00:19.313,0:00:21.007 regardless of aggregate income, 0:00:21.007,0:00:22.977 and then you had some level of consumption 0:00:22.977,0:00:25.143 that was essentially induced by having 0:00:25.143,0:00:27.276 some disposable income. 0:00:27.276,0:00:30.149 When we plotted this linear[br]model, we got a line. 0:00:30.149,0:00:32.005 We got a line right over here. 0:00:32.005,0:00:33.400 I pointed out in the last video 0:00:33.400,0:00:35.312 this does not have to be the only way 0:00:35.312,0:00:37.413 that a consumption[br]function can be described. 0:00:37.413,0:00:39.867 You might use some fancier[br]mathematical tools. 0:00:39.867,0:00:42.137 Maybe you can construct[br]a consumption function. 0:00:42.137,0:00:43.360 You have an argument. 0:00:43.360,0:00:45.002 You would argue that[br]the marginal propensity 0:00:45.002,0:00:47.532 to consume is higher at lower levels 0:00:47.532,0:00:50.401 of disposable income and[br]that it kind of tapers out 0:00:50.401,0:00:52.199 as disposable income, as aggregate 0:00:52.199,0:00:54.004 disposable income goes up. 0:00:54.004,0:00:55.822 You might think that maybe you should have 0:00:55.822,0:00:57.741 a fancier consumption function 0:00:57.741,0:00:59.902 that when you graph it[br]would look like this 0:00:59.902,0:01:01.407 and then you would have to use things 0:01:01.407,0:01:03.872 fancier than just what[br]we used right over here. 0:01:03.872,0:01:05.400 What I want to do in this video 0:01:05.400,0:01:08.153 is focus more on a linear model. 0:01:08.153,0:01:10.074 The reason why I'm going to focus on 0:01:10.074,0:01:12.817 a linear model is because,[br]one, it's simpler. 0:01:12.817,0:01:14.486 It'll be easier to manipulate. 0:01:14.486,0:01:16.933 It's also the model that tends to be used 0:01:16.933,0:01:18.736 right when people are starting to digest 0:01:18.736,0:01:20.668 things like consumption functions 0:01:20.668,0:01:24.133 and building on them to learn about things 0:01:24.133,0:01:25.600 like, and we'll do this in a few videos, 0:01:25.600,0:01:27.129 the Keynesian Cross. 0:01:27.129,0:01:29.160 What I'm going to do is,[br]I'm going to do two things. 0:01:29.160,0:01:31.069 I'm going to generalize this linear 0:01:31.069,0:01:32.935 consumption function,[br]and I'm going to make it 0:01:32.935,0:01:35.334 a function not just of disposal income, 0:01:35.334,0:01:38.067 not just of aggregate disposable income, 0:01:38.067,0:01:39.493 which is what we did in the last video, 0:01:39.493,0:01:43.131 but as a function of[br]income, of aggregate income. 0:01:43.131,0:01:45.566 Then we will plot that generalized one 0:01:45.566,0:01:46.820 based on the variables. 0:01:46.820,0:01:48.075 It's really going to be the same thing. 0:01:48.075,0:01:49.402 We're just not going to use these numbers. 0:01:49.402,0:01:51.071 We're going to use[br]variables in their place. 0:01:51.071,0:01:54.408 Let's give ourselves a[br]linear consumption function. 0:01:54.408,0:01:58.707 We can say that aggregate consumption 0:01:58.707,0:02:00.266 where we're going to have some base level 0:02:00.266,0:02:02.390 of consumption no matter[br]what, even if people 0:02:02.390,0:02:04.810 have no aggregate income,[br]they need to survive. 0:02:04.810,0:02:06.063 They need food on the table. 0:02:06.063,0:02:08.476 Maybe they'll have to dig[br]in savings somehow to do it. 0:02:08.476,0:02:10.663 So, some base level of consumption. 0:02:10.663,0:02:13.892 I'll call that lower case c sub zero. 0:02:13.892,0:02:17.394 Or lowercase c with a subscript[br]of zero right over there. 0:02:17.394,0:02:20.328 That's the base level[br]of aggregate consumption 0:02:20.328,0:02:23.991 or it's sometimes referred[br]to as autonomous consumption. 0:02:23.991,0:02:30.922 This is autonomous[br]consumption because people 0:02:30.922,0:02:32.662 will do it on their own, or in aggregate 0:02:32.662,0:02:34.265 they will do it on their[br]own, even if they have 0:02:34.265,0:02:36.451 no aggregate income. 0:02:36.451,0:02:39.591 Then we will have the part that is due, 0:02:39.591,0:02:42.396 directly due, to having[br]some aggregate income. 0:02:42.396,0:02:44.884 We call that the induced consumption, 0:02:44.884,0:02:46.379 because you can view it as being induced 0:02:46.379,0:02:48.258 by having some aggregate income. 0:02:48.258,0:02:51.194 Above and beyond what the[br]base level of consumption, 0:02:51.194,0:02:54.382 people are going to consume some fraction 0:02:54.382,0:02:56.219 of their disposable income. 0:02:56.219,0:03:04.217 So we'll say disposable income. 0:03:04.217,0:03:05.733 They're not going to consume all 0:03:05.733,0:03:06.639 of their disposable income. 0:03:06.639,0:03:07.736 They might save some of it. 0:03:07.736,0:03:09.468 So they're going to consume the fraction 0:03:09.468,0:03:12.664 that's essentially their[br]marginal propensity to consume. 0:03:12.664,0:03:17.051 This right over here, I'll[br]do that in this orange color. 0:03:17.051,0:03:22.367 Marginal propensity to consume. 0:03:22.367,0:03:23.753 Hopefully this makes intuitive sense. 0:03:23.753,0:03:25.317 This says, look, if this was 100, 0:03:25.317,0:03:27.646 people are going to[br]consume 100 no matter what, 0:03:27.646,0:03:30.389 100 billion whatever[br]your unit of currency is. 0:03:30.389,0:03:31.725 Now, if their marginal propensity 0:03:31.725,0:03:34.651 to consume is, let's say, it is 1/3. 0:03:34.651,0:03:37.313 You have now above and beyond this 0:03:37.313,0:03:40.581 people have disposable[br]income of let's say 900, 0:03:40.581,0:03:43.644 this is saying that[br]they want to consume 1/3 0:03:43.644,0:03:46.481 of that disposable income they're getting. 0:03:46.481,0:03:48.186 That is, if you give them 900 of extra 0:03:48.186,0:03:50.050 disposable income, they're propensity 0:03:50.050,0:03:52.730 to consume that incremental income, 0:03:52.730,0:03:54.146 they're going to consume 1/3 of it. 0:03:54.146,0:03:56.318 So this would be 1/3, so it would be 900. 0:03:56.318,0:03:57.782 Let me give an example. 0:03:57.782,0:04:00.587 If you had a situation,[br]you could have a situation, 0:04:00.587,0:04:05.447 where c-nought is equal to 100. 0:04:05.447,0:04:15.156 If you have disposable[br]income is equal to 900, 0:04:15.156,0:04:18.315 and c1 is equal to 1/3, or we could say 0:04:18.315,0:04:21.886 0.333 repeating forever, c1 is 1/3. 0:04:21.886,0:04:23.584 Then this makes sense. 0:04:23.584,0:04:25.721 On their own people[br]would consume this much, 0:04:25.721,0:04:27.319 but now they have this disposable income. 0:04:27.319,0:04:29.227 Their marginal propensity to consume 0:04:29.227,0:04:30.914 if you give them 900 extra of income, 0:04:30.914,0:04:33.178 they're going to consume 1/3 of that. 0:04:33.178,0:04:35.473 So then you're going to[br]have, your consumption 0:04:35.473,0:04:38.185 is going to be equal to, for[br]this case right over here, 0:04:38.185,0:04:47.794 your consumption is going to[br]be 100 plus 1/3 times 900. 0:04:47.794,0:04:49.766 So your consumption in this situation, 0:04:49.766,0:04:53.542 your induced consumption, 1/3 times 900, 0:04:53.542,0:04:56.931 would be 300, maybe it's[br]in billions of dollars, 0:04:56.931,0:04:58.458 300 billion dollars. 0:04:58.458,0:05:00.669 Then your autonomous[br]consumption would be 100. 0:05:00.669,0:05:04.927 They would add up to 400. 0:05:04.927,0:05:07.869 Once again, this is autonomous[br]and this is induced. 0:05:07.869,0:05:16.091 Autonomous, this right over[br]here is induced consumption. 0:05:16.091,0:05:17.915 Now, I did write it in general terms. 0:05:17.915,0:05:21.208 I'm using variables here[br]instead of, or constants, really 0:05:21.208,0:05:25.621 instead of using the numbers[br]we saw in the last example. 0:05:25.621,0:05:27.578 But I also said that I would express 0:05:27.578,0:05:30.950 aggregate consumption[br]as a function not just 0:05:30.950,0:05:33.714 of disposable income[br]but of aggregate income; 0:05:33.714,0:05:35.702 not just of aggregate disposable income 0:05:35.702,0:05:37.214 but aggregate income. 0:05:37.214,0:05:39.383 The relationship is fairly simple between 0:05:39.383,0:05:42.131 disposable income and overall income. 0:05:42.131,0:05:46.194 We saw over here, in[br]aggregate, you have income, 0:05:46.194,0:05:47.979 but the government in[br]most modern economies 0:05:47.979,0:05:50.382 takes some fraction of that out for taxes. 0:05:50.382,0:05:53.195 What's left over is disposable income. 0:05:53.195,0:05:57.004 Just a reminder, income in aggregate, 0:05:57.004,0:05:58.540 aggregate income is the same thing as 0:05:58.540,0:05:59.625 aggregate expenditures, 0:05:59.625,0:06:01.052 which is the same thing[br]as aggregate output. 0:06:01.052,0:06:04.382 This right over here is GDP. 0:06:04.382,0:06:06.541 So this right over here is, let me do this 0:06:06.541,0:06:08.867 in a color, I've used[br]almost all my colors. 0:06:08.867,0:06:11.248 This is equal to GDP. 0:06:11.248,0:06:14.649 Disposable income is essentially GDP, 0:06:14.649,0:06:20.890 or you could say aggregate[br]income, minus taxes. 0:06:20.890,0:06:22.947 I'm going to do the taxes[br]in a different color. 0:06:22.947,0:06:26.594 Minus taxes. 0:06:26.594,0:06:27.987 So we can express disposable income 0:06:27.987,0:06:32.120 as aggregate income, this right over here 0:06:32.120,0:06:36.873 is the same thing as[br]aggregate income minus taxes. 0:06:36.873,0:06:38.992 We could rewrite our[br]whole thing over again. 0:06:38.992,0:06:43.801 Aggregate consumption is equal[br]to autonomous consumption 0:06:43.801,0:06:46.323 plus the marginal propensity to consume 0:06:46.323,0:06:51.739 times aggregate income,[br]which is the same thing 0:06:51.739,0:06:58.507 as GDP, times aggregate[br]income minus taxes. 0:06:58.507,0:07:01.179 We fully generalized[br]our consumption function 0:07:01.179,0:07:04.328 and now we've written it as a[br]function of aggregate income, 0:07:04.328,0:07:06.999 not just aggregate disposable income. 0:07:06.999,0:07:09.268 To make you comfortable[br]that this is still a line 0:07:09.268,0:07:11.945 if we were to plot it as a function 0:07:11.945,0:07:14.213 of aggregate income instead[br]of disposable income, 0:07:14.213,0:07:16.419 let me manipulate this thing a little bit. 0:07:16.419,0:07:19.342 We could distribute c1, which is our 0:07:19.342,0:07:21.595 marginal propensity to consume, and we get 0:07:21.595,0:07:27.198 aggregate consumption is equal[br]to autonomous consumption 0:07:27.198,0:07:28.681 and then we're going to distribute this, 0:07:28.681,0:07:31.196 plus c, so we're going to multiply it 0:07:31.196,0:07:32.431 times both of these terms, 0:07:32.431,0:07:34.599 plus our marginal propensity to consume 0:07:34.599,0:07:38.640 times aggregate income, 0:07:38.640,0:07:41.883 and then minus our marginal[br]propensity to consume 0:07:41.883,0:07:46.799 times our taxes. 0:07:46.799,0:07:50.142 Since we want it as a[br]function of aggregate income, 0:07:50.142,0:07:52.059 everything else here is really a constant. 0:07:52.059,0:07:54.059 We're assuming that those[br]aren't going to change. 0:07:54.059,0:07:55.421 Those are constant variables. 0:07:55.421,0:07:57.392 What we could do is we could rewrite this 0:07:57.392,0:07:59.330 in a form that you're[br]probably familiar with. 0:07:59.330,0:08:01.266 Back in algebra class[br]you probably remember 0:08:01.266,0:08:07.403 you can write it in the form y=mx+b where 0:08:07.403,0:08:09.594 x is the independent variable, 0:08:09.594,0:08:11.191 y is the dependent variable. 0:08:11.191,0:08:12.256 If you were to plot this, 0:08:12.256,0:08:17.899 on the horizontal axis is your x axis, 0:08:17.899,0:08:20.350 your vertical axis is your y axis. 0:08:20.350,0:08:22.272 This right over here[br]would have a y intercept, 0:08:22.272,0:08:26.664 or your vertical axis intercept[br]of b, right over there. 0:08:26.664,0:08:29.009 Then it would be a line with slope m. 0:08:29.009,0:08:32.730 If you were to take your[br]rise divided by your run, 0:08:32.730,0:08:34.409 or how much you move up[br]when you move to the right 0:08:34.409,0:08:38.330 a certain amount, that gives you your m. 0:08:38.330,0:08:40.138 Slope is equal to m. 0:08:40.138,0:08:41.662 The same analogy is here. 0:08:41.662,0:08:43.880 We can rewrite this in that form, 0:08:43.880,0:08:46.828 where our dependent[br]variable is no longer y. 0:08:46.828,0:08:48.956 Our dependent variable[br]is aggregate consumption. 0:08:48.956,0:08:53.161 Our independent variable is[br]not x, it is aggregate income. 0:08:53.161,0:08:54.602 So let's write it in that form. 0:08:54.602,0:08:57.868 We can write it as dependent variable, c, 0:08:57.868,0:08:59.471 which we'll plot on the vertical axis, 0:08:59.471,0:09:03.367 is equal to the marginal[br]propensity to consume 0:09:03.367,0:09:07.354 times aggregate income, 0:09:07.354,0:09:08.832 I'll do that purple color, 0:09:08.832,0:09:09.933 times aggregate income, 0:09:09.933,0:09:15.031 plus autonomous consumption, 0:09:15.031,0:09:22.280 minus marginal propensity[br]to consume times taxes. 0:09:22.280,0:09:23.838 It looks all complicated, but you just 0:09:23.838,0:09:27.082 have to realize that this[br]part right over here, 0:09:27.082,0:09:29.612 this is all a constant. 0:09:29.612,0:09:34.937 It is analogous to the[br]b if you were to write 0:09:34.937,0:09:37.457 things in kind of[br]traditional slope intercept 0:09:37.457,0:09:38.934 form right over here. 0:09:38.934,0:09:40.790 When we plot the line, if you have no 0:09:40.790,0:09:44.437 aggregate income, this is what your 0:09:44.437,0:09:45.870 consumption is going to be. 0:09:45.870,0:09:48.037 Let me draw that. 0:09:48.037,0:09:54.847 Once again, our dependent[br]variable is aggregate consumption. 0:09:54.847,0:09:57.190 Our independent variable[br]in this is no longer 0:09:57.190,0:09:59.255 disposable income like[br]we did in the last video. 0:09:59.255,0:10:04.933 It is now aggregate income. 0:10:04.933,0:10:06.734 If there's no aggregate income, 0:10:06.734,0:10:08.455 this is the independent[br]variable right over here, 0:10:08.455,0:10:09.750 if there's no aggregate income, 0:10:09.750,0:10:11.188 then your consumption is just going to be 0:10:11.188,0:10:12.926 this value right over here. 0:10:12.926,0:10:14.394 So your consumption is just going to be 0:10:14.394,0:10:17.147 that value right over[br]there, which is c-nought 0:10:17.147,0:10:20.579 minus c1 times t. 0:10:20.579,0:10:25.719 Then as you have larger values of 0:10:25.719,0:10:28.678 aggregate income, c1, that fraction of it, 0:10:28.678,0:10:32.130 is what's going to contribute[br]to the induced consumption. 0:10:32.130,0:10:34.517 What you essentially[br]have is this is the slope 0:10:34.517,0:10:36.667 of our line, this right[br]over here is our slope. 0:10:36.667,0:10:38.503 Just to kind of draw the analogy, 0:10:38.503,0:10:42.085 if you were to say y[br]is equal to mx plus b. 0:10:42.085,0:10:43.872 Actually, maybe I'll write it like this. 0:10:43.872,0:10:49.658 If you were to write c is equal to m ... 0:10:49.658,0:10:51.888 and I don't want to[br]confuse you if this m and b 0:10:51.888,0:10:53.183 seem completely foreign. 0:10:53.183,0:10:55.625 It comes from kind of[br]a traditional algebra 0:10:55.625,0:10:58.109 grounding in slope and y intercept. 0:10:58.109,0:11:04.919 If I were to say c is equal to my plus b, 0:11:04.919,0:11:05.975 this is the slope. 0:11:05.975,0:11:10.300 This is our vertical or our[br]dependent variable intercept 0:11:10.300,0:11:11.607 right over here. 0:11:11.607,0:11:13.568 That's where we intercept the dependent 0:11:13.568,0:11:14.805 variable axis. 0:11:14.805,0:11:16.084 And this is our slope. 0:11:16.084,0:11:18.195 It's our marginal propensity to consume. 0:11:18.195,0:11:21.473 Our line will look something like this, 0:11:21.473,0:11:25.436 where the slope is equal to the marginal 0:11:25.436,0:11:28.672 propensity to consume,[br]which is equal to c1. 0:11:28.672,0:11:30.233 If people all of a sudden are more likely 0:11:30.233,0:11:32.733 to spend a larger[br]fraction of their income, 0:11:32.733,0:11:36.777 then the marginal propensity to consume 0:11:36.777,0:11:38.941 would be higher and our[br]slope would be higher. 0:11:38.941,0:11:40.363 We would have a line that looks like that. 0:11:40.363,0:11:41.934 We always assume that the marginal 0:11:41.934,0:11:44.319 propensity to consume will be less than 1. 0:11:44.319,0:11:45.942 So we'll never have a slope of 1. 0:11:45.942,0:11:47.637 We'll also never have a negative slope 0:11:47.637,0:11:49.410 because we assume that this is positive. 0:11:49.410,0:11:51.780 If people are more likely[br]to save than consume 0:11:51.780,0:11:54.612 when they have extra[br]income, then this line 0:11:54.612,0:11:56.101 might look something like that. 0:11:56.101,0:11:57.840 It might have a lower slope.