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. 00:00:22.120 --> 00:00:23.790 PROFESSOR: Now what I'm going to do is, I'm going to turn 00:00:23.790 --> 00:00:27.340 and start producer theory, OK, which will not be in the exam, 00:00:27.340 --> 00:00:29.830 but be the next subject to the course. 00:00:29.830 --> 00:00:31.850 OK, and we're going to spend a little bit longer on this. 00:00:31.850 --> 00:00:33.590 So what we've been doing so far is saying, look, we 00:00:33.590 --> 00:00:35.430 introduced the course with supply and demand curves, 00:00:35.430 --> 00:00:37.820 elasticities, all that. 00:00:37.820 --> 00:00:39.820 Hint, all that's on the exam too. 00:00:39.820 --> 00:00:41.220 OK, and all that. 00:00:41.220 --> 00:00:42.930 Then we say, well gee, where do supply and 00:00:42.930 --> 00:00:44.810 demand curves come from? 00:00:44.810 --> 00:00:47.990 Well, demand curves come from utility maximization. 00:00:47.990 --> 00:00:51.150 And we talked about how where indifference curves come from, 00:00:51.150 --> 00:00:55.380 how the tangency with the budget constraints leads to 00:00:55.380 --> 00:00:56.550 the demand curve. 00:00:56.550 --> 00:00:57.590 That's where demand curves come from. 00:00:57.590 --> 00:01:00.050 We talked about what underlies demand curves is income and 00:01:00.050 --> 00:01:01.920 substitution effects. 00:01:01.920 --> 00:01:05.730 OK, now let's come to supply curves. 00:01:05.730 --> 00:01:07.000 What underlies supply curves? 00:01:07.000 --> 00:01:10.390 Now on the one hand, this will be much easier than demand 00:01:10.390 --> 00:01:13.030 curves, because a lot of the logic is the same. 00:01:13.030 --> 00:01:16.100 So we can march more quickly through the analysis, because 00:01:16.100 --> 00:01:19.830 it's basically the same kind of tangency of curves with 00:01:19.830 --> 00:01:23.130 straight lines that yield supply curves that we've seen 00:01:23.130 --> 00:01:24.380 with consumer theory. 00:01:24.380 --> 00:01:28.810 On the other hand, supply curves are a ton harder, 00:01:28.810 --> 00:01:31.790 because now we don't just have the 00:01:31.790 --> 00:01:34.700 price as given to consumers. 00:01:34.700 --> 00:01:36.990 The suppliers actually make up the price. 00:01:36.990 --> 00:01:39.040 With consumers, we said the price -- you just went to the 00:01:39.040 --> 00:01:40.065 store. you're given a price. 00:01:40.065 --> 00:01:42.120 And you choose what to buy at those prices. 00:01:42.120 --> 00:01:43.180 Well, who set those prices? 00:01:43.180 --> 00:01:44.140 Producers do. 00:01:44.140 --> 00:01:46.560 And that's what determines the underlying supply curve. 00:01:46.560 --> 00:01:48.630 So life gets a little bit more difficult with producers. 00:01:48.630 --> 00:01:50.220 And that's why I'll probably spend about twice as many 00:01:50.220 --> 00:01:53.100 lectures talking about producer theory as we've spent 00:01:53.100 --> 00:01:56.150 talking about consumer theory. 00:01:56.150 --> 00:02:00.590 Now, let's go to the basics. 00:02:00.590 --> 00:02:06.770 The basics are, just as we had consumers making decisions, we 00:02:06.770 --> 00:02:08.550 thought of a consumer as somebody choosing across a 00:02:08.550 --> 00:02:13.000 bundle of goods, pizza versus movies, now we're going to 00:02:13.000 --> 00:02:17.970 think of a producer very simply as a black box, where 00:02:17.970 --> 00:02:21.120 inputs go in and outputs come out. 00:02:21.120 --> 00:02:23.250 So think of the firm. 00:02:23.250 --> 00:02:25.920 Let's think of a firm, a producer, as 00:02:25.920 --> 00:02:29.180 just some black box. 00:02:29.180 --> 00:02:30.820 We're literally thinking a flow chart. 00:02:30.820 --> 00:02:35.350 You've got inputs that go in and outputs that come out. 00:02:35.350 --> 00:02:39.490 And that black box, that firm, just as individuals have a 00:02:39.490 --> 00:02:42.470 simple goal which is to maximize their utility, 00:02:42.470 --> 00:02:44.690 producers have a simple goal which is to 00:02:44.690 --> 00:02:47.600 maximize their profits. 00:02:47.600 --> 00:02:52.490 And profits are defined as revenue minus cost. OK? 00:02:52.490 --> 00:02:57.830 Producers are these black boxes, where their goal is to 00:02:57.830 --> 00:03:05.760 maximize their profits, which is revenue minus cost. And the 00:03:05.760 --> 00:03:10.915 key to maximizing profits is efficient production. 00:03:16.970 --> 00:03:19.740 The key to maximizing profits is going to be to produce 00:03:19.740 --> 00:03:23.760 goods as efficiently as possible. 00:03:23.760 --> 00:03:29.000 OK, so profit maximization requires production 00:03:29.000 --> 00:03:30.790 efficiency. 00:03:30.790 --> 00:03:33.580 To maximize your profits, you need to produce as efficiently 00:03:33.580 --> 00:03:34.830 as possible. 00:03:38.040 --> 00:03:43.420 Now, you might ask yourself, gee, I can read about all 00:03:43.420 --> 00:03:47.570 these companies that have executive corporate jets, and 00:03:47.570 --> 00:03:49.750 the guys in these lavish lifestyles, and that doesn't 00:03:49.750 --> 00:03:52.700 seem very efficient production. 00:03:52.700 --> 00:03:54.140 I'll come back to that. 00:03:54.140 --> 00:03:56.540 OK, in a couple of lectures, we'll talk about do firms 00:03:56.540 --> 00:03:59.250 actually maximize profits, and whether they do or not. 00:03:59.250 --> 00:04:01.800 But for now, let's take as a given that they do. 00:04:01.800 --> 00:04:04.990 OK, just as it is a given that consumers maximize utility, 00:04:04.990 --> 00:04:08.270 let's take as a given that firms maximize their profits. 00:04:08.270 --> 00:04:09.490 OK? 00:04:09.490 --> 00:04:15.060 Now, to decide how to efficiently produce goods, 00:04:15.060 --> 00:04:17.370 we're going to turn and today discuss 00:04:17.370 --> 00:04:18.855 firm production functions. 00:04:24.160 --> 00:04:26.560 OK, today, we'll focus on production functions. 00:04:26.560 --> 00:04:30.960 That's essentially the technology by which a firm 00:04:30.960 --> 00:04:36.740 takes inputs, or what we call factors of production, and 00:04:36.740 --> 00:04:40.110 turns them into outputs, is through 00:04:40.110 --> 00:04:41.520 this production function. 00:04:41.520 --> 00:04:45.040 So just like your utility function is a tool for which 00:04:45.040 --> 00:04:49.510 we take bundles of goods and turn them into happiness, a 00:04:49.510 --> 00:04:51.970 production function is a tool for which we take bundles of 00:04:51.970 --> 00:04:54.590 inputs and turn them into outputs. 00:04:54.590 --> 00:04:57.030 OK, but something that's a little easier to understand 00:04:57.030 --> 00:04:59.330 this, you could think of a factory where stuff comes in, 00:04:59.330 --> 00:05:02.580 and think of a belt, a mechanical belt, going through 00:05:02.580 --> 00:05:04.320 and stuff goes in and other stuff comes out. 00:05:04.320 --> 00:05:06.840 You could think of that production function. 00:05:06.840 --> 00:05:09.880 We're going to think about two different kinds of inputs that 00:05:09.880 --> 00:05:11.000 firms are going to use. 00:05:11.000 --> 00:05:12.790 Once again, to make life easy, we're going to assume firms 00:05:12.790 --> 00:05:14.970 only use two kinds of inputs. 00:05:14.970 --> 00:05:18.250 Later, we'll expand this, but from mostly intuition you can 00:05:18.250 --> 00:05:19.560 get from thinking about this-- two kinds of 00:05:19.560 --> 00:05:23.760 inputs, labor and capital. 00:05:23.760 --> 00:05:28.590 Labor and capital are the two kinds of inputs firms use. 00:05:28.590 --> 00:05:30.340 Labor is clear. 00:05:30.340 --> 00:05:34.550 It's just hours of labor, hours of work. 00:05:34.550 --> 00:05:35.550 OK? 00:05:35.550 --> 00:05:39.140 It's just hours of work in production. 00:05:39.140 --> 00:05:40.820 Capital is a lot trickier. 00:05:40.820 --> 00:05:42.800 And we'll spend a lot of time this semester struggling with 00:05:42.800 --> 00:05:45.810 what capital really means. 00:05:45.810 --> 00:05:49.020 Basically for now, think of capital as everything else 00:05:49.020 --> 00:05:52.080 that goes into production, the machines, the buildings, the 00:05:52.080 --> 00:05:54.470 land, everything. 00:05:54.470 --> 00:05:56.180 Think of capital as everything else that goes into 00:05:56.180 --> 00:05:57.230 production. 00:05:57.230 --> 00:05:58.960 So basically, when you produce stuff, you produce it with 00:05:58.960 --> 00:06:00.740 workers working with stuff. 00:06:00.740 --> 00:06:01.990 Capital's the stuff. 00:06:04.210 --> 00:06:07.230 Now, this capital is sort of a composite of everything else 00:06:07.230 --> 00:06:08.590 that goes into production. 00:06:08.590 --> 00:06:12.540 And once again, we'll add some more detail on this later. 00:06:12.540 --> 00:06:18.220 OK, and the output is some output, q. 00:06:18.220 --> 00:06:19.600 That's the units of production. 00:06:19.600 --> 00:06:23.000 That's the output that is produced by the firm. 00:06:23.000 --> 00:06:27.910 So basically, we can think of a production function is q is 00:06:27.910 --> 00:06:30.810 some function of l and k. 00:06:30.810 --> 00:06:33.820 That's a production function, that the output you produce as 00:06:33.820 --> 00:06:34.670 your firm-- 00:06:34.670 --> 00:06:38.060 and by the way, we're going to use little q to represent a 00:06:38.060 --> 00:06:41.710 firm's output, and big Q to represent market output. 00:06:41.710 --> 00:06:45.540 OK, so little q, and if I slip in this, yell at me, OK? 00:06:45.540 --> 00:06:48.330 But we're going to try to consistently use little q to 00:06:48.330 --> 00:06:50.830 represent a given firm's output, and big Q to be the 00:06:50.830 --> 00:06:52.660 market's output-- 00:06:52.660 --> 00:06:55.700 So little q is some function of the amount of workers you 00:06:55.700 --> 00:06:59.080 have and the amount of capital you use. 00:06:59.080 --> 00:07:03.960 Now, the important distinction we're going to make here is 00:07:03.960 --> 00:07:10.585 between variable versus fixed inputs. 00:07:13.390 --> 00:07:16.850 Variable versus fixed inputs is an important distinction 00:07:16.850 --> 00:07:18.750 we're going to draw. 00:07:18.750 --> 00:07:23.210 Variable inputs are inputs that are easily changed, like 00:07:23.210 --> 00:07:25.580 how many hours somebody works. 00:07:25.580 --> 00:07:28.100 In principle, you could just have some work five hours one 00:07:28.100 --> 00:07:30.600 day, one hour the next day, 10 hours the day after that. 00:07:30.600 --> 00:07:33.290 It's easy to change hours of work. 00:07:33.290 --> 00:07:35.540 So that's a variable input. 00:07:35.540 --> 00:07:38.860 Fixed inputs are things which are harder to change quickly, 00:07:38.860 --> 00:07:42.010 like the size of the building that the workers 00:07:42.010 --> 00:07:44.540 are building in. 00:07:44.540 --> 00:07:46.550 Once that building's built, it's pretty hard to change it. 00:07:46.550 --> 00:07:49.330 You can't like lop off 2/3 of it on one day and add it back 00:07:49.330 --> 00:07:50.290 the next day. 00:07:50.290 --> 00:07:53.980 OK, that's more of the fixed inputs. 00:07:53.980 --> 00:07:56.080 And this will lead to a critical distinction for 00:07:56.080 --> 00:07:59.090 production theory, which is the short run 00:07:59.090 --> 00:08:00.750 versus the long run. 00:08:04.200 --> 00:08:05.910 The short run versus the long run. 00:08:05.910 --> 00:08:11.150 The long run is the period over which 00:08:11.150 --> 00:08:14.240 all inputs are variable. 00:08:14.240 --> 00:08:17.550 The short run is a period over which some inputs are fixed. 00:08:17.550 --> 00:08:19.380 Let me say it again, it's very important. 00:08:19.380 --> 00:08:21.020 The short run is the period over which 00:08:21.020 --> 00:08:23.180 some inputs are fixed. 00:08:23.180 --> 00:08:25.580 The long run is the period over which 00:08:25.580 --> 00:08:26.970 all inputs are variable. 00:08:29.530 --> 00:08:31.410 Now, what does that mean? 00:08:31.410 --> 00:08:33.110 I can't tell you. 00:08:33.110 --> 00:08:33.710 OK? 00:08:33.710 --> 00:08:38.590 I can tell you that, clearly, tomorrow is the short run. 00:08:38.590 --> 00:08:41.299 Clearly, you can't vary all your inputs over one day. 00:08:41.299 --> 00:08:42.940 And probably next month is the short run. 00:08:42.940 --> 00:08:45.670 And probably even next year is the short run. 00:08:45.670 --> 00:08:48.570 There's a lot of inputs that it takes more than a month to 00:08:48.570 --> 00:08:49.760 change, or a year to change. 00:08:49.760 --> 00:08:52.120 On the other hand, 10 years from now is almost certainly 00:08:52.120 --> 00:08:53.580 the long run. 00:08:53.580 --> 00:08:55.610 There's very few inputs to production you can't change 00:08:55.610 --> 00:08:58.120 over a 10-year period. 00:08:58.120 --> 00:08:59.870 So we know a day are the short run. 00:08:59.870 --> 00:09:01.010 And we know 10 years is the long run. 00:09:01.010 --> 00:09:02.610 We don't really know where the transition is, but in 00:09:02.610 --> 00:09:04.810 substance that doesn't matter for you guys. 00:09:04.810 --> 00:09:07.570 What matters is the definition of short run, long run. 00:09:07.570 --> 00:09:09.290 When someone asks you what the long run is, you say it's the 00:09:09.290 --> 00:09:11.770 period of time over which all inputs are variable. 00:09:11.770 --> 00:09:13.070 That's what matters. 00:09:13.070 --> 00:09:14.520 So it doesn't matter if you define it in days 00:09:14.520 --> 00:09:15.920 or months or years. 00:09:15.920 --> 00:09:18.465 It's a theoretical concept, which the break from the short 00:09:18.465 --> 00:09:21.750 run to the long run is the break between when some inputs 00:09:21.750 --> 00:09:24.595 are fixed and all inputs are variable. 00:09:24.595 --> 00:09:26.070 OK? 00:09:26.070 --> 00:09:28.370 Now of course, once again this is tricky. 00:09:28.370 --> 00:09:30.100 And economists recognize this subtlety. 00:09:30.100 --> 00:09:32.480 A lot of times, economists will talk about quasi-fixed 00:09:32.480 --> 00:09:37.020 factors of production, which are things which could change 00:09:37.020 --> 00:09:38.320 in between the short run and the long run. 00:09:38.320 --> 00:09:40.010 So for instance, take labor. 00:09:40.010 --> 00:09:43.760 OK, we'll talk about labor as a variable unit of production 00:09:43.760 --> 00:09:45.100 you can change in the short run. 00:09:45.100 --> 00:09:47.200 But in fact, we know in practice you can't. 00:09:47.200 --> 00:09:50.430 Most jobs, you can't ask the guys to come for an hour one 00:09:50.430 --> 00:09:52.230 day, and 10 hours the next day, five hours the day after 00:09:52.230 --> 00:09:55.360 that, maybe some jobs like hourly construction. 00:09:55.360 --> 00:09:59.040 But most jobs you guys will have, OK, your labor isn't 00:09:59.040 --> 00:09:59.720 that variable. 00:09:59.720 --> 00:10:01.340 We're typically on some kind of 00:10:01.340 --> 00:10:03.420 reasonably set work schedule. 00:10:03.420 --> 00:10:05.930 Now that work schedule can evolve. 00:10:05.930 --> 00:10:09.020 OK, but it can't change day by day. 00:10:09.020 --> 00:10:10.500 None of us are going to have jobs where they're going to 00:10:10.500 --> 00:10:13.000 say, look, work two hours today, 12 hours the 00:10:13.000 --> 00:10:14.240 next day, et cetera. 00:10:14.240 --> 00:10:17.260 OK, we're all going to have jobs with a fairly smooth 00:10:17.260 --> 00:10:17.900 distribution. 00:10:17.900 --> 00:10:20.990 There'll be peaks and valleys, but a fairly smooth 00:10:20.990 --> 00:10:22.770 distribution of our labor effort. 00:10:22.770 --> 00:10:26.250 So really, truly, there's very few inputs which are truly 00:10:26.250 --> 00:10:28.190 perfectly variable. 00:10:28.190 --> 00:10:29.370 OK? 00:10:29.370 --> 00:10:31.770 Just like there are no inputs which are truly perfectly 00:10:31.770 --> 00:10:35.930 fixed, but for the purposes of this model, let's think about 00:10:35.930 --> 00:10:38.310 labor as a variable input. 00:10:38.310 --> 00:10:40.370 Let's think about labor as being like hourly labor, like 00:10:40.370 --> 00:10:43.010 hourly construction, OK? 00:10:43.010 --> 00:10:45.430 And let's think about capital as being a fixed input, like a 00:10:45.430 --> 00:10:48.670 building that you can't pare down or rebuild overnight, but 00:10:48.670 --> 00:10:51.590 over a 10-year period you can. 00:10:51.590 --> 00:10:52.530 OK? 00:10:52.530 --> 00:10:55.730 Questions about that? 00:10:55.730 --> 00:10:57.397 Once again, we talked about simplifying assumptions at the 00:10:57.397 --> 00:10:58.390 beginning of the semester. 00:10:58.390 --> 00:11:00.700 This is our set of simplifying assumptions. 00:11:00.700 --> 00:11:04.320 Simplifying assumptions are that firms produce goods with 00:11:04.320 --> 00:11:09.070 two inputs, labor and capital, that labor is variable, which 00:11:09.070 --> 00:11:11.930 means you can change it minute to minute or day to day, and 00:11:11.930 --> 00:11:13.605 capital is fixed, which means you can only change 00:11:13.605 --> 00:11:16.190 it in the long run. 00:11:16.190 --> 00:11:19.160 OK? 00:11:19.160 --> 00:11:23.340 All right, so armed with that, let's now talk about how firms 00:11:23.340 --> 00:11:25.730 make short-run production decisions. 00:11:30.030 --> 00:11:32.610 And once again, these are a lot of assumptions. 00:11:32.610 --> 00:11:34.900 But at the end of the day, I'm going to be able to teach you 00:11:34.900 --> 00:11:37.830 in a couple of lectures how firms make decisions. 00:11:37.830 --> 00:11:39.910 And I'm going to be about 80% right. 00:11:39.910 --> 00:11:41.360 So that's pretty good. 00:11:41.360 --> 00:11:43.510 OK, so there are some assumptions, but we're going 00:11:43.510 --> 00:11:47.000 to go a long way with these assumptions. 00:11:47.000 --> 00:11:51.600 So let's start by considering the short run, and considering 00:11:51.600 --> 00:11:56.160 that period of time over which labor is variable 00:11:56.160 --> 00:11:58.970 but capital is fixed. 00:11:58.970 --> 00:12:01.340 Labor is variable but capital is fixed. 00:12:01.340 --> 00:12:04.580 That is, you have a given plant, but you can adjust how 00:12:04.580 --> 00:12:08.630 many workers you use every day in that plant. 00:12:08.630 --> 00:12:11.290 And now the firm has to decide, given that that plant 00:12:11.290 --> 00:12:14.210 exists, how many workers should I hire 00:12:14.210 --> 00:12:16.610 to produce my good? 00:12:16.610 --> 00:12:18.090 How many workers should I hire to produce my good? 00:12:18.090 --> 00:12:20.850 And the key concept that's going to determine that is 00:12:20.850 --> 00:12:29.350 something we'll call the marginal product of labor, 00:12:29.350 --> 00:12:34.580 which is the change in total output resulting from the next 00:12:34.580 --> 00:12:36.090 unit of labor used-- 00:12:36.090 --> 00:12:41.590 that is, delta q, delta l-- 00:12:41.590 --> 00:12:43.260 is the marginal product of labor. 00:12:43.260 --> 00:12:47.310 It's going to be the change in total output from another unit 00:12:47.310 --> 00:12:50.500 of labor, once again holding capital constant because 00:12:50.500 --> 00:12:51.730 that's fixed. 00:12:51.730 --> 00:12:56.580 So really, it's really at a given k bar, but that's 00:12:56.580 --> 00:12:58.780 implicit in the fact it's the short run. 00:12:58.780 --> 00:13:02.620 So the given level of capital, what is the change in output 00:13:02.620 --> 00:13:04.000 for another unit of labor? 00:13:04.000 --> 00:13:05.270 And once we get to the short run, I shouldn't 00:13:05.270 --> 00:13:05.800 have to write this. 00:13:05.800 --> 00:13:07.680 If I tell you short run, you should know this is true. 00:13:07.680 --> 00:13:12.060 But technically, we would write that out. 00:13:12.060 --> 00:13:17.520 Now, what we're going to do here is we're typically going 00:13:17.520 --> 00:13:21.280 to assume this-- 00:13:21.280 --> 00:13:22.600 hint, hint-- 00:13:22.600 --> 00:13:24.980 if you're comfortable with consumer theory, this is like 00:13:24.980 --> 00:13:26.680 marginal utility. 00:13:26.680 --> 00:13:28.660 Marginal product is like marginal utility. 00:13:28.660 --> 00:13:31.550 Just as the marginal utility was your utility from another 00:13:31.550 --> 00:13:35.650 unit of one good, holding the other good fixed, marginal 00:13:35.650 --> 00:13:38.860 product is the marginal production from another unit 00:13:38.860 --> 00:13:42.290 of an input, holding the other input fixed. 00:13:42.290 --> 00:13:45.520 So just sort of a parallel to keep in mind. 00:13:45.520 --> 00:13:49.660 And just as we've assumed and discussed the intuition for 00:13:49.660 --> 00:13:52.780 diminishing marginal utility, we're going to typically 00:13:52.780 --> 00:13:57.280 assume diminishing marginal product. 00:13:57.280 --> 00:14:04.340 So we're going to assume diminishing marginal product. 00:14:04.340 --> 00:14:10.340 That is, from a given level of labor, the next worker you add 00:14:10.340 --> 00:14:14.780 increases your total product by less than the previous one. 00:14:14.780 --> 00:14:18.290 Now once again, just like we have a non- satiation rule in 00:14:18.290 --> 00:14:20.180 utility, we're not going to say the next 00:14:20.180 --> 00:14:21.800 worker doesn't help. 00:14:21.800 --> 00:14:23.330 Every worker helps. 00:14:23.330 --> 00:14:25.920 But every worker helps less and less and less, just like 00:14:25.920 --> 00:14:27.880 every pizza means less and less and less to you. 00:14:31.510 --> 00:14:37.045 Now, the trick here, once again, this is like consumer 00:14:37.045 --> 00:14:38.140 theory, only more subtle. 00:14:38.140 --> 00:14:40.620 With consumer theory, it's pretty clear that once you had 00:14:40.620 --> 00:14:43.160 one pizza, clearly, the second pizza means less. 00:14:43.160 --> 00:14:45.680 And once you've seen one movie, your first-place prize, 00:14:45.680 --> 00:14:47.620 the movie you most want to see, clearly the next movie 00:14:47.620 --> 00:14:49.560 you want to see means a little bit less. 00:14:49.560 --> 00:14:51.330 Producer theory is a little more subtle. 00:14:51.330 --> 00:14:56.550 And you can imagine ranges over which more workers help. 00:14:56.550 --> 00:14:58.110 They can work together. 00:14:58.110 --> 00:15:00.410 So that actually two workers can do more than twice what 00:15:00.410 --> 00:15:03.190 one worker can do. 00:15:03.190 --> 00:15:04.480 And we'll talk about that. 00:15:04.480 --> 00:15:08.070 But we're going to focus in the main on ranges over which 00:15:08.070 --> 00:15:09.995 each additional worker does less and less and less. 00:15:12.610 --> 00:15:15.520 And the reason is because, to remember, this 00:15:15.520 --> 00:15:16.270 is less than two-- 00:15:16.270 --> 00:15:17.550 Yeah? 00:15:17.550 --> 00:15:21.710 AUDIENCE: Is there going to be a point where actually 00:15:21.710 --> 00:15:24.608 additional workers won't do anything, because of like 00:15:24.608 --> 00:15:27.030 constrain to the amounts of other inputs? 00:15:27.030 --> 00:15:29.210 PROFESSOR: Once again, we're not going to get-- just like 00:15:29.210 --> 00:15:32.110 there's a point at which extra pizza will make you barf-- 00:15:32.110 --> 00:15:34.590 OK, we're assuming we don't get to that point. 00:15:34.590 --> 00:15:37.610 But yes, technically of course, at some point more is 00:15:37.610 --> 00:15:38.090 not better. 00:15:38.090 --> 00:15:40.060 At some point, extra workers just sit around. 00:15:40.060 --> 00:15:42.110 And so I agree. 00:15:42.110 --> 00:15:43.840 So basically, it's a little tricky. 00:15:43.840 --> 00:15:45.350 You could imagine an initial range where more 00:15:45.350 --> 00:15:47.280 workers would help. 00:15:47.280 --> 00:15:49.280 Then there's the main range we'll focus on each additional 00:15:49.280 --> 00:15:50.845 worker does less and less and less. 00:15:50.845 --> 00:15:52.880 And you could imagine that running out, which is a worker 00:15:52.880 --> 00:15:53.660 does nothing. 00:15:53.660 --> 00:15:56.930 But let's just now assume we don't get there. 00:15:56.930 --> 00:15:59.650 So basically, what's the intuition? 00:15:59.650 --> 00:16:02.526 Now the intuition for in utility theory, for 00:16:02.526 --> 00:16:04.210 diminishing marginal utility, I thought was pretty easy, 00:16:04.210 --> 00:16:05.940 which is each pizza means less. 00:16:05.940 --> 00:16:09.010 The intuition for why each worker does less, I find a 00:16:09.010 --> 00:16:09.640 little bit harder. 00:16:09.640 --> 00:16:12.240 You could say, well, gee, why should one worker do less than 00:16:12.240 --> 00:16:13.120 the next worker? 00:16:13.120 --> 00:16:16.300 Why shouldn't the next worker do less than the first? 00:16:16.300 --> 00:16:19.250 And the key is this part, that we're 00:16:19.250 --> 00:16:21.400 holding capital constant. 00:16:21.400 --> 00:16:25.520 The reason each worker does less is because they only have 00:16:25.520 --> 00:16:28.870 the same amount of stuff to work with. 00:16:28.870 --> 00:16:30.870 And the classic example we use here is the example 00:16:30.870 --> 00:16:32.120 of digging a hole. 00:16:34.190 --> 00:16:36.610 You go to dig a hole and your capital's a shovel. 00:16:36.610 --> 00:16:38.950 And let's say for some reason the shovels are out, so you 00:16:38.950 --> 00:16:41.060 can't get another shovel for a while. 00:16:41.060 --> 00:16:42.640 OK, so there's one shovel. 00:16:42.640 --> 00:16:46.210 So you have one worker digging a hole, then the next worker 00:16:46.210 --> 00:16:47.950 comes along and that's where he can help because he can 00:16:47.950 --> 00:16:51.100 spell the first worker. 00:16:51.100 --> 00:16:53.400 And maybe the next worker's just as good because he can 00:16:53.400 --> 00:16:56.390 work more hours, but probably it's a little bit less good. 00:16:56.390 --> 00:16:58.490 But certainly by the time you add a fourth and a fifth and a 00:16:58.490 --> 00:17:01.390 sixth person, with one shovel, they probably each help 00:17:01.390 --> 00:17:03.380 because they can rotate and rest each other. 00:17:03.380 --> 00:17:06.550 But certainly the sixth person is not going to help dig the 00:17:06.550 --> 00:17:08.930 hole as much as that second person did, or the third, or 00:17:08.930 --> 00:17:12.430 fourth, or fifth person, because only one shovel. 00:17:12.430 --> 00:17:13.900 So they can share a little bit and share the 00:17:13.900 --> 00:17:14.980 burden a little bit. 00:17:14.980 --> 00:17:18.040 But at some point each additional worker helps less 00:17:18.040 --> 00:17:20.300 because they have to share the same shovel. 00:17:20.300 --> 00:17:22.780 So that's what diminishing marginal product is, because 00:17:22.780 --> 00:17:24.369 capital's fixed. 00:17:24.369 --> 00:17:26.430 With a certain amount of capital to work with, each 00:17:26.430 --> 00:17:28.890 additional worker just can't help as 00:17:28.890 --> 00:17:30.140 much as the one before. 00:17:32.580 --> 00:17:35.410 Now eventually, you can add more shovels. 00:17:35.410 --> 00:17:36.430 And you could have wheelbarrows. 00:17:36.430 --> 00:17:37.810 So some people could run the wheelbarrows, some people 00:17:37.810 --> 00:17:39.230 could run the shovels. 00:17:39.230 --> 00:17:40.840 But that's the long run. 00:17:40.840 --> 00:17:44.620 In the short run, there's the one shovel, so each additional 00:17:44.620 --> 00:17:47.330 worker does less good. 00:17:47.330 --> 00:17:49.000 And that's the intuition. 00:17:49.000 --> 00:17:52.460 Once again, not as clean as with consumption, where it's 00:17:52.460 --> 00:17:54.290 easy to see each additional pizza is worth less, because 00:17:54.290 --> 00:17:57.510 you could imagine the second worker might actually help. 00:17:57.510 --> 00:17:59.080 They could rest, et cetera, and you could imagine 00:17:59.080 --> 00:18:00.720 eventually the ninth worker does nothing because there's 00:18:00.720 --> 00:18:02.070 nothing left to do. 00:18:02.070 --> 00:18:04.780 But let's focus on that range where it's intuitive. 00:18:04.780 --> 00:18:07.500 We're staying between the second and sixth worker, which 00:18:07.500 --> 00:18:09.060 is when a worker would help, but they help less 00:18:09.060 --> 00:18:10.460 and less and less. 00:18:10.460 --> 00:18:13.920 OK, and that's the diminishing marginal product. 00:18:13.920 --> 00:18:15.170 Questions about that? 00:18:17.400 --> 00:18:20.176 That's short-run production. 00:18:20.176 --> 00:18:21.400 And we're going to come back to this. 00:18:21.400 --> 00:18:24.350 But I just want to introduce these concepts. 00:18:24.350 --> 00:18:26.900 Now let's talk about long-run production. 00:18:36.210 --> 00:18:39.560 Now in the long run, all inputs are variable. 00:18:39.560 --> 00:18:41.620 That's how we defined the long run. 00:18:41.620 --> 00:18:45.000 So now a firm doesn't just choose how many workers to 00:18:45.000 --> 00:18:47.420 hire, or how many hours of labor to buy. 00:18:47.420 --> 00:18:53.290 It chooses both l and k, and has to trade them off, just 00:18:53.290 --> 00:18:55.730 like you chose both pizzas and movies and had 00:18:55.730 --> 00:18:58.410 to trade them off. 00:18:58.410 --> 00:19:04.300 So the long-run production theory is the same, basically 00:19:04.300 --> 00:19:06.990 the same mechanics, as utility theory. 00:19:06.990 --> 00:19:08.440 There's a production function. 00:19:08.440 --> 00:19:09.240 You have two inputs. 00:19:09.240 --> 00:19:10.700 You trade them off. 00:19:10.700 --> 00:19:12.230 Just like you're a consumer. 00:19:12.230 --> 00:19:14.300 You have two goods to consume. 00:19:14.300 --> 00:19:15.980 You trade them off. 00:19:15.980 --> 00:19:19.540 The difference is going to be that ultimately production is 00:19:19.540 --> 00:19:20.380 going to self-- 00:19:20.380 --> 00:19:22.440 the difference is, when you decide how to trade them off 00:19:22.440 --> 00:19:25.430 as a consumer, you're given a budget constraint. 00:19:25.430 --> 00:19:28.620 The difference with production is the budget constraint is 00:19:28.620 --> 00:19:30.940 going to be itself determined by the same system. 00:19:30.940 --> 00:19:33.650 So you're not only going to develop your production 00:19:33.650 --> 00:19:35.190 function, but you're going to develop your budget constraint 00:19:35.190 --> 00:19:36.350 and, you're going to decide both. 00:19:36.350 --> 00:19:38.380 It's a little bit funky but we'll get to it. 00:19:38.380 --> 00:19:40.750 But for now, let's just think about the parallels to 00:19:40.750 --> 00:19:44.740 consumer theory, and think about a production function 00:19:44.740 --> 00:19:45.890 which is q-- 00:19:45.890 --> 00:19:46.750 little q-- 00:19:46.750 --> 00:19:48.880 is the square root of k times l. 00:19:48.880 --> 00:19:51.360 That same functional form I used with pizza and movies, 00:19:51.360 --> 00:19:53.590 where utility is the square root of pizza times movies. 00:19:53.590 --> 00:19:58.450 Now I'm going to say what you produce of your good is the 00:19:58.450 --> 00:20:00.310 square root of k times l. 00:20:00.310 --> 00:20:01.567 Now let's go to figure 8-3. 00:20:04.090 --> 00:20:11.520 And what we see here is, if you're trading off k and l and 00:20:11.520 --> 00:20:14.440 deciding to produce, then you get what's called isoquants. 00:20:18.210 --> 00:20:20.750 Isoquants are the parallel to indifference curves. 00:20:20.750 --> 00:20:22.990 Once again, this is all the same mechanics. 00:20:22.990 --> 00:20:27.010 Just as there were sets of goods across which you were 00:20:27.010 --> 00:20:31.030 indifferent, two pizzas and one movie versus one pizza and 00:20:31.030 --> 00:20:32.410 two movies. 00:20:32.410 --> 00:20:35.620 Isoquants are sets of inputs along which 00:20:35.620 --> 00:20:38.120 production is the same. 00:20:38.120 --> 00:20:41.300 So along a given isoquant, q is fixed. 00:20:41.300 --> 00:20:44.830 Each of those isoquants is a different level of q, but they 00:20:44.830 --> 00:20:49.790 show how you can vary k and l to get the same amount of q. 00:20:49.790 --> 00:20:52.830 So producing q equals square root of 2. 00:20:52.830 --> 00:20:57.120 I can use two units of capital and one unit of labor, or one 00:20:57.120 --> 00:20:59.990 unit of capital and two of labor. 00:20:59.990 --> 00:21:04.590 So I can choose lots of combinations of k and l along 00:21:04.590 --> 00:21:09.300 that isoquant to produce a given amount of output. 00:21:09.300 --> 00:21:11.390 And isoquants have all the same features as in 00:21:11.390 --> 00:21:12.660 indifference curves. 00:21:12.660 --> 00:21:15.440 The further out the better because you're producing more. 00:21:15.440 --> 00:21:17.040 They can't cross. 00:21:17.040 --> 00:21:18.830 All the same set of things we have in the indifference 00:21:18.830 --> 00:21:20.350 curves are true with isoquants as well. 00:21:24.280 --> 00:21:27.210 And they slope downwards because there's a trade off 00:21:27.210 --> 00:21:29.780 between capital and labor. 00:21:29.780 --> 00:21:33.200 Now, what's going to determine the slope of an isoquant? 00:21:33.200 --> 00:21:35.330 Can someone tell me what determines 00:21:35.330 --> 00:21:36.830 the slope of an isoquant? 00:21:40.670 --> 00:21:43.185 What determines if isoquants are steep or shallow? 00:21:47.545 --> 00:21:49.720 Well, what determines the slope of a indifference curve? 00:21:49.720 --> 00:21:51.540 Yes, go ahead. 00:21:51.540 --> 00:21:54.970 AUDIENCE: It's based on the ratio of how much labor is 00:21:54.970 --> 00:21:56.440 worth versus capital? 00:21:56.440 --> 00:21:57.500 PROFESSOR: Right, and what do we call that? 00:21:57.500 --> 00:21:59.170 What determines how much they're worth from each other? 00:21:59.170 --> 00:22:01.770 What determines the slope of a indifference curve? 00:22:01.770 --> 00:22:03.920 The marginal rate of substitution, it was the 00:22:03.920 --> 00:22:06.400 substitutability between goods. 00:22:06.400 --> 00:22:10.220 Likewise, the substitutability between labor and capital will 00:22:10.220 --> 00:22:13.550 determine the slope of these isoquants. 00:22:13.550 --> 00:22:19.030 So to see an example, let's do an extreme example here. 00:22:19.030 --> 00:22:24.370 Let's consider goods that are perfectly substitutable. 00:22:24.370 --> 00:22:26.420 So like, I don't know, just like a Harvard undergraduate 00:22:26.420 --> 00:22:27.650 and a beanie baby. 00:22:27.650 --> 00:22:30.980 OK, perfectly substitutable. 00:22:30.980 --> 00:22:34.150 Figure 8-4a shows the case of perfectly 00:22:34.150 --> 00:22:37.070 substitutable inputs. 00:22:37.070 --> 00:22:41.750 In that case, you would have a linear isoquant, because what 00:22:41.750 --> 00:22:44.590 that would mean is you don't care if you have three capital 00:22:44.590 --> 00:22:47.990 and one labor, or three labor and one capital. 00:22:47.990 --> 00:22:49.720 You don't care. 00:22:49.720 --> 00:22:53.670 You don't care if you have two labor and two capital, or 00:22:53.670 --> 00:22:55.310 three labor and one capital, as long as you 00:22:55.310 --> 00:22:56.590 get a total of four. 00:22:56.590 --> 00:22:58.080 That's all that matters. 00:22:58.080 --> 00:22:59.530 They're perfectly substitutable inputs, which 00:22:59.530 --> 00:23:03.890 would say that it would be something like q equals k plus 00:23:03.890 --> 00:23:05.550 l would be the case of perfectly 00:23:05.550 --> 00:23:06.640 substitutable inputs. 00:23:06.640 --> 00:23:09.970 You don't care if it's k or l, you just care about the total. 00:23:09.970 --> 00:23:11.400 That'd be perfectly substitutable inputs. 00:23:11.400 --> 00:23:14.590 That would be a linear isoquant. 00:23:14.590 --> 00:23:18.030 OK, on the other hand, let's think about goods which are 00:23:18.030 --> 00:23:22.020 not at all substitutable like cereal and cereal boxes. 00:23:22.020 --> 00:23:23.240 The cereal wouldn't be any good unless you have a 00:23:23.240 --> 00:23:24.330 box to put it in. 00:23:24.330 --> 00:23:25.480 The box doesn't do anything unless you have 00:23:25.480 --> 00:23:26.760 cereal to put in it. 00:23:26.760 --> 00:23:30.370 That would be like in 8-4b. 00:23:30.370 --> 00:23:34.360 8-4b would show you non-substitutable inputs where 00:23:34.360 --> 00:23:42.160 basically, given the amount of one input, it doesn't matter 00:23:42.160 --> 00:23:43.060 how much you have of the other. 00:23:43.060 --> 00:23:46.810 So for example, if you take these-- these we often call 00:23:46.810 --> 00:23:49.220 non-substitutable isoquants-- 00:23:49.220 --> 00:23:53.030 Leontief production functions. 00:23:53.030 --> 00:23:57.130 Leontief production function, for Wassily Leontief, some old 00:23:57.130 --> 00:23:59.000 economist. 00:23:59.000 --> 00:24:03.180 And basically, the Leontief production function is that 00:24:03.180 --> 00:24:09.520 your production, q equals the Min of k and l, is the 00:24:09.520 --> 00:24:11.570 Leontief production function. 00:24:11.570 --> 00:24:15.130 So given how much k you have, given you have 10 cereal 00:24:15.130 --> 00:24:19.850 boxes, once you have 10 chunks of cereal, it doesn't matter 00:24:19.850 --> 00:24:21.860 if you have 10, 11, 12, 1 million. 00:24:21.860 --> 00:24:24.590 You only have 10 cereal boxes. 00:24:24.590 --> 00:24:28.650 So given an amount of k, then it doesn't matter how much l 00:24:28.650 --> 00:24:30.970 you have. Once you get to the amount of l you need to fill 00:24:30.970 --> 00:24:33.960 the cereal boxes, it doesn't matter, and vice versa. 00:24:33.960 --> 00:24:38.270 So basically, they're perfectly non-substitutable. 00:24:38.270 --> 00:24:40.350 So all that determines your output is which you 00:24:40.350 --> 00:24:42.460 have the least of. 00:24:42.460 --> 00:24:45.660 OK, so substitutabilities determine the slope of the 00:24:45.660 --> 00:24:49.270 isoquants and of this production function. 00:24:49.270 --> 00:24:52.300 Now in general, we'll be in between these cases. 00:24:52.300 --> 00:24:54.130 There'll be some substitutability. 00:24:54.130 --> 00:24:56.610 Goods won't be perfectly substitutable, but they'll be 00:24:56.610 --> 00:24:59.060 somewhat substitutable. 00:24:59.060 --> 00:25:01.370 So in general, we'll be in between these cases. 00:25:01.370 --> 00:25:04.690 And more generally, just as the slope of the indifference 00:25:04.690 --> 00:25:08.020 curve is the marginal rate of substitution, the slope of the 00:25:08.020 --> 00:25:10.620 isoquant we will call the marginal rate of technical 00:25:10.620 --> 00:25:13.060 substitution. 00:25:13.060 --> 00:25:14.690 The marginal rate of technical substitution-- the rate at 00:25:14.690 --> 00:25:17.910 which you can substitute one input for another in a 00:25:17.910 --> 00:25:21.500 production function is the marginal rate of technical 00:25:21.500 --> 00:25:22.750 substitution-- 00:25:24.510 --> 00:25:35.900 which we'll define as delta k, delta l for a given q bar, the 00:25:35.900 --> 00:25:38.870 rate at which you can trade off k for l 00:25:38.870 --> 00:25:40.955 to hold q bar fixed. 00:25:44.990 --> 00:25:48.035 Now, as with marginal rate of substitution, the marginal 00:25:48.035 --> 00:25:49.990 rate of technical substitution will 00:25:49.990 --> 00:25:51.780 change along the isoquant. 00:25:51.780 --> 00:25:56.690 So if you go to figure 8-5, here we've drawn a typical 00:25:56.690 --> 00:26:00.680 isoquant for the production function q equals square root 00:26:00.680 --> 00:26:03.100 of k times l. 00:26:03.100 --> 00:26:04.490 So the production function is q equals the square 00:26:04.490 --> 00:26:05.590 root of k times l. 00:26:05.590 --> 00:26:06.910 And here's a isoquant. 00:26:06.910 --> 00:26:09.580 This is the isoquant of all combinations 00:26:09.580 --> 00:26:11.335 which produce two units. 00:26:11.335 --> 00:26:15.320 This is the q equals 2 isoquant. 00:26:15.320 --> 00:26:17.770 Now, unlike utility-- remember utility?-- 00:26:17.770 --> 00:26:20.620 we said where u equals 2 was meaningless. 00:26:20.620 --> 00:26:22.980 Utility was an ordinal concept, 00:26:22.980 --> 00:26:24.150 not a cardinal concept. 00:26:24.150 --> 00:26:26.780 Here, quantity is meaningful. 00:26:26.780 --> 00:26:28.730 If you produce four, you would have only produced twice as 00:26:28.730 --> 00:26:30.130 much as if you produced two. 00:26:30.130 --> 00:26:32.300 We can care about both the ordinality and the cardinality 00:26:32.300 --> 00:26:33.790 of these outcomes. 00:26:33.790 --> 00:26:37.690 So we can say, what are the combinations of inputs which 00:26:37.690 --> 00:26:38.970 lead you to produce two units? 00:26:38.970 --> 00:26:40.890 What's all these combinations of inputs? 00:26:40.890 --> 00:26:43.040 So whereas you can have one unit of labor and four units 00:26:43.040 --> 00:26:46.695 of capital, two of each, or four units of labor and one 00:26:46.695 --> 00:26:48.420 unit of capital, all will produce two 00:26:48.420 --> 00:26:49.640 units of the output. 00:26:49.640 --> 00:26:52.560 And what you can see is that the marginal rate of technical 00:26:52.560 --> 00:26:53.750 substitution varies. 00:26:53.750 --> 00:26:57.770 So for instance, when we start with four units of capital and 00:26:57.770 --> 00:27:01.580 one unit of labor, and we think about adding a second 00:27:01.580 --> 00:27:05.040 unit of labor, then the marginal rate of technical 00:27:05.040 --> 00:27:07.230 substitution is minus 2. 00:27:07.230 --> 00:27:11.290 That is, one unit of labor is worth two units of capital. 00:27:11.290 --> 00:27:14.020 In other words, we can produce the same amount of widgets of 00:27:14.020 --> 00:27:19.740 q, but if we replace two units of capital with one unit of 00:27:19.740 --> 00:27:23.490 labor, so at that point we're very capital-intensive, and 00:27:23.490 --> 00:27:26.790 that unit of labor is very valuable. 00:27:26.790 --> 00:27:31.290 On the other hand, now if you imagine we're down at 4-1, at 00:27:31.290 --> 00:27:32.650 the third point-- 00:27:32.650 --> 00:27:35.050 we are probably using a, b, c-- 00:27:35.050 --> 00:27:37.980 now we're at the third point, where you have we have four 00:27:37.980 --> 00:27:40.680 units of labor and one unit of capital. 00:27:40.680 --> 00:27:46.640 Now, if you'd be willing to give up two units of labor 00:27:46.640 --> 00:27:48.836 just to get one unit of capital, that's the marginal 00:27:48.836 --> 00:27:52.110 rate of technical substitution is now minus 1/2. 00:27:52.110 --> 00:27:54.330 When you're very labor-intensive, you'd be 00:27:54.330 --> 00:27:57.550 happy to give up a lot of labor to get a little capital. 00:27:57.550 --> 00:28:00.490 Once again, the principle of diminishing marginal product, 00:28:00.490 --> 00:28:02.830 just like the principle of diminishing marginal utility, 00:28:02.830 --> 00:28:07.050 implies that the marginal rate of technical substitution is 00:28:07.050 --> 00:28:10.770 going to be falling as you go down the isoquant. 00:28:10.770 --> 00:28:12.920 Just like the marginal rate of substitution fell as you went 00:28:12.920 --> 00:28:15.460 down the indifference curve, the marginal rate of technical 00:28:15.460 --> 00:28:19.895 substitution is going to fall as you go down the isoquant. 00:28:23.530 --> 00:28:24.590 And why is this? 00:28:24.590 --> 00:28:27.180 Once again it's because of this diminishing marginal 00:28:27.180 --> 00:28:28.220 productivity. 00:28:28.220 --> 00:28:32.440 That is, as you add more and more labor, given capital, 00:28:32.440 --> 00:28:34.770 each unit of labor can do less and less. 00:28:34.770 --> 00:28:36.800 And likewise, as you add more and more capital, given an 00:28:36.800 --> 00:28:38.550 amount of workers to use it, each unit of capital can do 00:28:38.550 --> 00:28:39.820 less and less. 00:28:39.820 --> 00:28:43.750 So it's a very different approach, but gets you the 00:28:43.750 --> 00:28:47.890 same answer, which is with consumption, each piece does 00:28:47.890 --> 00:28:51.010 less and less for you, but we can see that as consumers. 00:28:51.010 --> 00:28:54.000 Here's the notions of labor, each worker does less and less 00:28:54.000 --> 00:28:55.610 for you, holding capital fixed. 00:28:55.610 --> 00:28:58.300 And each machine by the same logic, if you have one guy in 00:28:58.300 --> 00:28:59.620 the hole, it doesn't matter how many 00:28:59.620 --> 00:29:01.010 shovels you throw there. 00:29:01.010 --> 00:29:02.770 He still is only one guy. 00:29:02.770 --> 00:29:05.860 So each machines is doing less and less by the same logic. 00:29:05.860 --> 00:29:08.980 And those diminishing marginal products lead to this 00:29:08.980 --> 00:29:10.880 decreasing marginal rate of technical substitution as you 00:29:10.880 --> 00:29:12.130 move along the isoquant. 00:29:14.390 --> 00:29:16.002 That's about the most technical statement I'll make 00:29:16.002 --> 00:29:17.600 all semester. 00:29:17.600 --> 00:29:21.480 OK, questions about that, about what's going on here? 00:29:21.480 --> 00:29:23.490 That's production theory. 00:29:23.490 --> 00:29:26.660 That's what you need to know to know basically how firms 00:29:26.660 --> 00:29:28.210 produce things. 00:29:28.210 --> 00:29:31.000 Now, what we're going to do is, now take this basic 00:29:31.000 --> 00:29:35.910 production theory, and turn it into actually understanding 00:29:35.910 --> 00:29:38.990 how firms make decisions on how much to produce. 00:29:38.990 --> 00:29:40.990 But before we do that, I want to talk about one other 00:29:40.990 --> 00:29:45.340 concept, which is very important for thinking about 00:29:45.340 --> 00:29:46.790 production theory. 00:29:46.790 --> 00:29:48.990 And it comes back to these assumptions that we make which 00:29:48.990 --> 00:29:51.480 might be a little bit unrealistic, which is the 00:29:51.480 --> 00:29:54.330 concept of returns to scale. 00:30:00.050 --> 00:30:01.575 The concept of returns to scale. 00:30:05.410 --> 00:30:10.220 So here the question is, what happens if we increase all 00:30:10.220 --> 00:30:12.300 inputs proportionally? 00:30:12.300 --> 00:30:13.740 Return to scale. 00:30:13.740 --> 00:30:16.870 By scale, I mean, what if we just double everything, twice 00:30:16.870 --> 00:30:19.400 as much labor and twice as much capital. 00:30:19.400 --> 00:30:21.660 That's an increase in scale, increasing all inputs 00:30:21.660 --> 00:30:25.530 proportionally, twice as much labor, twice as much capital, 00:30:25.530 --> 00:30:27.660 half as much labor, half as much capital. 00:30:27.660 --> 00:30:32.160 So a change in scale is an equal increase or decrease in 00:30:32.160 --> 00:30:34.060 all inputs? 00:30:34.060 --> 00:30:35.300 Equal proportional. 00:30:35.300 --> 00:30:41.390 So what happens if we increase all inputs, increase or 00:30:41.390 --> 00:30:45.600 decrease proportionally? 00:30:45.600 --> 00:30:47.960 And this is an interesting case, because it's like, OK, 00:30:47.960 --> 00:30:49.890 what if we just make the firm half as big? 00:30:49.890 --> 00:30:51.140 What happens? 00:30:53.140 --> 00:30:55.530 Well, the answer is, it depends on 00:30:55.530 --> 00:30:57.490 the production process. 00:30:57.490 --> 00:31:02.660 Some production processes will exhibit what we call constant 00:31:02.660 --> 00:31:04.970 returns to scale. 00:31:04.970 --> 00:31:06.390 This is a convenient form. 00:31:06.390 --> 00:31:08.550 It's convenient because the way constant returns to scale 00:31:08.550 --> 00:31:16.930 works is, it says that f of 2l, 2k, is equal to 2 00:31:16.930 --> 00:31:21.050 times f of l, k. 00:31:21.050 --> 00:31:24.060 That is, if it's constant, you can just pull the 2 out. 00:31:24.060 --> 00:31:27.920 Doubling the inputs leads to doubling the outputs, which 00:31:27.920 --> 00:31:30.510 equals to 2q, I'll write here. 00:31:30.510 --> 00:31:33.510 Doubling the inputs equals doubling the outputs. 00:31:33.510 --> 00:31:36.700 So if I have twice as much labor and capital, that's the 00:31:36.700 --> 00:31:38.980 same as twice producing what I had with the original labor 00:31:38.980 --> 00:31:41.970 and capital which will get me twice the original production. 00:31:41.970 --> 00:31:43.940 That's the constant returns to scale. 00:31:43.940 --> 00:31:47.400 So every time I double my firm, I get exactly twice as 00:31:47.400 --> 00:31:50.140 much stuff out. 00:31:50.140 --> 00:31:54.030 We can contrast that with increasing returns to scale, 00:31:54.030 --> 00:32:01.530 IRS, which says that f of 2l, 2k, is greater than 2 00:32:01.530 --> 00:32:05.380 times f of l, k. 00:32:05.380 --> 00:32:08.620 Or it's greater than 2q. 00:32:08.620 --> 00:32:11.400 That is, when I double my firm, I produce more than 00:32:11.400 --> 00:32:13.580 twice as much stuff. 00:32:13.580 --> 00:32:15.240 That'd be increasing returns to scale. 00:32:17.790 --> 00:32:20.000 On the other hand, we could also have decreasing returns 00:32:20.000 --> 00:32:23.420 to scale, which not surprisingly means that f of 00:32:23.420 --> 00:32:31.970 2l, 2k, is less than 2 times f of l, k, or less than 2q. 00:32:34.590 --> 00:32:37.620 That would be decreasing returns to scale, which is 00:32:37.620 --> 00:32:42.010 when I double my firm I get less than twice as much stuff. 00:32:42.010 --> 00:32:47.345 Can anyone give me an example or some reason why returns to 00:32:47.345 --> 00:32:50.340 scale is going to be increasing or decreasing? 00:32:50.340 --> 00:32:51.910 Think about firms out there. 00:32:51.910 --> 00:32:54.090 Give me some that, by returns to scale, would be increasing 00:32:54.090 --> 00:32:56.360 or decreasing, any examples you can think of. 00:32:56.360 --> 00:32:57.260 There's no right answer here. 00:32:57.260 --> 00:32:58.320 Yeah. 00:32:58.320 --> 00:32:58.780 Go ahead, on the end. 00:32:58.780 --> 00:33:02.372 AUDIENCE: Oh, if you're mining something, you can only get to 00:33:02.372 --> 00:33:05.007 stuff at one time, so having more equipment and more people 00:33:05.007 --> 00:33:07.390 doesn't mean you can get more out of it? 00:33:07.390 --> 00:33:09.590 PROFESSOR: Right, so if there's a limited resource, 00:33:09.590 --> 00:33:11.150 you could imagine decreasing returns to scale. 00:33:11.150 --> 00:33:11.320 Good. 00:33:11.320 --> 00:33:12.250 What else? 00:33:12.250 --> 00:33:12.982 Yeah. 00:33:12.982 --> 00:33:15.184 AUDIENCE: If the company gets harder to manage, that could 00:33:15.184 --> 00:33:17.710 be decreasing returns to scale? 00:33:17.710 --> 00:33:19.440 PROFESSOR: Right, exactly. 00:33:19.440 --> 00:33:23.760 If you're an entrepreneur, you've got a great idea, but 00:33:23.760 --> 00:33:25.460 it turns out that idea only works if you really are 00:33:25.460 --> 00:33:26.520 hands-on about it. 00:33:26.520 --> 00:33:28.640 You're not Mark Zuckerberg, who can just farm the thing 00:33:28.640 --> 00:33:29.830 out, it's really your idea. 00:33:29.830 --> 00:33:30.730 And you've got to be there. 00:33:30.730 --> 00:33:32.500 Then after it expands and you lose control of the 00:33:32.500 --> 00:33:34.900 production, it might not be as effective because you're not 00:33:34.900 --> 00:33:36.850 there making it happen. 00:33:36.850 --> 00:33:37.900 Any ideas why return-- 00:33:37.900 --> 00:33:38.730 Yeah. 00:33:38.730 --> 00:33:40.170 AUDIENCE: If you or [UNINTELLIGIBLE] 00:33:45.460 --> 00:33:46.050 PROFESSOR: So that's an example of 00:33:46.050 --> 00:33:47.490 increasing returns to scale. 00:33:47.490 --> 00:33:50.820 Increasing returns to scale would be, gee, maybe if I'm 00:33:50.820 --> 00:33:55.760 bigger, I can get a better deal on the inputs. 00:33:55.760 --> 00:33:58.570 But that's not quite right, because we haven't really got 00:33:58.570 --> 00:33:59.650 into prices yet. 00:33:59.650 --> 00:34:01.280 I'm looking-- that's really a market response-- 00:34:01.280 --> 00:34:03.370 I'm looking for a more technological story, a 00:34:03.370 --> 00:34:04.810 technological story of increasing returns. 00:34:04.810 --> 00:34:05.390 Go ahead. 00:34:05.390 --> 00:34:07.115 AUDIENCE: If you're bigger, you can hire a specialist to 00:34:07.115 --> 00:34:11.310 do work, like a manager who can [INAUDIBLE] 00:34:11.310 --> 00:34:11.810 PROFESSOR: Exactly. 00:34:11.810 --> 00:34:14.290 So it's the opposite, which is, let's say you have an idea 00:34:14.290 --> 00:34:16.840 which is pretty good, but in fact it's replicable. 00:34:16.840 --> 00:34:21.560 And right now, you're trying to manage some guys. 00:34:21.560 --> 00:34:23.239 And then all of a sudden, when you get twice as big, you 00:34:23.239 --> 00:34:26.050 bring other people in who can effectively replicate your 00:34:26.050 --> 00:34:28.929 idea, and really expand it in a very effective way. 00:34:28.929 --> 00:34:32.370 You can have increasing returns to scale. 00:34:32.370 --> 00:34:34.850 Now, so an example of what that looks like, if you go to 00:34:34.850 --> 00:34:42.070 the last page in the handout, figure 8-6a shows constant 00:34:42.070 --> 00:34:43.340 returns to scale. 00:34:43.340 --> 00:34:45.020 So let's start with 8-6a, that's 00:34:45.020 --> 00:34:46.429 constant returns to scale. 00:34:46.429 --> 00:34:49.190 So here-- and these are from the textbook-- 00:34:49.190 --> 00:34:52.830 for example, when we doubled the inputs from 100 labor, 100 00:34:52.830 --> 00:34:57.480 capital, to 200 labor, 200 capital, you doubled output. 00:34:57.480 --> 00:34:59.480 Those are constant returns to scale isoquants. 00:34:59.480 --> 00:35:01.300 The last page shows decreasing and 00:35:01.300 --> 00:35:03.010 increasing returns to scale. 00:35:03.010 --> 00:35:05.670 So for instance, tobacco is an example of decreasing returns 00:35:05.670 --> 00:35:09.710 to scale, because there's only so much leaf that you have 00:35:09.710 --> 00:35:11.820 that you can produce. 00:35:11.820 --> 00:35:15.260 So here, when you double the inputs from 100 to 200, your 00:35:15.260 --> 00:35:18.930 output only goes from 100 to 142. 00:35:18.930 --> 00:35:20.950 OK, and if you want to double the 200 units, you've got to 00:35:20.950 --> 00:35:23.320 go way the heck up there on inputs. 00:35:23.320 --> 00:35:26.310 On the other hand, primary metal production is something 00:35:26.310 --> 00:35:28.550 where you can have increasing returns to scale, because 00:35:28.550 --> 00:35:32.460 there's such high costs of building a plant that once 00:35:32.460 --> 00:35:36.860 it's built, so just like I said, gee, in fact that second 00:35:36.860 --> 00:35:38.170 digger of the hole might actually make it more 00:35:38.170 --> 00:35:38.770 productive. 00:35:38.770 --> 00:35:41.700 Once that plant's built, there's one worker banging 00:35:41.700 --> 00:35:43.790 around the plant, a second worker adds a huge amount to 00:35:43.790 --> 00:35:45.740 productivity because they can specialize. 00:35:45.740 --> 00:35:47.400 Basically, increasing returns to scale is going to come from 00:35:47.400 --> 00:35:48.900 specialization. 00:35:48.900 --> 00:35:51.380 So if you build this big plant to build primary, to build 00:35:51.380 --> 00:35:54.630 steel, one worker in that plant is no good, because he's 00:35:54.630 --> 00:35:55.960 got to pour the steel, then run over and 00:35:55.960 --> 00:35:57.080 cool it down, et cetera. 00:35:57.080 --> 00:35:59.168 Once you have two, they can specialize, and three, they 00:35:59.168 --> 00:36:00.470 can specialize more. 00:36:00.470 --> 00:36:01.840 You might think of something like that would have 00:36:01.840 --> 00:36:04.310 increasing returns to scale through specialization. 00:36:04.310 --> 00:36:08.040 And that's illustrated here, where doubling the inputs 00:36:08.040 --> 00:36:10.410 actually leads to more than doubling the output. 00:36:10.410 --> 00:36:12.300 Now we're going to talk about all these cases. 00:36:12.300 --> 00:36:15.140 Typically, economists are suspicious of increasing 00:36:15.140 --> 00:36:16.350 returns to scale. 00:36:16.350 --> 00:36:20.400 Anybody, anybody who ever has an IPO, whoever starts a firm 00:36:20.400 --> 00:36:21.230 will always tell you that they have 00:36:21.230 --> 00:36:22.530 increasing returns to scale. 00:36:22.530 --> 00:36:24.750 Well, we say, I've got a great idea and the bigger, the more, 00:36:24.750 --> 00:36:26.420 the better it's going to be. 00:36:26.420 --> 00:36:28.680 And they're generally wrong. 00:36:28.680 --> 00:36:30.920 Generally, we think of increasing returns to scale as 00:36:30.920 --> 00:36:32.510 being like a free lunch. 00:36:32.510 --> 00:36:33.855 And we don't like free lunches, we economists. 00:36:33.855 --> 00:36:36.640 We think, gee, if it's really increasing returns to scale, 00:36:36.640 --> 00:36:38.400 you would have already expanded there. 00:36:38.400 --> 00:36:40.332 OK, if it's really such a good idea to get bigger, why aren't 00:36:40.332 --> 00:36:42.470 you bigger already? 00:36:42.470 --> 00:36:43.470 Now, it doesn't mean you can-- 00:36:43.470 --> 00:36:43.720 Yeah. 00:36:43.720 --> 00:36:44.930 AUDIENCE: Well, they need capital. 00:36:44.930 --> 00:36:46.480 PROFESSOR: Well, they need capital, and so that would be 00:36:46.480 --> 00:36:46.980 their argument. 00:36:46.980 --> 00:36:47.620 And that's great. 00:36:47.620 --> 00:36:48.910 And typically, they're wrong. 00:36:48.910 --> 00:36:51.010 But that would be why you would argue that they need 00:36:51.010 --> 00:36:51.990 capital to get bigger. 00:36:51.990 --> 00:36:54.170 So typically, we like decreasing returns to scale. 00:36:54.170 --> 00:36:55.590 That's going to be our sort of default 00:36:55.590 --> 00:36:56.520 assumption of the world. 00:36:56.520 --> 00:37:00.560 In other words, here's a way to think about it, think about 00:37:00.560 --> 00:37:03.255 we're dealing with mature firms. We're modeling, for 00:37:03.255 --> 00:37:04.070 instance, mature firms. 00:37:04.070 --> 00:37:06.680 We think that for mature firms, at least, there's not 00:37:06.680 --> 00:37:08.470 increasing returns to scale, because in a mature firm they 00:37:08.470 --> 00:37:09.410 would have hit that point already. 00:37:09.410 --> 00:37:11.640 Now they're on the decreasing part. 00:37:11.640 --> 00:37:13.360 So that's where we're going to focus for 00:37:13.360 --> 00:37:14.370 the rest of the semester. 00:37:14.370 --> 00:37:16.090 OK, let me stop there. 00:37:16.090 --> 00:37:18.120 And good luck tomorrow night. 00:37:18.120 --> 00:37:19.350 And we'll come back to talk more about 00:37:19.350 --> 00:37:20.600 production on Wednesday.