WEBVTT 00:00:00.000 --> 00:00:02.475 align:middle line:90% [SQUEAKING] 00:00:02.475 --> 00:00:04.455 align:middle line:90% [RUSTLING] 00:00:04.455 --> 00:00:07.920 align:middle line:90% [CLICKING] 00:00:07.920 --> 00:00:10.910 align:middle line:90% 00:00:10.910 --> 00:00:15.620 align:middle line:84% ROBERT TOWNSEND: So today is a review session. 00:00:15.620 --> 00:00:19.960 align:middle line:84% But let me start by looking at the class schedule. 00:00:19.960 --> 00:00:22.070 align:middle line:90% And today is the review session. 00:00:22.070 --> 00:00:24.490 align:middle line:84% So there's no readings for today. 00:00:24.490 --> 00:00:28.420 align:middle line:84% Note the lectures are numbered seven, eight, 00:00:28.420 --> 00:00:31.120 align:middle line:90% so today doesn't count somehow. 00:00:31.120 --> 00:00:34.230 align:middle line:84% But it does show up on the class schedule. 00:00:34.230 --> 00:00:36.790 align:middle line:84% It does not show up as a numbered lecture on the reading 00:00:36.790 --> 00:00:37.720 align:middle line:90% list. 00:00:37.720 --> 00:00:41.530 align:middle line:84% I find these, going over randomly selected questions 00:00:41.530 --> 00:00:45.160 align:middle line:84% on the study guide, to be very helpful. 00:00:45.160 --> 00:00:49.450 align:middle line:84% Taking a bit of time to go over, as we usually do, in this case 00:00:49.450 --> 00:00:53.600 align:middle line:84% after the end of lecture seven, is definitely worthwhile. 00:00:53.600 --> 00:00:58.330 align:middle line:84% So this question was already asked of me. 00:00:58.330 --> 00:01:01.600 align:middle line:84% So granted, it's kind of a hard question to write and maybe 00:01:01.600 --> 00:01:03.790 align:middle line:90% not so obvious how to answer. 00:01:03.790 --> 00:01:06.220 align:middle line:84% Go back to the medieval village economy 00:01:06.220 --> 00:01:08.170 align:middle line:84% and think about how you would model it 00:01:08.170 --> 00:01:11.230 align:middle line:90% in general equilibrium terms. 00:01:11.230 --> 00:01:13.980 align:middle line:90% Volunteer. 00:01:13.980 --> 00:01:17.910 align:middle line:84% How do we model the medieval village economy 00:01:17.910 --> 00:01:21.640 align:middle line:90% in general equilibrium terms? 00:01:21.640 --> 00:01:25.600 align:middle line:84% And he's ready to answer this but we already talked about it. 00:01:25.600 --> 00:01:28.070 align:middle line:90% Yes, who's speaking? 00:01:28.070 --> 00:01:30.790 align:middle line:84% STUDENT: I was going to say that it includes 00:01:30.790 --> 00:01:35.440 align:middle line:84% the possible consumption set, and the production vectors that 00:01:35.440 --> 00:01:41.340 align:middle line:84% are possible, and the endowment for that economy. 00:01:41.340 --> 00:01:43.950 align:middle line:84% ROBERT TOWNSEND: And the preferences. 00:01:43.950 --> 00:01:45.300 align:middle line:90% STUDENT: Yeah, and that. 00:01:45.300 --> 00:01:47.670 align:middle line:84% ROBERT TOWNSEND: Yeah, so that's good. 00:01:47.670 --> 00:01:51.780 align:middle line:84% So then what aspects of the medieval economy 00:01:51.780 --> 00:01:55.920 align:middle line:84% do you remember from figures and so 00:01:55.920 --> 00:01:59.475 align:middle line:84% on that look like one of those things? 00:01:59.475 --> 00:02:03.220 align:middle line:90% 00:02:03.220 --> 00:02:05.370 align:middle line:90% What about production? 00:02:05.370 --> 00:02:13.220 align:middle line:90% 00:02:13.220 --> 00:02:15.800 align:middle line:84% Well, either this question is too hard or too easy. 00:02:15.800 --> 00:02:16.640 align:middle line:90% I'm not sure which. 00:02:16.640 --> 00:02:19.780 align:middle line:90% 00:02:19.780 --> 00:02:21.970 align:middle line:84% So one answer I didn't give, the key just now, 00:02:21.970 --> 00:02:27.390 align:middle line:84% is we actually thought about the medieval village 00:02:27.390 --> 00:02:30.760 align:middle line:84% when we did the dynamics of storage, and starvation, 00:02:30.760 --> 00:02:32.080 align:middle line:90% and so on. 00:02:32.080 --> 00:02:35.640 align:middle line:84% And we wrote down a production technology 00:02:35.640 --> 00:02:37.290 align:middle line:90% mapping inputs and outputs. 00:02:37.290 --> 00:02:40.780 align:middle line:90% 00:02:40.780 --> 00:02:46.140 align:middle line:84% So we were doing production, and we took a stand on utility. 00:02:46.140 --> 00:02:50.030 align:middle line:84% And so that was an example of a medieval village economy, 00:02:50.030 --> 00:02:51.905 align:middle line:84% except there was only one person in it. 00:02:51.905 --> 00:02:52.405 align:middle line:90% But-- 00:02:52.405 --> 00:03:00.590 align:middle line:90% 00:03:00.590 --> 00:03:02.560 align:middle line:84% If you go back to those pictures, 00:03:02.560 --> 00:03:07.950 align:middle line:84% we have a map with a given person 00:03:07.950 --> 00:03:13.780 align:middle line:84% having its plots spread out all over the map of the village. 00:03:13.780 --> 00:03:18.790 align:middle line:90% 00:03:18.790 --> 00:03:21.400 align:middle line:84% So do you think they have the same production technologies 00:03:21.400 --> 00:03:23.350 align:middle line:84% or different production technologies? 00:03:23.350 --> 00:03:27.340 align:middle line:90% 00:03:27.340 --> 00:03:28.627 align:middle line:90% Anybody can answer. 00:03:28.627 --> 00:03:30.085 align:middle line:84% This is a little discussion period. 00:03:30.085 --> 00:03:42.870 align:middle line:90% 00:03:42.870 --> 00:03:45.300 align:middle line:84% Well, if it were the same production technology, 00:03:45.300 --> 00:03:48.060 align:middle line:84% then why on Earth would they be spreading their land out 00:03:48.060 --> 00:03:49.890 align:middle line:84% over the village into different spots? 00:03:49.890 --> 00:03:58.220 align:middle line:90% 00:03:58.220 --> 00:04:00.230 align:middle line:84% So it seems likely they're different production 00:04:00.230 --> 00:04:00.888 align:middle line:90% technologies. 00:04:00.888 --> 00:04:02.930 align:middle line:84% In what way do you think they might be different? 00:04:02.930 --> 00:04:09.132 align:middle line:90% 00:04:09.132 --> 00:04:10.340 align:middle line:90% I'm going to call on someone. 00:04:10.340 --> 00:04:11.360 align:middle line:90% This isn't working. 00:04:11.360 --> 00:04:14.270 align:middle line:84% Ewan, can you try to answer that-- 00:04:14.270 --> 00:04:16.010 align:middle line:84% in what reasonable way do you think 00:04:16.010 --> 00:04:17.779 align:middle line:84% the production technology is different 00:04:17.779 --> 00:04:20.135 align:middle line:90% across different plots? 00:04:20.135 --> 00:04:23.580 align:middle line:90% 00:04:23.580 --> 00:04:26.130 align:middle line:84% STUDENT: Maybe the multiplier that 00:04:26.130 --> 00:04:29.970 align:middle line:84% determines the state of the world is independent, 00:04:29.970 --> 00:04:32.913 align:middle line:84% or there are fewer correlations the further out you go. 00:04:32.913 --> 00:04:34.080 align:middle line:90% ROBERT TOWNSEND: Yeah, good. 00:04:34.080 --> 00:04:35.400 align:middle line:90% OK. 00:04:35.400 --> 00:04:37.230 align:middle line:84% So what in the storage economy was 00:04:37.230 --> 00:04:40.980 align:middle line:84% that epsilon might have different realizations 00:04:40.980 --> 00:04:42.960 align:middle line:84% for different plots, and then we get 00:04:42.960 --> 00:04:48.030 align:middle line:84% into all that stuff about correlations, and covariances, 00:04:48.030 --> 00:04:50.550 align:middle line:90% and so on. 00:04:50.550 --> 00:04:52.570 align:middle line:90% Yeah. 00:04:52.570 --> 00:04:56.590 align:middle line:84% So as I was saying, the key at the beginning, this 00:04:56.590 --> 00:04:58.540 align:middle line:90% is kind of a difficult question. 00:04:58.540 --> 00:05:02.980 align:middle line:84% That's why she asked me at right when we logged on at 2:30. 00:05:02.980 --> 00:05:04.540 align:middle line:90% It's difficult-- why? 00:05:04.540 --> 00:05:06.640 align:middle line:84% Because you're so used to seeing me 00:05:06.640 --> 00:05:11.950 align:middle line:84% show you slides of things, like here's the model, 00:05:11.950 --> 00:05:13.480 align:middle line:84% and then you're, like, OK, I guess 00:05:13.480 --> 00:05:16.010 align:middle line:90% I better learn this model. 00:05:16.010 --> 00:05:18.800 align:middle line:84% And I just put you in the different position of asking 00:05:18.800 --> 00:05:21.690 align:middle line:90% you to choose the model. 00:05:21.690 --> 00:05:24.840 align:middle line:84% That is a very interesting skill and it is not something 00:05:24.840 --> 00:05:26.370 align:middle line:90% you get to practice very often. 00:05:26.370 --> 00:05:29.200 align:middle line:90% 00:05:29.200 --> 00:05:32.620 align:middle line:84% That's why I think this question is hard in the sense 00:05:32.620 --> 00:05:34.310 align:middle line:84% that you're not used to doing that. 00:05:34.310 --> 00:05:36.700 align:middle line:84% But that's the way economists have to think about things. 00:05:36.700 --> 00:05:38.420 align:middle line:90% We make decisions. 00:05:38.420 --> 00:05:41.380 align:middle line:84% It's not like God is giving us preferences, endowments, 00:05:41.380 --> 00:05:42.610 align:middle line:90% and technology. 00:05:42.610 --> 00:05:49.740 align:middle line:84% We're kind of making it up, hopefully for good reason. 00:05:49.740 --> 00:05:54.560 align:middle line:84% All right, so that's why I earmarked that question today. 00:05:54.560 --> 00:05:57.650 align:middle line:84% For the set of feasible allocations in an Edgeworth box 00:05:57.650 --> 00:06:04.100 align:middle line:84% economy, which allocations are Pareto optimal and which not? 00:06:04.100 --> 00:06:06.975 align:middle line:84% And if we had the whiteboard, I would ask you to draw it, 00:06:06.975 --> 00:06:08.600 align:middle line:84% but I'm not going to be that ambitious. 00:06:08.600 --> 00:06:12.780 align:middle line:84% So can someone just tell me in words? 00:06:12.780 --> 00:06:15.660 align:middle line:90% How about Paolo. 00:06:15.660 --> 00:06:17.507 align:middle line:90% Can you take a stab at this. 00:06:17.507 --> 00:06:18.340 align:middle line:90% STUDENT: Yeah, sure. 00:06:18.340 --> 00:06:24.030 align:middle line:84% So the set of all Pareto optimal allocations inside of the box 00:06:24.030 --> 00:06:27.240 align:middle line:84% are the set of points for which the indifference 00:06:27.240 --> 00:06:31.710 align:middle line:84% curves for person one and person two are tangent to each other 00:06:31.710 --> 00:06:33.120 align:middle line:90% because then you can optimize. 00:06:33.120 --> 00:06:35.430 align:middle line:84% There's no lens-shaped region for you 00:06:35.430 --> 00:06:36.930 align:middle line:90% to do something that's better. 00:06:36.930 --> 00:06:39.450 align:middle line:84% And everything else is just like a non-Pareto optimal 00:06:39.450 --> 00:06:40.610 align:middle line:90% allocation. 00:06:40.610 --> 00:06:43.415 align:middle line:84% ROBERT TOWNSEND: OK, that's great, excellent answer. 00:06:43.415 --> 00:06:46.840 align:middle line:90% 00:06:46.840 --> 00:06:50.855 align:middle line:84% And maybe if we get that far in our review session, 00:06:50.855 --> 00:06:52.480 align:middle line:84% all the way back here to lecture seven, 00:06:52.480 --> 00:06:55.030 align:middle line:84% we can take a look at some of those pictures. 00:06:55.030 --> 00:07:00.280 align:middle line:90% 00:07:00.280 --> 00:07:01.190 align:middle line:90% Here's another one. 00:07:01.190 --> 00:07:04.600 align:middle line:84% What is the relationship between maximized linear welfare 00:07:04.600 --> 00:07:07.420 align:middle line:90% functions and Pareto optimality? 00:07:07.420 --> 00:07:11.100 align:middle line:90% 00:07:11.100 --> 00:07:16.290 align:middle line:84% STUDENT: So whenever we maximize a linear welfare function, 00:07:16.290 --> 00:07:18.540 align:middle line:84% the resulting allocation is guaranteed 00:07:18.540 --> 00:07:21.070 align:middle line:90% to be Pareto optimal. 00:07:21.070 --> 00:07:26.400 align:middle line:84% And I think conversely, any Pareto-optimal allocation 00:07:26.400 --> 00:07:28.772 align:middle line:84% optimizes some linear social welfare function. 00:07:28.772 --> 00:07:30.105 align:middle line:90% ROBERT TOWNSEND: Perfect answer. 00:07:30.105 --> 00:07:32.730 align:middle line:90% 00:07:32.730 --> 00:07:34.020 align:middle line:90% Now I'm a happy camper. 00:07:34.020 --> 00:07:35.670 align:middle line:90% Thank you. 00:07:35.670 --> 00:07:39.870 align:middle line:84% You guys do really well on these more precisely worded 00:07:39.870 --> 00:07:41.640 align:middle line:90% questions. 00:07:41.640 --> 00:07:42.810 align:middle line:90% That's a very good answer. 00:07:42.810 --> 00:07:43.560 align:middle line:90% Thank you so much. 00:07:43.560 --> 00:07:46.320 align:middle line:90% 00:07:46.320 --> 00:07:48.525 align:middle line:84% And let's see-- that's probably enough of that. 00:07:48.525 --> 00:07:51.650 align:middle line:90% 00:07:51.650 --> 00:07:56.420 align:middle line:84% So I'm going to scroll through these lectures 00:07:56.420 --> 00:07:58.260 align:middle line:90% with two goals in mind. 00:07:58.260 --> 00:08:03.050 align:middle line:84% One, as I go through the slides, sometimes pretty quickly, 00:08:03.050 --> 00:08:06.000 align:middle line:84% please let me know if you have a question. 00:08:06.000 --> 00:08:07.580 align:middle line:84% Even if you didn't plan to ask it, 00:08:07.580 --> 00:08:08.957 align:middle line:90% you might think of something. 00:08:08.957 --> 00:08:11.540 align:middle line:84% It might come back to you when you're looking at the material. 00:08:11.540 --> 00:08:15.980 align:middle line:84% And secondly, I will try to summarize a bit in key spots 00:08:15.980 --> 00:08:19.500 align:middle line:84% and draw some connections of one lecture to another one. 00:08:19.500 --> 00:08:21.170 align:middle line:90% So that's the plan. 00:08:21.170 --> 00:08:23.690 align:middle line:84% The substance of this first lecture 00:08:23.690 --> 00:08:27.890 align:middle line:84% had to do with economics as a science of experiments. 00:08:27.890 --> 00:08:30.950 align:middle line:84% And I covered these four different authors. 00:08:30.950 --> 00:08:32.870 align:middle line:90% Let me just not dwell on it. 00:08:32.870 --> 00:08:36.440 align:middle line:84% The point was economics as an experiment, 00:08:36.440 --> 00:08:41.179 align:middle line:84% in the sense of physics and combining various disciplines 00:08:41.179 --> 00:08:41.929 align:middle line:90% to do this. 00:08:41.929 --> 00:08:44.030 align:middle line:84% And Koopmans is making this point 00:08:44.030 --> 00:08:46.580 align:middle line:84% that it's much more than just measurement. 00:08:46.580 --> 00:08:49.820 align:middle line:84% And constantly in the course, I am showing you 00:08:49.820 --> 00:08:53.220 align:middle line:84% measurements of things, facts, and statistics, and so on. 00:08:53.220 --> 00:08:55.740 align:middle line:84% But like Koopmans, that's not enough. 00:08:55.740 --> 00:08:59.390 align:middle line:84% We want to have a good sense of the context of the problem 00:08:59.390 --> 00:09:03.620 align:middle line:84% or economy, but we want to go on and understand behavior 00:09:03.620 --> 00:09:06.260 align:middle line:90% and then make predictions. 00:09:06.260 --> 00:09:08.690 align:middle line:84% I guess the best illustration of our 00:09:08.690 --> 00:09:13.010 align:middle line:84% doing this so far might be the medieval storage problem, 00:09:13.010 --> 00:09:16.190 align:middle line:84% where we wrote that we took the medieval village we were 00:09:16.190 --> 00:09:20.390 align:middle line:84% discussing earlier, talked about preferences, endowments, 00:09:20.390 --> 00:09:21.290 align:middle line:90% and technology. 00:09:21.290 --> 00:09:24.800 align:middle line:84% We did some calibration to put in serious numbers 00:09:24.800 --> 00:09:27.660 align:middle line:84% representing risk, and returns, and so on. 00:09:27.660 --> 00:09:30.650 align:middle line:84% And then we simulated the economy 00:09:30.650 --> 00:09:33.060 align:middle line:84% and pretty much got it to match the data. 00:09:33.060 --> 00:09:37.190 align:middle line:84% So that was, I guess, the most full-blown application 00:09:37.190 --> 00:09:41.930 align:middle line:84% we've done so far in this tradition of Koopmans, 00:09:41.930 --> 00:09:45.710 align:middle line:84% although Koopmans goes on to talk about what he thinks is 00:09:45.710 --> 00:09:48.020 align:middle line:90% the real goal, which is policy. 00:09:48.020 --> 00:09:51.320 align:middle line:84% And we did not do any policy simulations in that. 00:09:51.320 --> 00:09:53.660 align:middle line:84% We didn't change something and ask 00:09:53.660 --> 00:09:56.660 align:middle line:84% if we could remedy the problem, for example. 00:09:56.660 --> 00:10:00.800 align:middle line:84% But we will be doing much more of that as the class goes on. 00:10:00.800 --> 00:10:04.460 align:middle line:84% Matzkin has this language about exogenous and endogenous 00:10:04.460 --> 00:10:05.000 align:middle line:90% variables. 00:10:05.000 --> 00:10:08.030 align:middle line:84% And we've, again in that medieval village economy, 00:10:08.030 --> 00:10:11.870 align:middle line:84% I think I was using that terminology-- 00:10:11.870 --> 00:10:15.050 align:middle line:84% things that are taken as given versus things 00:10:15.050 --> 00:10:17.180 align:middle line:90% we want to explain. 00:10:17.180 --> 00:10:20.750 align:middle line:84% Angrist was talking about randomized controlled trials 00:10:20.750 --> 00:10:24.530 align:middle line:84% and comparing them to quasi-natural experiments. 00:10:24.530 --> 00:10:29.270 align:middle line:84% This first example was paying bicycle messengers 00:10:29.270 --> 00:10:30.800 align:middle line:90% a higher wage. 00:10:30.800 --> 00:10:33.260 align:middle line:84% And a couple of comments on that-- 00:10:33.260 --> 00:10:38.030 align:middle line:84% when we get to utility functions and utility maximization 00:10:38.030 --> 00:10:41.540 align:middle line:84% subject to budgets, we actually had a picture 00:10:41.540 --> 00:10:44.480 align:middle line:84% of someone choosing how much labor to supply 00:10:44.480 --> 00:10:46.290 align:middle line:90% as a function of the wage. 00:10:46.290 --> 00:10:49.160 align:middle line:84% So this should not be abstract anymore. 00:10:49.160 --> 00:10:52.790 align:middle line:84% And we actually did look at an RCT 00:10:52.790 --> 00:10:55.580 align:middle line:84% in China that had to do with changing 00:10:55.580 --> 00:10:59.930 align:middle line:84% the price of a staple commodity, which was featured in problem 00:10:59.930 --> 00:11:01.010 align:middle line:90% set one. 00:11:01.010 --> 00:11:03.140 align:middle line:90% So what am I doing? 00:11:03.140 --> 00:11:04.890 align:middle line:84% What on Earth am I doing right now? 00:11:04.890 --> 00:11:07.460 align:middle line:84% I'm not trying to give this lecture again. 00:11:07.460 --> 00:11:10.640 align:middle line:84% I'm trying to tell you that we're delivering on it. 00:11:10.640 --> 00:11:13.490 align:middle line:84% I mentioned these concepts in the very first lecture, 00:11:13.490 --> 00:11:15.050 align:middle line:90% was probably quite abstract. 00:11:15.050 --> 00:11:17.420 align:middle line:84% But now we're already beginning to be 00:11:17.420 --> 00:11:21.230 align:middle line:84% able to fill in with the material that came afterwards. 00:11:21.230 --> 00:11:27.590 align:middle line:84% Yeah, I think this is more issues of modeling. 00:11:27.590 --> 00:11:29.540 align:middle line:84% Lucas artificial economies-- I'll 00:11:29.540 --> 00:11:32.150 align:middle line:84% go back to that dynamic lecture where 00:11:32.150 --> 00:11:37.160 align:middle line:84% I said they could be feeding grain to the animals 00:11:37.160 --> 00:11:39.230 align:middle line:90% or turning it into beer. 00:11:39.230 --> 00:11:41.360 align:middle line:90% And I said we would ignore that. 00:11:41.360 --> 00:11:43.550 align:middle line:84% That represented a choice so that we 00:11:43.550 --> 00:11:46.130 align:middle line:84% could focus on what arguably were the two 00:11:46.130 --> 00:11:48.300 align:middle line:90% most important storage devices. 00:11:48.300 --> 00:11:50.900 align:middle line:84% So we constructed an artificial economy 00:11:50.900 --> 00:11:53.330 align:middle line:90% to compare to the real data. 00:11:53.330 --> 00:11:55.700 align:middle line:90% And Lucas mentioned computation. 00:11:55.700 --> 00:11:57.980 align:middle line:84% And you can see through these lectures 00:11:57.980 --> 00:12:00.800 align:middle line:84% that I have not shied away from telling you 00:12:00.800 --> 00:12:03.440 align:middle line:90% how to determine solutions. 00:12:03.440 --> 00:12:06.320 align:middle line:84% We did this with Lagrangian stuff, 00:12:06.320 --> 00:12:08.360 align:middle line:84% with a set of first-order conditions 00:12:08.360 --> 00:12:11.630 align:middle line:84% you could use to help predict and understand the solution. 00:12:11.630 --> 00:12:14.300 align:middle line:84% And then we went to linear programs. 00:12:14.300 --> 00:12:16.730 align:middle line:90% We went to dynamic programs. 00:12:16.730 --> 00:12:19.250 align:middle line:84% And we'll do more as we go along, 00:12:19.250 --> 00:12:22.490 align:middle line:84% depending on what we need to do, depending on the lecture. 00:12:22.490 --> 00:12:24.830 align:middle line:84% And then this list of economies-- 00:12:24.830 --> 00:12:28.910 align:middle line:84% we had a great discussion about this on the last slide 00:12:28.910 --> 00:12:30.560 align:middle line:90% of the dynamic problem. 00:12:30.560 --> 00:12:34.850 align:middle line:84% We shifted gears, and went to a modern US economy 00:12:34.850 --> 00:12:36.590 align:middle line:90% with some credit instruments. 00:12:36.590 --> 00:12:38.240 align:middle line:90% And I'll come back to that. 00:12:38.240 --> 00:12:41.390 align:middle line:84% But this first economy, the medieval village economy, 00:12:41.390 --> 00:12:44.840 align:middle line:84% you've obviously seen depicted in about three different 00:12:44.840 --> 00:12:46.520 align:middle line:90% lectures so far. 00:12:46.520 --> 00:12:49.730 align:middle line:84% The Thai village economy has entered 00:12:49.730 --> 00:12:53.060 align:middle line:84% into the discussion, economies where they didn't 00:12:53.060 --> 00:12:56.210 align:middle line:84% try to diversify ex ante, and they 00:12:56.210 --> 00:12:59.930 align:middle line:84% need to potentially to share risk ex post. 00:12:59.930 --> 00:13:01.760 align:middle line:84% And we haven't done much with trade yet, 00:13:01.760 --> 00:13:05.330 align:middle line:84% although we haven't touched these other two yet. 00:13:05.330 --> 00:13:08.750 align:middle line:84% The Lucas trees we did in that dynamic lecture 00:13:08.750 --> 00:13:12.920 align:middle line:84% because we talked about yield to seed ratios, how much harvest 00:13:12.920 --> 00:13:15.770 align:middle line:84% they're getting per unit of land planted in seed. 00:13:15.770 --> 00:13:18.440 align:middle line:84% And then I turned again, at the end of that lecture, 00:13:18.440 --> 00:13:22.010 align:middle line:84% to a dynamic problem in a different economy, where 00:13:22.010 --> 00:13:26.180 align:middle line:84% they had an asset that was like a borrowing or lending 00:13:26.180 --> 00:13:28.680 align:middle line:90% contract with its own return. 00:13:28.680 --> 00:13:32.310 align:middle line:84% So we went from farming to financial assets. 00:13:32.310 --> 00:13:34.460 align:middle line:90% So hopefully, that's an example. 00:13:34.460 --> 00:13:36.440 align:middle line:90% This we just did-- 00:13:36.440 --> 00:13:37.550 align:middle line:90% what's an economy? 00:13:37.550 --> 00:13:40.370 align:middle line:84% Preferences, endowments, and technology. 00:13:40.370 --> 00:13:45.350 align:middle line:84% We've now got examples of it and we developed notation for it. 00:13:45.350 --> 00:13:48.920 align:middle line:84% And throughout, I keep trying to emphasize 00:13:48.920 --> 00:13:55.010 align:middle line:84% this can be applied to economies with dynamics with geography 00:13:55.010 --> 00:13:56.660 align:middle line:90% and with uncertainty. 00:13:56.660 --> 00:14:00.020 align:middle line:84% Hopefully, you're getting bored with my comments, 00:14:00.020 --> 00:14:03.590 align:middle line:84% in the sense of yeah, yeah, yeah, we know. 00:14:03.590 --> 00:14:06.320 align:middle line:84% I hope you do know, but my experience 00:14:06.320 --> 00:14:09.230 align:middle line:84% has been these things bear repeating. 00:14:09.230 --> 00:14:10.710 align:middle line:90% What are we going to do? 00:14:10.710 --> 00:14:13.850 align:middle line:84% We did that in the first lecture, then we did it . 00:14:13.850 --> 00:14:16.830 align:middle line:84% And now we're coming back to what did we do. 00:14:16.830 --> 00:14:21.210 align:middle line:90% So it is a review, after all. 00:14:21.210 --> 00:14:24.510 align:middle line:84% Lecture two was about consumer choice. 00:14:24.510 --> 00:14:27.630 align:middle line:84% And we reviewed what's an economy-- preference, 00:14:27.630 --> 00:14:29.610 align:middle line:90% endowments, and technology-- 00:14:29.610 --> 00:14:33.810 align:middle line:84% as if to say now we're going to focus only on preferences. 00:14:33.810 --> 00:14:38.550 align:middle line:84% Motivationally, I'm very nervous about this part of the course 00:14:38.550 --> 00:14:41.610 align:middle line:84% and also the same slide for production, 00:14:41.610 --> 00:14:44.970 align:middle line:84% because then we kind of forget the whole general economy 00:14:44.970 --> 00:14:48.090 align:middle line:84% thing, which is the prize that we want to get to. 00:14:48.090 --> 00:14:49.620 align:middle line:84% But we can't get to the big picture 00:14:49.620 --> 00:14:51.480 align:middle line:84% with all the ingredients combined 00:14:51.480 --> 00:14:53.920 align:middle line:90% until we understand the pieces. 00:14:53.920 --> 00:14:56.550 align:middle line:84% So this piece was about the consumer. 00:14:56.550 --> 00:15:00.870 align:middle line:84% And we applied it, though we did try to not just make things 00:15:00.870 --> 00:15:02.310 align:middle line:90% to memorize or theory. 00:15:02.310 --> 00:15:05.100 align:middle line:84% We tried to apply it at the end of this lecture 00:15:05.100 --> 00:15:06.720 align:middle line:90% and in the following two-- 00:15:06.720 --> 00:15:10.330 align:middle line:84% maximization of utility subject to budgets. 00:15:10.330 --> 00:15:14.680 align:middle line:84% So we described the consumption set, various special versions 00:15:14.680 --> 00:15:16.480 align:middle line:90% that have time and geography. 00:15:16.480 --> 00:15:17.780 align:middle line:90% And we've talked about this. 00:15:17.780 --> 00:15:20.110 align:middle line:84% This is, again, one of the great, little questions 00:15:20.110 --> 00:15:22.840 align:middle line:84% we had at the beginning of the following class. 00:15:22.840 --> 00:15:25.240 align:middle line:84% And we talked about consumer preferences, 00:15:25.240 --> 00:15:28.450 align:middle line:84% rank-ordering goods, defined rational choice 00:15:28.450 --> 00:15:30.670 align:middle line:84% as preferences which are complete, transitive, 00:15:30.670 --> 00:15:32.200 align:middle line:90% and continuous. 00:15:32.200 --> 00:15:34.870 align:middle line:84% And then we talked about a utility function 00:15:34.870 --> 00:15:36.670 align:middle line:90% representing preferences. 00:15:36.670 --> 00:15:38.770 align:middle line:84% A couple of things came up here-- 00:15:38.770 --> 00:15:42.520 align:middle line:84% it was ordinal and not cardinal, and we talked about that. 00:15:42.520 --> 00:15:45.850 align:middle line:84% But we will and did need cardinal representations 00:15:45.850 --> 00:15:49.750 align:middle line:84% when we got to uncertainty and dynamic decision problems. 00:15:49.750 --> 00:15:53.860 align:middle line:84% Second thing is this was a chat on Piazza. 00:15:53.860 --> 00:15:58.690 align:middle line:84% This slide goes from having a continuous utility. 00:15:58.690 --> 00:16:01.120 align:middle line:84% Any preference that can be represented 00:16:01.120 --> 00:16:04.060 align:middle line:84% by a continuous utility function is 00:16:04.060 --> 00:16:06.130 align:middle line:84% rational in the sense of the definition 00:16:06.130 --> 00:16:07.270 align:middle line:90% of the previous slide. 00:16:07.270 --> 00:16:11.260 align:middle line:84% And then someone initiated the obvious question, 00:16:11.260 --> 00:16:15.010 align:middle line:84% does it also go the other way-- that any rational preference 00:16:15.010 --> 00:16:18.580 align:middle line:84% function can be represented as a continuous utility? 00:16:18.580 --> 00:16:20.230 align:middle line:84% And the answer was, yes, although there 00:16:20.230 --> 00:16:23.650 align:middle line:84% was a good discussion about distinguishing continuity 00:16:23.650 --> 00:16:25.780 align:middle line:84% on the one hand from the other two ingredients-- 00:16:25.780 --> 00:16:27.610 align:middle line:90% completeness and transitivity. 00:16:27.610 --> 00:16:30.910 align:middle line:84% So that was a great discussion on Piazza. 00:16:30.910 --> 00:16:33.280 align:middle line:84% Local nonsatiation-- this is kind 00:16:33.280 --> 00:16:36.860 align:middle line:84% of a definition of being close by and getting better. 00:16:36.860 --> 00:16:38.890 align:middle line:90% I talked about no bliss points. 00:16:38.890 --> 00:16:41.680 align:middle line:84% I think in words, we talked about utility functions 00:16:41.680 --> 00:16:45.250 align:middle line:84% with bliss points, but we never put any pictures in. 00:16:45.250 --> 00:16:48.100 align:middle line:84% You might be thinking, could I draw a picture 00:16:48.100 --> 00:16:50.740 align:middle line:84% with a bliss point, and what would it look like? 00:16:50.740 --> 00:16:52.270 align:middle line:90% More is preferred to less. 00:16:52.270 --> 00:16:55.690 align:middle line:84% Largely I'm scrolling through this, and hopefully quickly, 00:16:55.690 --> 00:16:58.600 align:middle line:84% just to make sure if you have questions or not. 00:16:58.600 --> 00:17:02.350 align:middle line:84% Indifference curves, the whole family of indifference curves. 00:17:02.350 --> 00:17:04.900 align:middle line:84% Indifferent serves can't cross because then they 00:17:04.900 --> 00:17:06.130 align:middle line:90% wouldn't be transitive. 00:17:06.130 --> 00:17:09.490 align:middle line:84% Margin rates of substitution were defined, typically 00:17:09.490 --> 00:17:12.579 align:middle line:84% diminishing, although not necessarily. 00:17:12.579 --> 00:17:16.089 align:middle line:84% And various displays of into families of indifference 00:17:16.089 --> 00:17:18.310 align:middle line:84% for different utility functions, running all the way 00:17:18.310 --> 00:17:21.849 align:middle line:84% from perfect substitutes to perfect complements. 00:17:21.849 --> 00:17:25.119 align:middle line:84% This one over here, the right-angled indifference 00:17:25.119 --> 00:17:29.110 align:middle line:84% curves, represent Leontiefian preferences 00:17:29.110 --> 00:17:31.870 align:middle line:84% where there's no substitutability. 00:17:31.870 --> 00:17:34.893 align:middle line:84% We're about to get to maximizing utility subject to budgets. 00:17:34.893 --> 00:17:36.310 align:middle line:84% You might play around a little bit 00:17:36.310 --> 00:17:40.090 align:middle line:84% and see what happens with these particular preferences 00:17:40.090 --> 00:17:41.360 align:middle line:90% when you do that. 00:17:41.360 --> 00:17:43.060 align:middle line:84% What happens when you change prices? 00:17:43.060 --> 00:17:44.890 align:middle line:84% That would be an interesting experiment 00:17:44.890 --> 00:17:49.180 align:middle line:84% to conduct because you'll get really sharp predictions that 00:17:49.180 --> 00:17:52.060 align:middle line:84% are distinct from what you would get in this more 00:17:52.060 --> 00:17:53.950 align:middle line:90% typical smooth case. 00:17:53.950 --> 00:17:58.090 align:middle line:84% And I'm anticipating reviewing the production lecture 00:17:58.090 --> 00:18:00.070 align:middle line:90% in two lectures away. 00:18:00.070 --> 00:18:03.850 align:middle line:84% So now, you're able to go back and forth between what 00:18:03.850 --> 00:18:06.520 align:middle line:84% do indifference curves look like and consumption 00:18:06.520 --> 00:18:12.460 align:middle line:84% versus isoquants or isoproduct lines in production. 00:18:12.460 --> 00:18:17.110 align:middle line:84% This one, the Leontief thing, we didn't talk about it much 00:18:17.110 --> 00:18:20.560 align:middle line:84% in consumer theory but we did talk about it in production, 00:18:20.560 --> 00:18:23.120 align:middle line:84% and you probably didn't make the connection. 00:18:23.120 --> 00:18:27.070 align:middle line:84% But I'll try to remember to point out where we actually 00:18:27.070 --> 00:18:29.450 align:middle line:90% used it in production. 00:18:29.450 --> 00:18:33.610 align:middle line:84% These are examples of utility functions and definitions 00:18:33.610 --> 00:18:37.330 align:middle line:84% of convexity and quasi-concavity. 00:18:37.330 --> 00:18:39.760 align:middle line:84% There are a lot of different concepts here. 00:18:39.760 --> 00:18:42.670 align:middle line:84% They were all illustrated as holding or not 00:18:42.670 --> 00:18:45.880 align:middle line:84% holding, depending on how we draw these pictures. 00:18:45.880 --> 00:18:48.620 align:middle line:84% Convexity turns out to be important, 00:18:48.620 --> 00:18:50.800 align:middle line:84% especially when we're drawing pictures 00:18:50.800 --> 00:18:53.440 align:middle line:90% of tangencies and optimization. 00:18:53.440 --> 00:18:55.750 align:middle line:84% Things can really go kind of crazy 00:18:55.750 --> 00:18:57.370 align:middle line:90% when you don't have convexity. 00:18:57.370 --> 00:19:01.240 align:middle line:84% Here, it's convexity of the weak upper contour set of it, 00:19:01.240 --> 00:19:03.190 align:middle line:90% weakly preferred bundles. 00:19:03.190 --> 00:19:05.920 align:middle line:84% A little more technical derivation of the marginal rate 00:19:05.920 --> 00:19:09.850 align:middle line:84% of substitution, and something about homothetic preferences, 00:19:09.850 --> 00:19:11.860 align:middle line:84% where the slope of the indifference curves 00:19:11.860 --> 00:19:16.090 align:middle line:84% are determined entirely by the ratio of the two goods. 00:19:16.090 --> 00:19:18.970 align:middle line:84% We kept coming back to this picture in different ways. 00:19:18.970 --> 00:19:21.280 align:middle line:84% In the next lecture in fact, there's 00:19:21.280 --> 00:19:24.490 align:middle line:84% something about angles curves, and necessities, 00:19:24.490 --> 00:19:26.260 align:middle line:90% and Giffen goods, and so on. 00:19:26.260 --> 00:19:28.810 align:middle line:84% Suffice it to say that if you're moving 00:19:28.810 --> 00:19:30.460 align:middle line:90% outwards along this ray-- 00:19:30.460 --> 00:19:34.000 align:middle line:84% because maybe your income is increased, holding prices 00:19:34.000 --> 00:19:38.800 align:middle line:84% constant-- the goods x1 and x2 are increasing proportionally 00:19:38.800 --> 00:19:40.900 align:middle line:84% with the distance along this ray. 00:19:40.900 --> 00:19:43.990 align:middle line:84% And likewise, since prices are fixed, 00:19:43.990 --> 00:19:48.640 align:middle line:84% expenditure is also moving proportionally along this ray. 00:19:48.640 --> 00:19:50.560 align:middle line:84% The preferences were not homothetic. 00:19:50.560 --> 00:19:52.930 align:middle line:84% Then this would not be a line from the origin. 00:19:52.930 --> 00:19:54.550 align:middle line:90% It would start to bend. 00:19:54.550 --> 00:19:57.010 align:middle line:84% And that actually was what was going 00:19:57.010 --> 00:19:59.920 align:middle line:84% on when we talked about income effects and substitution 00:19:59.920 --> 00:20:00.490 align:middle line:90% effects. 00:20:00.490 --> 00:20:03.070 align:middle line:84% That's coming up in the next lecture. 00:20:03.070 --> 00:20:05.560 align:middle line:84% We haven't used this utility function very much, 00:20:05.560 --> 00:20:08.550 align:middle line:90% although it will appear soon. 00:20:08.550 --> 00:20:10.860 align:middle line:84% And we did talk about utility functions 00:20:10.860 --> 00:20:12.750 align:middle line:90% which are completely linear. 00:20:12.750 --> 00:20:16.140 align:middle line:84% So finally, we get to the utility maximization problem-- 00:20:16.140 --> 00:20:18.180 align:middle line:84% max utility is subject to a budget-- 00:20:18.180 --> 00:20:22.680 align:middle line:84% and defined homogeneity in this consumer theory context, 00:20:22.680 --> 00:20:26.010 align:middle line:84% and started to generate these pictures of income budget 00:20:26.010 --> 00:20:29.010 align:middle line:84% lines, and the set of all possible purchases 00:20:29.010 --> 00:20:33.870 align:middle line:84% in and under the budget line, and the utility-maximizing 00:20:33.870 --> 00:20:34.620 align:middle line:90% positions. 00:20:34.620 --> 00:20:38.160 align:middle line:84% Although again, this is kind of the classic smooth diagram 00:20:38.160 --> 00:20:41.130 align:middle line:84% that sometimes is the only diagram you see. 00:20:41.130 --> 00:20:43.500 align:middle line:84% I'm bending over backwards to show you 00:20:43.500 --> 00:20:47.610 align:middle line:84% different pictures like this one, where the maximum is not 00:20:47.610 --> 00:20:49.290 align:middle line:90% interior. 00:20:49.290 --> 00:20:53.220 align:middle line:84% You do want to keep an eye out about whether they would be 00:20:53.220 --> 00:20:57.570 align:middle line:84% happy with this quantity of y, or whether they would actually 00:20:57.570 --> 00:20:59.730 align:middle line:84% like to go negative and just cannot do it 00:20:59.730 --> 00:21:01.560 align:middle line:90% because of the consumption set. 00:21:01.560 --> 00:21:05.450 align:middle line:84% And we formalize that as an example 00:21:05.450 --> 00:21:07.940 align:middle line:84% of the use of the Lagrangian, where 00:21:07.940 --> 00:21:12.110 align:middle line:84% you write out this expression with all the constraints. 00:21:12.110 --> 00:21:17.210 align:middle line:84% And this is the generalized routine for optimization, 00:21:17.210 --> 00:21:19.550 align:middle line:84% and actually applying it to the case 00:21:19.550 --> 00:21:22.850 align:middle line:84% where we have these non-negativity constraints 00:21:22.850 --> 00:21:24.990 align:middle line:90% on the two goods. 00:21:24.990 --> 00:21:28.440 align:middle line:84% This is the most general way to deal with the problem. 00:21:28.440 --> 00:21:32.090 align:middle line:84% It doesn't mean all these constraints to are binding. 00:21:32.090 --> 00:21:34.760 align:middle line:84% They may be binding and may be not. 00:21:34.760 --> 00:21:38.120 align:middle line:84% Typically with non-satiation, a household with this constraint 00:21:38.120 --> 00:21:39.930 align:middle line:84% will want to spend all its income, 00:21:39.930 --> 00:21:42.500 align:middle line:84% so that's usually binding, although you 00:21:42.500 --> 00:21:44.540 align:middle line:84% could try to draw a picture where it's not. 00:21:44.540 --> 00:21:46.880 align:middle line:84% Back, by the way, to the bliss point, 00:21:46.880 --> 00:21:48.570 align:middle line:90% but I've never shown you that. 00:21:48.570 --> 00:21:51.530 align:middle line:84% And just because it says "greater than or equal to," 00:21:51.530 --> 00:21:53.270 align:middle line:84% in other words, non-negative, doesn't 00:21:53.270 --> 00:21:55.310 align:middle line:84% mean they would want it to go negative. 00:21:55.310 --> 00:22:00.250 align:middle line:84% That depends on what this picture looks like. 00:22:00.250 --> 00:22:04.580 align:middle line:84% And then we did the example utility functions. 00:22:04.580 --> 00:22:05.960 align:middle line:90% This is Cobb-Douglas. 00:22:05.960 --> 00:22:11.060 align:middle line:84% And you do the algebra, and you get this result 00:22:11.060 --> 00:22:15.740 align:middle line:84% that pX times X is total expenditures on X. 00:22:15.740 --> 00:22:19.320 align:middle line:84% And it's a constant, alpha times income. 00:22:19.320 --> 00:22:24.160 align:middle line:84% So this is an example of budget shares being constant. 00:22:24.160 --> 00:22:28.820 align:middle line:84% As income vary, X and Y will vary. 00:22:28.820 --> 00:22:31.460 align:middle line:84% The amount spent will vary, but it's 00:22:31.460 --> 00:22:33.110 align:middle line:90% going to vary in a linear way. 00:22:33.110 --> 00:22:34.535 align:middle line:90% It's one-to-one with income. 00:22:34.535 --> 00:22:37.440 align:middle line:90% 00:22:37.440 --> 00:22:40.780 align:middle line:84% And that Cobb-Douglas, this guy here, 00:22:40.780 --> 00:22:42.810 align:middle line:90% that's homothetic preferences. 00:22:42.810 --> 00:22:45.810 align:middle line:84% I don't think I said that when I was lecturing on this. 00:22:45.810 --> 00:22:48.190 align:middle line:90% Maybe I did. 00:22:48.190 --> 00:22:51.780 align:middle line:84% So in this case, you can almost see it in the algebra-- 00:22:51.780 --> 00:22:56.980 align:middle line:84% the marginal rate of substitution, which is here, 00:22:56.980 --> 00:23:02.160 align:middle line:84% depends only on the ratio of Y to X because this alpha is 00:23:02.160 --> 00:23:02.980 align:middle line:90% a constant. 00:23:02.980 --> 00:23:05.760 align:middle line:84% So this is a homothetic utility function. 00:23:05.760 --> 00:23:08.200 align:middle line:84% And finally, we got to labor supply, 00:23:08.200 --> 00:23:11.160 align:middle line:84% which is like an application, since I 00:23:11.160 --> 00:23:14.010 align:middle line:84% was worried that you'll lose the context of what 00:23:14.010 --> 00:23:15.850 align:middle line:90% we're trying to do. 00:23:15.850 --> 00:23:21.120 align:middle line:84% So we had this picture, this beautiful picture, of someone 00:23:21.120 --> 00:23:23.550 align:middle line:90% starting with leisure. 00:23:23.550 --> 00:23:27.390 align:middle line:84% This was the first time I think we talked about an endowment. 00:23:27.390 --> 00:23:33.340 align:middle line:84% So they're endowed with 24 hours a day or less sleep time. 00:23:33.340 --> 00:23:36.140 align:middle line:84% I don't know if you sleep eight hours, 00:23:36.140 --> 00:23:38.060 align:middle line:90% but now we're down to 16. 00:23:38.060 --> 00:23:42.200 align:middle line:84% And they can take that time and enjoy it in leisure 00:23:42.200 --> 00:23:44.600 align:middle line:90% or run it to 0 and work. 00:23:44.600 --> 00:23:48.770 align:middle line:84% This diagram is in the space of goods that consumers want. 00:23:48.770 --> 00:23:50.150 align:middle line:84% They're going to end up consuming 00:23:50.150 --> 00:23:53.150 align:middle line:84% positive amounts of leisure, positive amounts 00:23:53.150 --> 00:23:56.450 align:middle line:84% of consumption, like x1, x2, with both 00:23:56.450 --> 00:23:57.920 align:middle line:90% of them being positive. 00:23:57.920 --> 00:24:00.890 align:middle line:84% The slope of the budget line represents the wage. 00:24:00.890 --> 00:24:03.200 align:middle line:84% You might play around a bit and ask 00:24:03.200 --> 00:24:07.640 align:middle line:84% if you could draw the picture where the choice is not 00:24:07.640 --> 00:24:10.310 align:middle line:84% over leisure but labor, in which case 00:24:10.310 --> 00:24:12.080 align:middle line:84% you'd be moving to the left here. 00:24:12.080 --> 00:24:15.020 align:middle line:84% And then you'd have to draw the budget line-- 00:24:15.020 --> 00:24:16.410 align:middle line:90% it's going to look similar-- 00:24:16.410 --> 00:24:18.505 align:middle line:90% and then draw preferences. 00:24:18.505 --> 00:24:19.880 align:middle line:84% I'll show you what I have in mind 00:24:19.880 --> 00:24:23.510 align:middle line:84% when we get back to that Robinson Crusoe economy. 00:24:23.510 --> 00:24:26.520 align:middle line:90% Now let's go to lecture three. 00:24:26.520 --> 00:24:29.270 align:middle line:84% I'm going to spend a little bit less time on this 00:24:29.270 --> 00:24:31.410 align:middle line:84% in terms of going through each and every slide, 00:24:31.410 --> 00:24:35.200 align:middle line:84% but try to focus more on some of the key aspects. 00:24:35.200 --> 00:24:37.320 align:middle line:90% So we had this demand system. 00:24:37.320 --> 00:24:39.757 align:middle line:84% This would represent data, but we're 00:24:39.757 --> 00:24:41.340 align:middle line:84% going to assume right away it's coming 00:24:41.340 --> 00:24:43.680 align:middle line:90% from utility maximization. 00:24:43.680 --> 00:24:46.200 align:middle line:84% So you can think about this as restrictions 00:24:46.200 --> 00:24:51.190 align:middle line:84% on data implied by utility maximization. 00:24:51.190 --> 00:24:55.810 align:middle line:84% This is in the spirit of Frisch and RCTs 00:24:55.810 --> 00:24:57.080 align:middle line:90% and various other things. 00:24:57.080 --> 00:24:58.270 align:middle line:90% So we're increasing income. 00:24:58.270 --> 00:25:00.040 align:middle line:90% What would happen? 00:25:00.040 --> 00:25:03.370 align:middle line:84% This is the linear expansion path. 00:25:03.370 --> 00:25:05.090 align:middle line:84% But it doesn't have to look like that. 00:25:05.090 --> 00:25:07.300 align:middle line:90% It could look like this. 00:25:07.300 --> 00:25:10.660 align:middle line:84% So this actually has a negative slope 00:25:10.660 --> 00:25:14.140 align:middle line:84% as you increase income because the amount purchased of goods 00:25:14.140 --> 00:25:15.730 align:middle line:90% is going down. 00:25:15.730 --> 00:25:18.850 align:middle line:84% It could be entirely vertical, actually. 00:25:18.850 --> 00:25:22.060 align:middle line:84% I think you could imagine how to draw it that way. 00:25:22.060 --> 00:25:24.130 align:middle line:84% That utility function I said we didn't 00:25:24.130 --> 00:25:27.700 align:middle line:84% do much, which was transferable utility, x1 plus log 00:25:27.700 --> 00:25:32.650 align:middle line:84% x2, that would give you a vertical line like this, 00:25:32.650 --> 00:25:33.940 align:middle line:90% or horizontal. 00:25:33.940 --> 00:25:35.560 align:middle line:84% I don't remember which good was which, 00:25:35.560 --> 00:25:40.060 align:middle line:84% but now the quantities are going down or up 00:25:40.060 --> 00:25:41.650 align:middle line:90% and the prices are constant. 00:25:41.650 --> 00:25:44.260 align:middle line:84% Because all we're doing is moving income. 00:25:44.260 --> 00:25:46.240 align:middle line:84% Hence, the expenditure shares are 00:25:46.240 --> 00:25:50.020 align:middle line:84% moving in this diagram, not just the quantities, 00:25:50.020 --> 00:25:51.980 align:middle line:84% because of the nature of the experiment. 00:25:51.980 --> 00:25:57.920 align:middle line:84% So we defined inferior goods and normal goods, and got to Engel. 00:25:57.920 --> 00:26:00.290 align:middle line:84% Engel's law being, in particular, 00:26:00.290 --> 00:26:02.780 align:middle line:84% proportion of total expenditure on food 00:26:02.780 --> 00:26:04.610 align:middle line:90% goes down as income goes up. 00:26:04.610 --> 00:26:05.900 align:middle line:90% So someone asks me-- 00:26:05.900 --> 00:26:09.420 align:middle line:84% I think it was in the Piazza chat or was it in class-- 00:26:09.420 --> 00:26:10.430 align:middle line:90% no, it was in class. 00:26:10.430 --> 00:26:13.160 align:middle line:84% One of you asked me, are we talking 00:26:13.160 --> 00:26:16.920 align:middle line:84% about quantities or shares of expenses? 00:26:16.920 --> 00:26:17.990 align:middle line:90% So it's kind of related. 00:26:17.990 --> 00:26:20.370 align:middle line:84% In order for Engel's things to be true, 00:26:20.370 --> 00:26:23.810 align:middle line:84% some good must be, by definition, a necessity. 00:26:23.810 --> 00:26:27.290 align:middle line:84% But necessities were defined by this diagram 00:26:27.290 --> 00:26:30.800 align:middle line:84% where we just changed income and didn't change prices. 00:26:30.800 --> 00:26:33.920 align:middle line:84% Just trying to tie these loose ends together. 00:26:33.920 --> 00:26:36.590 align:middle line:84% Then we showed you what's going on in the US. 00:26:36.590 --> 00:26:40.580 align:middle line:84% One of you made a great comment about this diagram, 00:26:40.580 --> 00:26:42.290 align:middle line:90% it's kind of being tautological. 00:26:42.290 --> 00:26:44.420 align:middle line:84% And my answer was yes, but it's also 00:26:44.420 --> 00:26:46.020 align:middle line:90% quantifying the differences. 00:26:46.020 --> 00:26:49.070 align:middle line:84% And here we did the income and substitution effects 00:26:49.070 --> 00:26:52.340 align:middle line:84% from price changes, in particular emphasizing 00:26:52.340 --> 00:26:55.970 align:middle line:84% the income effect of price changes for increases 00:26:55.970 --> 00:26:59.720 align:middle line:84% and decreases in prices, and plotted out the demand curves. 00:26:59.720 --> 00:27:02.880 align:middle line:84% Some people just start with demand curves, like this. 00:27:02.880 --> 00:27:04.580 align:middle line:90% So where did it come from? 00:27:04.580 --> 00:27:06.920 align:middle line:84% In particular with aggregate demand, 00:27:06.920 --> 00:27:08.960 align:middle line:90% is it down-sloping like this? 00:27:08.960 --> 00:27:10.550 align:middle line:84% What's going to happen in the economy 00:27:10.550 --> 00:27:13.700 align:middle line:84% as a function of the virus has to do with these elasticities 00:27:13.700 --> 00:27:14.910 align:middle line:90% and so on. 00:27:14.910 --> 00:27:17.540 align:middle line:84% But I prefer not to start with this as a primitive. 00:27:17.540 --> 00:27:21.590 align:middle line:84% I prefer to derive it and put restrictions on it 00:27:21.590 --> 00:27:24.440 align:middle line:84% from these underlying first principles. 00:27:24.440 --> 00:27:26.660 align:middle line:84% Then we defined Giffen's paradox-- 00:27:26.660 --> 00:27:28.430 align:middle line:90% that in the famine, the Irish-- 00:27:28.430 --> 00:27:32.390 align:middle line:84% which destroyed the potatoes, they were eating more potatoes. 00:27:32.390 --> 00:27:35.690 align:middle line:84% We decided that couldn't literally be factually true, 00:27:35.690 --> 00:27:39.050 align:middle line:84% and that Giffen's thing, I thought, had never been tested. 00:27:39.050 --> 00:27:42.740 align:middle line:84% And then I discovered Jensen and Miller, 00:27:42.740 --> 00:27:44.210 align:middle line:90% and they shared their data. 00:27:44.210 --> 00:27:47.070 align:middle line:84% And of course, the paper was published and so on. 00:27:47.070 --> 00:27:51.140 align:middle line:84% So this was an important part of the course for two reasons. 00:27:51.140 --> 00:27:54.350 align:middle line:84% It's meant to bring the concepts of Giffen goods, 00:27:54.350 --> 00:27:56.930 align:middle line:84% and hence the distinction between income and substitution 00:27:56.930 --> 00:27:59.300 align:middle line:90% effects, to life in real data. 00:27:59.300 --> 00:28:04.760 align:middle line:84% It was also, as I said earlier, an example of an actual RCT 00:28:04.760 --> 00:28:05.940 align:middle line:90% in practice. 00:28:05.940 --> 00:28:08.840 align:middle line:84% So it's not just as if we were running an experiment. 00:28:08.840 --> 00:28:10.190 align:middle line:90% They ran the experiment. 00:28:10.190 --> 00:28:11.970 align:middle line:90% They actually did it. 00:28:11.970 --> 00:28:14.060 align:middle line:84% They had households that were treated, 00:28:14.060 --> 00:28:17.840 align:middle line:84% households that were control, looked at behavior, 00:28:17.840 --> 00:28:20.190 align:middle line:90% and they did find Giffen goods. 00:28:20.190 --> 00:28:24.300 align:middle line:84% So it's an important part to bring the theory to life. 00:28:24.300 --> 00:28:28.820 align:middle line:84% The second thing is it was a big part of problem set one. 00:28:28.820 --> 00:28:32.000 align:middle line:84% And that came with the experience of reading 00:28:32.000 --> 00:28:35.330 align:middle line:84% a professional paper, having the data there ready 00:28:35.330 --> 00:28:38.180 align:middle line:84% for you to manipulate, run some code 00:28:38.180 --> 00:28:41.810 align:middle line:84% to replicate what these guys did, and to extend it. 00:28:41.810 --> 00:28:43.820 align:middle line:84% And many of you answered those questions. 00:28:43.820 --> 00:28:48.100 align:middle line:84% Some of you did not or didn't answer all of it. 00:28:48.100 --> 00:28:50.200 align:middle line:84% At a minimum for now, you should understand 00:28:50.200 --> 00:28:54.020 align:middle line:84% what it was that these guys did, and why they did it, 00:28:54.020 --> 00:28:57.590 align:middle line:84% and what they found, quite apart from answering that problem. 00:28:57.590 --> 00:29:01.930 align:middle line:84% So uncompensated and compensated demand, 00:29:01.930 --> 00:29:05.980 align:middle line:84% also known as Hicksian versus Marshallian demand. 00:29:05.980 --> 00:29:08.240 align:middle line:90% This eliminates income effects. 00:29:08.240 --> 00:29:11.470 align:middle line:84% So you move along indifference curves when you change prices, 00:29:11.470 --> 00:29:13.930 align:middle line:84% so it's all driven by assumptions 00:29:13.930 --> 00:29:16.880 align:middle line:84% about the marginal rate of substitution. 00:29:16.880 --> 00:29:20.170 align:middle line:84% We tended to draw these smooth indifference curves 00:29:20.170 --> 00:29:23.380 align:middle line:84% with declining marginal rates of substitution, which is 00:29:23.380 --> 00:29:24.610 align:middle line:90% the right way to get started. 00:29:24.610 --> 00:29:27.220 align:middle line:84% But this concept should work as well when you have 00:29:27.220 --> 00:29:28.460 align:middle line:90% linear indifference curves. 00:29:28.460 --> 00:29:32.380 align:middle line:84% So that links back to that other diagram that I was mentioning, 00:29:32.380 --> 00:29:35.410 align:middle line:84% the one with the almost-linear indifference curve 00:29:35.410 --> 00:29:36.700 align:middle line:90% and the price. 00:29:36.700 --> 00:29:39.880 align:middle line:84% But in this case, we'd be doing that and also changing 00:29:39.880 --> 00:29:41.540 align:middle line:90% the price ratio. 00:29:41.540 --> 00:29:45.040 align:middle line:84% So we have compensated and uncompensated demand, 00:29:45.040 --> 00:29:47.810 align:middle line:90% leading to Slutsky's equation. 00:29:47.810 --> 00:29:50.050 align:middle line:84% And I don't know if I helped or hurt, 00:29:50.050 --> 00:29:54.040 align:middle line:84% but I actually jumped ahead to lecture 18 or something, 00:29:54.040 --> 00:29:56.750 align:middle line:84% and showed you eventually how we're going to use that. 00:29:56.750 --> 00:30:01.480 align:middle line:84% But I also told you to ignore that detour 00:30:01.480 --> 00:30:03.890 align:middle line:90% if it was confusing. 00:30:03.890 --> 00:30:07.600 align:middle line:84% But this whole lecture is about making predictions 00:30:07.600 --> 00:30:10.930 align:middle line:84% as prices change or income change. 00:30:10.930 --> 00:30:14.590 align:middle line:84% And this Slutsky equation turns out 00:30:14.590 --> 00:30:16.780 align:middle line:84% to be something you can measure in data. 00:30:16.780 --> 00:30:21.790 align:middle line:84% Even though we never see the compensated demand, 00:30:21.790 --> 00:30:24.940 align:middle line:84% the compensated demand has properties 00:30:24.940 --> 00:30:27.970 align:middle line:84% because the expenditure function is concave. 00:30:27.970 --> 00:30:31.000 align:middle line:84% So we can actually put some sign restrictions 00:30:31.000 --> 00:30:34.600 align:middle line:84% on the Marshallian demand in this way. 00:30:34.600 --> 00:30:38.320 align:middle line:84% It's all a bit surprising, but more on that later. 00:30:38.320 --> 00:30:40.670 align:middle line:84% Anyway, it's about making predictions. 00:30:40.670 --> 00:30:42.700 align:middle line:84% And then we did duality, which I was just 00:30:42.700 --> 00:30:48.010 align:middle line:84% alluding to, minimizing expenditures subject to-- 00:30:48.010 --> 00:30:49.270 align:middle line:90% here's the picture. 00:30:49.270 --> 00:30:52.210 align:middle line:84% So this was the first time we talked 00:30:52.210 --> 00:30:55.330 align:middle line:84% about maximizing utilities subject to budgets, hand 00:30:55.330 --> 00:30:58.840 align:middle line:84% in hand with minimizing expenditures to achieve 00:30:58.840 --> 00:31:01.220 align:middle line:90% a certain level of utility. 00:31:01.220 --> 00:31:03.760 align:middle line:84% So we defined a dual problem relative 00:31:03.760 --> 00:31:07.810 align:middle line:84% to the primary problem, and got some useful characteristics out 00:31:07.810 --> 00:31:09.340 align:middle line:90% of the dual. 00:31:09.340 --> 00:31:12.040 align:middle line:84% Although in fact, if it's a very teeny, 00:31:12.040 --> 00:31:14.920 align:middle line:84% weeny change, and it's all local, nothing happens. 00:31:14.920 --> 00:31:16.790 align:middle line:90% They're equivalent. 00:31:16.790 --> 00:31:19.390 align:middle line:84% At least, they're equivalent with these other underlying 00:31:19.390 --> 00:31:20.710 align:middle line:90% assumptions-- 00:31:20.710 --> 00:31:23.260 align:middle line:84% nice, smooth indifference curves, no bliss points, 00:31:23.260 --> 00:31:24.370 align:middle line:90% et cetera. 00:31:24.370 --> 00:31:28.690 align:middle line:84% You could experiment with putting in local satiation. 00:31:28.690 --> 00:31:30.640 align:middle line:84% And then you will discover that these things 00:31:30.640 --> 00:31:32.800 align:middle line:90% don't have to be the same. 00:31:32.800 --> 00:31:35.830 align:middle line:84% Maximizing utility subject to a budget 00:31:35.830 --> 00:31:38.380 align:middle line:84% and minimizing expenditure to achieve 00:31:38.380 --> 00:31:41.320 align:middle line:84% a certain level of utility will not 00:31:41.320 --> 00:31:45.730 align:middle line:84% be the same when you violate the assumption 00:31:45.730 --> 00:31:49.270 align:middle line:90% of local non-satiation. 00:31:49.270 --> 00:31:54.430 align:middle line:84% Anyway, we developed all this in the math, 00:31:54.430 --> 00:31:58.480 align:middle line:84% in the end of this lecture, and then 00:31:58.480 --> 00:32:02.110 align:middle line:84% ended just the way we did the previous one, with, hopefully, 00:32:02.110 --> 00:32:04.570 align:middle line:84% another attempt to bring this stuff to life, which 00:32:04.570 --> 00:32:07.870 align:middle line:84% is to give the household money incomes denoted 00:32:07.870 --> 00:32:10.540 align:middle line:84% by a first date or second date, and then 00:32:10.540 --> 00:32:12.980 align:middle line:90% talk about price changes. 00:32:12.980 --> 00:32:17.200 align:middle line:84% So it is about the distinction between income and substitution 00:32:17.200 --> 00:32:18.050 align:middle line:90% effects. 00:32:18.050 --> 00:32:24.200 align:middle line:84% But here, unlike income as exogenous and moving around, 00:32:24.200 --> 00:32:26.620 align:middle line:84% you have money incomes in the two dates. 00:32:26.620 --> 00:32:29.140 align:middle line:84% All we're doing is changing prices. 00:32:29.140 --> 00:32:31.840 align:middle line:84% We're changing the price of the good at date two 00:32:31.840 --> 00:32:34.570 align:middle line:84% relative to the price of the good at date one. 00:32:34.570 --> 00:32:36.700 align:middle line:84% So there were two different pictures here 00:32:36.700 --> 00:32:40.240 align:middle line:84% depending on whether initially, the household, as here, 00:32:40.240 --> 00:32:46.900 align:middle line:84% is a lender, eating less than its initial endowment. 00:32:46.900 --> 00:32:49.010 align:middle line:84% We talked about an income effect. 00:32:49.010 --> 00:32:52.330 align:middle line:84% You can see that as we move from the solid blue line 00:32:52.330 --> 00:32:56.290 align:middle line:84% to the pale blue line, in this upper quadrant at least, 00:32:56.290 --> 00:33:00.220 align:middle line:84% the new budget line lies further toward the northeast 00:33:00.220 --> 00:33:01.700 align:middle line:90% than the original one. 00:33:01.700 --> 00:33:04.690 align:middle line:84% And since they started here, locally the effect 00:33:04.690 --> 00:33:08.020 align:middle line:84% of the interest change is to give them more income. 00:33:08.020 --> 00:33:10.360 align:middle line:84% But they don't have to end up with higher 00:33:10.360 --> 00:33:11.740 align:middle line:90% consumption of the second good. 00:33:11.740 --> 00:33:14.050 align:middle line:84% They could have ended up with lower consumption. 00:33:14.050 --> 00:33:15.920 align:middle line:84% It's really hard to focus in there. 00:33:15.920 --> 00:33:18.290 align:middle line:84% I have to put it right there or something. 00:33:18.290 --> 00:33:21.970 align:middle line:84% So it would be a little bit lower than it was initially, 00:33:21.970 --> 00:33:25.280 align:middle line:84% and that's despite the increase in income. 00:33:25.280 --> 00:33:28.000 align:middle line:84% So that's the case where the substitution 00:33:28.000 --> 00:33:30.010 align:middle line:90% effect is getting washed out. 00:33:30.010 --> 00:33:34.660 align:middle line:84% So again, here, they start out as a borrower, 00:33:34.660 --> 00:33:38.440 align:middle line:84% and now when the interest rate goes up, 00:33:38.440 --> 00:33:42.100 align:middle line:84% they clearly have less income, which intuitively makes sense 00:33:42.100 --> 00:33:43.600 align:middle line:84% because they were already borrowing. 00:33:43.600 --> 00:33:45.580 align:middle line:84% And an increase in the interest rate 00:33:45.580 --> 00:33:49.060 align:middle line:84% can only increase the amount of debt if they stay put. 00:33:49.060 --> 00:33:51.700 align:middle line:90% But they would not stay put. 00:33:51.700 --> 00:33:54.520 align:middle line:84% Then the two effects have to do with income and substitution 00:33:54.520 --> 00:33:55.330 align:middle line:90% effects. 00:33:55.330 --> 00:33:59.560 align:middle line:84% They have the same sign for consumption today, 00:33:59.560 --> 00:34:04.920 align:middle line:84% but opposing signs for consumption tomorrow. 00:34:04.920 --> 00:34:06.620 align:middle line:84% So I think I went back the next class 00:34:06.620 --> 00:34:11.120 align:middle line:84% and made the comment that this is an important stepping stone 00:34:11.120 --> 00:34:14.420 align:middle line:84% toward modeling entire economies because we're giving 00:34:14.420 --> 00:34:15.770 align:middle line:90% the household an endowment. 00:34:15.770 --> 00:34:18.500 align:middle line:84% In the labor example, we gave the household 00:34:18.500 --> 00:34:20.540 align:middle line:90% an endowment of time. 00:34:20.540 --> 00:34:23.480 align:middle line:84% Here, we're giving the household an endowment of money income 00:34:23.480 --> 00:34:25.620 align:middle line:90% in each of two periods. 00:34:25.620 --> 00:34:27.770 align:middle line:84% So the endowments are part of an economy. 00:34:27.770 --> 00:34:30.800 align:middle line:84% Preferences are clearly being described here. 00:34:30.800 --> 00:34:33.980 align:middle line:84% Production was suppressed because it's just 00:34:33.980 --> 00:34:37.110 align:middle line:90% a consumer problem. 00:34:37.110 --> 00:34:40.319 align:middle line:90% So that was lecture three. 00:34:40.319 --> 00:34:43.190 align:middle line:90% 00:34:43.190 --> 00:34:46.540 align:middle line:90% Next up is lecture four. 00:34:46.540 --> 00:34:49.690 align:middle line:90% So I may speed up a little bit. 00:34:49.690 --> 00:34:51.870 align:middle line:84% That said, there's a ton of stuff in lecture four, 00:34:51.870 --> 00:34:55.380 align:middle line:84% and we did not get through it deliberately the first time. 00:34:55.380 --> 00:34:59.130 align:middle line:84% There's three or four slides at the end 00:34:59.130 --> 00:35:03.280 align:middle line:84% that we moved to the next lecture. 00:35:03.280 --> 00:35:05.380 align:middle line:84% Because by topic, it's about production, 00:35:05.380 --> 00:35:08.170 align:middle line:84% but there are just too many important concepts. 00:35:08.170 --> 00:35:10.990 align:middle line:84% Repeat-- preferences, endowment, technology-- now 00:35:10.990 --> 00:35:13.240 align:middle line:90% zero in on technology. 00:35:13.240 --> 00:35:15.340 align:middle line:84% That question that we were discussing 00:35:15.340 --> 00:35:19.660 align:middle line:84% about describe medieval villages as an economy also 00:35:19.660 --> 00:35:22.540 align:middle line:84% made reference to Northern Thai villages as an economy. 00:35:22.540 --> 00:35:23.690 align:middle line:90% Here's the picture. 00:35:23.690 --> 00:35:26.440 align:middle line:90% So what's the technology here? 00:35:26.440 --> 00:35:29.260 align:middle line:84% Land, labor, and capital are used as inputs 00:35:29.260 --> 00:35:30.730 align:middle line:90% to produce this crop. 00:35:30.730 --> 00:35:33.700 align:middle line:84% So this, in many respects, should not have been hard. 00:35:33.700 --> 00:35:35.260 align:middle line:84% But then again, I'm not asking you 00:35:35.260 --> 00:35:37.900 align:middle line:84% to memorize all these beautiful pictures, 00:35:37.900 --> 00:35:40.030 align:middle line:84% just saying that because I took this picture. 00:35:40.030 --> 00:35:40.630 align:middle line:90% Sorry. 00:35:40.630 --> 00:35:44.090 align:middle line:84% So production-- we have inputs and negative, outputs, 00:35:44.090 --> 00:35:50.170 align:middle line:84% which are positive, and vectors, and indexed by particular goods 00:35:50.170 --> 00:35:51.940 align:middle line:90% and by firms, potentially. 00:35:51.940 --> 00:35:54.790 align:middle line:84% We have this production possibility set, 00:35:54.790 --> 00:35:58.030 align:middle line:84% where inputs being negative, like labor over here, 00:35:58.030 --> 00:35:59.800 align:middle line:90% and outputs being positive. 00:35:59.800 --> 00:36:03.970 align:middle line:84% This one displays a region of increasing and decreasing 00:36:03.970 --> 00:36:07.510 align:middle line:84% returns to scale, to be defined momentarily. 00:36:07.510 --> 00:36:10.390 align:middle line:84% We went through these properties of production functions. 00:36:10.390 --> 00:36:14.710 align:middle line:84% And there was a good discussion coming up, namely 00:36:14.710 --> 00:36:18.820 align:middle line:84% decreasing constant and increasing returns to scale. 00:36:18.820 --> 00:36:22.120 align:middle line:84% This was the picture of decreasing returns to scale. 00:36:22.120 --> 00:36:24.610 align:middle line:84% This is a picture of increasing returns. 00:36:24.610 --> 00:36:29.060 align:middle line:84% This is a "typo" because according to the definition, 00:36:29.060 --> 00:36:31.900 align:middle line:84% you should take a point in the production set 00:36:31.900 --> 00:36:35.020 align:middle line:84% and multiply it by a lambda greater than 1, 00:36:35.020 --> 00:36:36.610 align:middle line:90% which I mentioned in class. 00:36:36.610 --> 00:36:39.070 align:middle line:84% We have not tried to correct the picture. 00:36:39.070 --> 00:36:40.690 align:middle line:84% That's because what this displays 00:36:40.690 --> 00:36:43.840 align:middle line:84% is a violation of decreasing returns 00:36:43.840 --> 00:36:46.720 align:middle line:84% relative to them being satisfied on the left. 00:36:46.720 --> 00:36:48.350 align:middle line:84% They're not satisfied on the right. 00:36:48.350 --> 00:36:50.230 align:middle line:84% So the picture is not wrong, it's just 00:36:50.230 --> 00:36:52.720 align:middle line:84% not a direct use of the definition of increasing 00:36:52.720 --> 00:36:57.080 align:middle line:84% returns, and this was constant returns. 00:36:57.080 --> 00:37:00.610 align:middle line:84% So this is aggregating production sets. 00:37:00.610 --> 00:37:04.760 align:middle line:84% This one plus this one equals this one plus the endowments. 00:37:04.760 --> 00:37:07.210 align:middle line:84% So there was a lovely discussion on Piazza 00:37:07.210 --> 00:37:13.170 align:middle line:84% about this thing, which is, have we generated a free lunch? 00:37:13.170 --> 00:37:14.910 align:middle line:84% Evidently from the picture, the answer 00:37:14.910 --> 00:37:20.010 align:middle line:84% is no because there is that finite production possibilities 00:37:20.010 --> 00:37:21.773 align:middle line:90% frontier over here. 00:37:21.773 --> 00:37:23.190 align:middle line:84% Depending on where you are, you're 00:37:23.190 --> 00:37:24.870 align:middle line:84% using one as an input and the other 00:37:24.870 --> 00:37:27.420 align:middle line:90% as an output or vice versa. 00:37:27.420 --> 00:37:30.630 align:middle line:84% The possibility is created here, however, 00:37:30.630 --> 00:37:35.730 align:middle line:84% that you use x as the input, getting y as the output. 00:37:35.730 --> 00:37:38.580 align:middle line:84% Take y as the output, put it in as an input 00:37:38.580 --> 00:37:40.530 align:middle line:90% in the second technology. 00:37:40.530 --> 00:37:44.830 align:middle line:84% Take y as the input, get x as the output. 00:37:44.830 --> 00:37:48.660 align:middle line:84% So if you kept going like that, and you got more in output 00:37:48.660 --> 00:37:52.230 align:middle line:84% than you used in input after going through one cycle, 00:37:52.230 --> 00:37:53.850 align:middle line:90% you could go to infinity. 00:37:53.850 --> 00:37:56.240 align:middle line:90% There'd be no end to it. 00:37:56.240 --> 00:37:57.920 align:middle line:84% It would not only be a free lunch, 00:37:57.920 --> 00:38:00.050 align:middle line:90% it'd be an infinite lunch. 00:38:00.050 --> 00:38:03.050 align:middle line:84% You could just keep going, in which case, 00:38:03.050 --> 00:38:04.940 align:middle line:84% although it's not entirely obvious, 00:38:04.940 --> 00:38:06.500 align:middle line:84% you could never draw this picture 00:38:06.500 --> 00:38:08.510 align:middle line:90% because there'd be no boundary. 00:38:08.510 --> 00:38:09.950 align:middle line:90% You'd always be in the interior. 00:38:09.950 --> 00:38:12.980 align:middle line:84% You could always do better just by cloning. 00:38:12.980 --> 00:38:17.240 align:middle line:84% And then we define the firm's problem, maximizing profits. 00:38:17.240 --> 00:38:18.650 align:middle line:90% We drew these pictures. 00:38:18.650 --> 00:38:22.370 align:middle line:84% Again, you get into the habit, if you're an economist- 00:38:22.370 --> 00:38:24.050 align:middle line:90% maximize subject to. 00:38:24.050 --> 00:38:28.370 align:middle line:84% Maximize linear function subject to convex constraints. 00:38:28.370 --> 00:38:30.200 align:middle line:84% You end up with these tangent cases. 00:38:30.200 --> 00:38:32.720 align:middle line:84% In this case, these are isoprofit lines 00:38:32.720 --> 00:38:34.280 align:middle line:90% not isobudget lines. 00:38:34.280 --> 00:38:37.730 align:middle line:84% We want to move out as far as we can on the isoprofit line. 00:38:37.730 --> 00:38:41.090 align:middle line:84% But the tangency is a similar thing 00:38:41.090 --> 00:38:44.270 align:middle line:84% if we move across these applications from consumer 00:38:44.270 --> 00:38:46.300 align:middle line:90% theory to producer theory. 00:38:46.300 --> 00:38:49.490 align:middle line:84% So hopefully, it's starting to become second nature. 00:38:49.490 --> 00:38:53.990 align:middle line:84% We defined properties of the production function, 00:38:53.990 --> 00:38:55.220 align:middle line:90% including convexity. 00:38:55.220 --> 00:38:56.120 align:middle line:90% And we proved it. 00:38:56.120 --> 00:39:00.560 align:middle line:84% And then almost out of order, this definition of homogeneity 00:39:00.560 --> 00:39:01.430 align:middle line:90% popped up. 00:39:01.430 --> 00:39:04.610 align:middle line:84% So one thing we didn't do was link these definitions 00:39:04.610 --> 00:39:08.120 align:middle line:84% of homogeneity of functions back to the discussion 00:39:08.120 --> 00:39:12.110 align:middle line:84% of increasing, decreasing, and constant returns to scale. 00:39:12.110 --> 00:39:14.340 align:middle line:84% But you should be able to do that. 00:39:14.340 --> 00:39:17.040 align:middle line:84% This was a proof of Hotelling's lemma. 00:39:17.040 --> 00:39:20.240 align:middle line:84% And it was an illustration of the envelope 00:39:20.240 --> 00:39:22.880 align:middle line:84% theorem, which is another tool that's 00:39:22.880 --> 00:39:24.410 align:middle line:90% going to keep popping up. 00:39:24.410 --> 00:39:27.680 align:middle line:84% Special versions of profit maximization, 00:39:27.680 --> 00:39:29.600 align:middle line:90% cost minimization-- 00:39:29.600 --> 00:39:33.230 align:middle line:84% so this is like the dual, except this one's going to get used, 00:39:33.230 --> 00:39:36.050 align:middle line:90% not just to show equivalence. 00:39:36.050 --> 00:39:38.130 align:middle line:90% What I mean by that is this-- 00:39:38.130 --> 00:39:42.800 align:middle line:84% so we have this isoproduction curve called isoquant, 00:39:42.800 --> 00:39:48.680 align:middle line:84% and we're going to try to find the cost-minimizing bundle that 00:39:48.680 --> 00:39:51.853 align:middle line:84% allows you to achieve that given level of output. 00:39:51.853 --> 00:39:53.270 align:middle line:84% Then you could do two experiments. 00:39:53.270 --> 00:39:56.120 align:middle line:84% Just like with the household, we varied 00:39:56.120 --> 00:39:57.890 align:middle line:90% income and varied prices. 00:39:57.890 --> 00:40:00.320 align:middle line:90% Here, you can vary prices. 00:40:00.320 --> 00:40:02.000 align:middle line:84% And that's the Walt Disney thing. 00:40:02.000 --> 00:40:04.310 align:middle line:90% So the input mix would change. 00:40:04.310 --> 00:40:06.260 align:middle line:84% What you could also do, although we 00:40:06.260 --> 00:40:09.530 align:middle line:84% decided not to overwhelm you, is pick 00:40:09.530 --> 00:40:11.720 align:middle line:90% a different level of output-- 00:40:11.720 --> 00:40:16.010 align:middle line:84% a higher level-- and find the cost-minimizing combination 00:40:16.010 --> 00:40:18.380 align:middle line:84% of inputs to support that higher output. 00:40:18.380 --> 00:40:23.780 align:middle line:84% And the definition of a cost curve was defined. 00:40:23.780 --> 00:40:27.290 align:middle line:84% Cost function takes the input prices as given, 00:40:27.290 --> 00:40:28.650 align:middle line:90% but also the output. 00:40:28.650 --> 00:40:31.470 align:middle line:84% So this is kind of obvious when you say it. 00:40:31.470 --> 00:40:33.620 align:middle line:84% This is the cost of producing a given output. 00:40:33.620 --> 00:40:35.060 align:middle line:90% Yes, that's true. 00:40:35.060 --> 00:40:38.240 align:middle line:90% But we never showed the picture. 00:40:38.240 --> 00:40:40.160 align:middle line:90% But we did show the costs. 00:40:40.160 --> 00:40:42.530 align:middle line:84% They're sitting here in this slide. 00:40:42.530 --> 00:40:45.320 align:middle line:84% Average cost, marginal costs, and what 00:40:45.320 --> 00:40:49.400 align:middle line:84% happens when you change prices with constant returns to scale? 00:40:49.400 --> 00:40:52.970 align:middle line:84% If the price were too high, the outcome 00:40:52.970 --> 00:40:55.070 align:middle line:84% would not be well defined because they 00:40:55.070 --> 00:40:56.900 align:middle line:90% would make infinite profit. 00:40:56.900 --> 00:41:01.310 align:middle line:84% And then when I presented this, I said there was a typo, 00:41:01.310 --> 00:41:02.720 align:middle line:90% and there is no typo. 00:41:02.720 --> 00:41:04.880 align:middle line:90% So I apologize twice. 00:41:04.880 --> 00:41:05.960 align:middle line:90% It's fine. 00:41:05.960 --> 00:41:09.980 align:middle line:84% What's going on is the dialogue in the text below is 00:41:09.980 --> 00:41:14.760 align:middle line:84% moving from here to the intermediate line to this line. 00:41:14.760 --> 00:41:18.650 align:middle line:84% So when price of the output is going up, 00:41:18.650 --> 00:41:19.820 align:middle line:90% this thing is going down. 00:41:19.820 --> 00:41:21.620 align:middle line:90% These lines are getting flatter. 00:41:21.620 --> 00:41:25.850 align:middle line:84% And when they get sufficiently flat, then you go ballistic 00:41:25.850 --> 00:41:28.610 align:middle line:84% and you can make infinite profits, which is 00:41:28.610 --> 00:41:30.440 align:middle line:90% consistent with this diagram. 00:41:30.440 --> 00:41:33.200 align:middle line:84% Except that it's never defined at a higher price 00:41:33.200 --> 00:41:36.970 align:middle line:84% because there is no determinate outcome. 00:41:36.970 --> 00:41:39.760 align:middle line:84% Then this thing I will set aside, 00:41:39.760 --> 00:41:44.050 align:middle line:84% but again, I asked you to try to write down a little bit 00:41:44.050 --> 00:41:48.100 align:middle line:84% better proof that these input ratios are constant when you 00:41:48.100 --> 00:41:50.260 align:middle line:90% have constant returns to scale. 00:41:50.260 --> 00:41:54.160 align:middle line:84% Although this is a version of in consumer theory, 00:41:54.160 --> 00:41:57.250 align:middle line:84% the idea that with homothetic utility, 00:41:57.250 --> 00:42:00.590 align:middle line:84% the expenditure shares don't move, and so on. 00:42:00.590 --> 00:42:03.070 align:middle line:90% So it is related to that. 00:42:03.070 --> 00:42:05.620 align:middle line:84% This was a picture of Robinson Crusoe. 00:42:05.620 --> 00:42:09.310 align:middle line:84% This was the first general equilibrium economy 00:42:09.310 --> 00:42:12.190 align:middle line:84% although it was only one person, with a production 00:42:12.190 --> 00:42:13.930 align:middle line:90% set and preferences. 00:42:13.930 --> 00:42:17.680 align:middle line:84% When I said you should be able to take that labor supply 00:42:17.680 --> 00:42:22.240 align:middle line:84% and convert it by making the labor supply negative, 00:42:22.240 --> 00:42:26.420 align:middle line:84% I had this in mind, except that unlike a production set, 00:42:26.420 --> 00:42:31.030 align:middle line:84% you just have a straight budget line emanating from the origin, 00:42:31.030 --> 00:42:33.550 align:middle line:84% and then you would maximize utility. 00:42:33.550 --> 00:42:37.000 align:middle line:84% You're just basically flipping the diagram from right 00:42:37.000 --> 00:42:39.230 align:middle line:90% to left like an overlay. 00:42:39.230 --> 00:42:40.780 align:middle line:90% But here, there is production. 00:42:40.780 --> 00:42:44.770 align:middle line:84% And this was an exciting part because we got to trade. 00:42:44.770 --> 00:42:48.340 align:middle line:84% So now we're talking about a real, live economy with two 00:42:48.340 --> 00:42:51.760 align:middle line:84% goods, agriculture and output, and looking 00:42:51.760 --> 00:42:55.060 align:middle line:84% at what the consumer would do if they were maximizing utility 00:42:55.060 --> 00:42:58.150 align:middle line:84% subject to that production set, as opposed to what 00:42:58.150 --> 00:43:02.480 align:middle line:84% they would do if they were able to trade in the world economy. 00:43:02.480 --> 00:43:06.460 align:middle line:84% They would produce more of the manufacturing good, 00:43:06.460 --> 00:43:10.960 align:middle line:84% and export it, and consume both goods in such a way 00:43:10.960 --> 00:43:13.580 align:middle line:90% that their utility is higher. 00:43:13.580 --> 00:43:16.300 align:middle line:84% So this is-- I can't remember if I emphasized it, 00:43:16.300 --> 00:43:19.360 align:middle line:84% but this illustrates the gains to trade. 00:43:19.360 --> 00:43:22.840 align:middle line:84% It's the gains to trade for a single consumer like Robinson 00:43:22.840 --> 00:43:25.450 align:middle line:84% Crusoe, which you can see evidently 00:43:25.450 --> 00:43:27.970 align:middle line:84% has higher utility because they get 00:43:27.970 --> 00:43:30.670 align:middle line:90% to trade away from the origin. 00:43:30.670 --> 00:43:32.200 align:middle line:84% Of course, we should ask ourselves 00:43:32.200 --> 00:43:35.470 align:middle line:84% whether this is a realistic description of the economy 00:43:35.470 --> 00:43:38.110 align:middle line:84% or whether we should populate it with more people, 00:43:38.110 --> 00:43:40.570 align:middle line:84% and potentially have heterogeneous utility 00:43:40.570 --> 00:43:41.252 align:middle line:90% functions. 00:43:41.252 --> 00:43:43.210 align:middle line:84% And for that, we're going to need to talk about 00:43:43.210 --> 00:43:45.220 align:middle line:84% whether or not we can aggregate up, 00:43:45.220 --> 00:43:49.970 align:middle line:84% which comes up in lecture 15 or 16, or something like that. 00:43:49.970 --> 00:43:54.730 align:middle line:84% And this is the US and England trading with one another. 00:43:54.730 --> 00:43:58.200 align:middle line:90% Questions? 00:43:58.200 --> 00:43:59.450 align:middle line:90% So I'm going to be brief. 00:43:59.450 --> 00:44:01.490 align:middle line:84% Otherwise, we're going to go over. 00:44:01.490 --> 00:44:04.730 align:middle line:84% This is decision making under uncertainty, and also 00:44:04.730 --> 00:44:07.410 align:middle line:90% illustrative of linear programs. 00:44:07.410 --> 00:44:10.200 align:middle line:84% So I think on this one in particular, 00:44:10.200 --> 00:44:13.160 align:middle line:84% I want you to let me know if you have questions. 00:44:13.160 --> 00:44:14.400 align:middle line:90% It is a bit unnatural. 00:44:14.400 --> 00:44:16.530 align:middle line:90% This part's all very natural. 00:44:16.530 --> 00:44:20.300 align:middle line:84% It just has to do with a household evaluating 00:44:20.300 --> 00:44:25.190 align:middle line:84% nontrivial lotteries over prizes, although we 00:44:25.190 --> 00:44:28.970 align:middle line:84% used it to define means and variances, coefficients 00:44:28.970 --> 00:44:32.060 align:middle line:84% of variation, and variances, and correlations. 00:44:32.060 --> 00:44:33.690 align:middle line:90% We did all of that. 00:44:33.690 --> 00:44:36.470 align:middle line:84% But then we went back to the award or the prize 00:44:36.470 --> 00:44:39.770 align:middle line:84% being two-dimensional, in this case, goods X1 and X2. 00:44:39.770 --> 00:44:43.070 align:middle line:84% So this is a discrete, non-convex consumption set. 00:44:43.070 --> 00:44:47.360 align:middle line:84% And miraculously, we turned it into a convex-looking set. 00:44:47.360 --> 00:44:49.970 align:middle line:84% And we had a good discussion at the beginning 00:44:49.970 --> 00:44:52.980 align:middle line:84% of the following class about how to do that. 00:44:52.980 --> 00:44:55.370 align:middle line:84% But I want to make sure you all understand it, 00:44:55.370 --> 00:44:58.410 align:middle line:84% because we're going to build on it in subsequent lectures. 00:44:58.410 --> 00:45:01.420 align:middle line:84% So one of you asked me in my office hours, 00:45:01.420 --> 00:45:03.290 align:middle line:84% it's kind of weird-- in finance, you 00:45:03.290 --> 00:45:06.740 align:middle line:84% take as given the returns on the assets or their beliefs 00:45:06.740 --> 00:45:07.790 align:middle line:90% about the returns. 00:45:07.790 --> 00:45:11.130 align:middle line:84% We don't talk about choosing the returns. 00:45:11.130 --> 00:45:14.010 align:middle line:84% But here you do, because you're choosing the lottery. 00:45:14.010 --> 00:45:16.280 align:middle line:84% You're choosing a random way, although it 00:45:16.280 --> 00:45:19.210 align:middle line:90% could be subject to a budget. 00:45:19.210 --> 00:45:21.040 align:middle line:90% I'm practically out of time. 00:45:21.040 --> 00:45:22.690 align:middle line:90% We went to concave utility. 00:45:22.690 --> 00:45:25.570 align:middle line:84% We talked about behavior under risk, different types 00:45:25.570 --> 00:45:28.000 align:middle line:84% of utility functions, this tree that we 00:45:28.000 --> 00:45:30.550 align:middle line:84% keep coming back to that was at the end of the lecture 00:45:30.550 --> 00:45:31.600 align:middle line:90% last time. 00:45:31.600 --> 00:45:35.260 align:middle line:84% This is Arrow-Debreu security, so in this case, instead 00:45:35.260 --> 00:45:38.168 align:middle line:84% of having a pure borrowing and lending economy or borrowing 00:45:38.168 --> 00:45:40.210 align:middle line:84% subject to a credit limit, we could have had them 00:45:40.210 --> 00:45:43.540 align:middle line:84% trading in an asset which yields a return of 1 00:45:43.540 --> 00:45:46.540 align:middle line:84% in one state and nothing in the other states. 00:45:46.540 --> 00:45:50.360 align:middle line:84% And you could be either making that promise as a borrower, 00:45:50.360 --> 00:45:54.290 align:middle line:84% so to speak, or buying it as an investor. 00:45:54.290 --> 00:45:56.980 align:middle line:84% So we can go from medieval villages 00:45:56.980 --> 00:45:59.650 align:middle line:90% to sophisticated securities. 00:45:59.650 --> 00:46:04.760 align:middle line:84% And then we kind of talked about this at the beginning of class. 00:46:04.760 --> 00:46:08.530 align:middle line:84% And this class ended with linear programming problems 00:46:08.530 --> 00:46:13.210 align:middle line:84% and how they crop up in general in utility maximization 00:46:13.210 --> 00:46:15.370 align:middle line:90% and linear activity analysis. 00:46:15.370 --> 00:46:19.090 align:middle line:84% This linear activity analysis is the Leontief thing 00:46:19.090 --> 00:46:21.980 align:middle line:84% I was alluding to when we went over preferences. 00:46:21.980 --> 00:46:23.170 align:middle line:90% These are constants. 00:46:23.170 --> 00:46:26.560 align:middle line:84% These A a j is the amount of good i, input i, 00:46:26.560 --> 00:46:29.830 align:middle line:84% required to produce good j, and it's a constant. 00:46:29.830 --> 00:46:32.560 align:middle line:84% The rate of substitution isn't varying 00:46:32.560 --> 00:46:36.370 align:middle line:84% that delivers these l-shaped isoquants. 00:46:36.370 --> 00:46:39.870 align:middle line:84% All right, so I'm going to have to stop because otherwise we're 00:46:39.870 --> 00:46:41.460 align:middle line:90% going to go over. 00:46:41.460 --> 00:46:46.110 align:middle line:90% So we almost got to the end. 00:46:46.110 --> 00:46:50.130 align:middle line:84% I don't think I have anything usually uncovered anyway. 00:46:50.130 --> 00:46:52.500 align:middle line:84% Because the other two lectures were 00:46:52.500 --> 00:46:55.650 align:middle line:84% the dynamics, which should be fresh in your mind-- we just 00:46:55.650 --> 00:46:58.140 align:middle line:84% covered it recently-- and the one 00:46:58.140 --> 00:47:00.900 align:middle line:84% that we did and reviewed at the beginning of the lecture 00:47:00.900 --> 00:47:05.150 align:middle line:84% today on Pareto-optimal allocations. 00:47:05.150 --> 00:47:12.000 align:middle line:90%