WEBVTT 00:00:00.720 --> 00:00:03.450 Hi, everybody, my name's Caroline Elliott, and in this short NOTE CONF {"raw":[100,100,100,58,97,56,100,100,89,100]} 00:00:03.450 --> 00:00:07.050 film, I'm going to explain my multivariate calculus is important NOTE CONF {"raw":[100,99,100,100,100,80,100,100,100,100]} 00:00:07.050 --> 00:00:07.890 for economists. NOTE CONF {"raw":[100,100]} 00:00:08.430 --> 00:00:09.970 Most specifically, I'll explain. NOTE CONF {"raw":[94,100,91,100]} 00:00:09.970 --> 00:00:14.370 My partial differentiation is important for industrial economists like myself. NOTE CONF {"raw":[55,100,100,100,100,100,100,100,100,100]} 00:00:15.760 --> 00:00:19.870 As an industrial economist, I look at the strategic decisions NOTE CONF {"raw":[100,100,100,100,100,99,100,100,100,100]} 00:00:19.870 --> 00:00:24.070 taken by firms in an oligopoly industry, we assume that NOTE CONF {"raw":[100,100,100,98,100,100,100,100,100,100]} 00:00:24.070 --> 00:00:26.230 there are only a small number of firms. NOTE CONF {"raw":[100,100,100,100,100,100,100,100]} 00:00:26.830 --> 00:00:30.580 And crucially, we assume that when those firms make strategic NOTE CONF {"raw":[100,100,100,84,100,100,100,100,100,100]} 00:00:30.580 --> 00:00:34.870 decisions, they need to take account of the expected strategic NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]} 00:00:34.870 --> 00:00:36.640 decisions of rivals as well. NOTE CONF {"raw":[100,100,99,100,100]} 00:00:37.450 --> 00:00:39.920 So firms decisions are interdependent. NOTE CONF {"raw":[100,54,100,100,99]} 00:00:41.170 --> 00:00:44.230 There are lots of examples of oligopoly industries in the NOTE CONF {"raw":[100,87,100,100,100,100,100,100,97,100]} 00:00:44.230 --> 00:00:44.920 real world. NOTE CONF {"raw":[100,100]} 00:00:45.400 --> 00:00:48.790 For example, we can consider the competition between Apple and NOTE CONF {"raw":[100,100,100,100,100,99,100,100,100,100]} 00:00:48.790 --> 00:00:51.970 Samsung in the production of mobile phones, or we could NOTE CONF {"raw":[100,98,100,100,100,100,100,100,100,100]} 00:00:51.970 --> 00:00:55.150 consider the competition between Coca-Cola and Pepsi. NOTE CONF {"raw":[100,100,100,100,99,100,100]} 00:00:57.720 --> 00:01:02.670 We typically assume the oligopoly firms strategically choose levels of, NOTE CONF {"raw":[100,100,85,88,100,99,100,100,100,100]} 00:01:02.670 --> 00:01:06.100 for example, outputs or price to maximise profits. NOTE CONF {"raw":[100,100,58,100,100,100,100,100]} 00:01:07.290 --> 00:01:10.770 We can extend the analysis and assume that a firm NOTE CONF {"raw":[100,100,100,98,100,100,100,100,100,100]} 00:01:11.220 --> 00:01:16.860 chooses the level of output and advertising and maybe research NOTE CONF {"raw":[100,100,100,100,99,100,81,99,100,100]} 00:01:16.860 --> 00:01:20.740 and development all simultaneously to maximise its profits. NOTE CONF {"raw":[100,100,100,100,100,97,100,98]} 00:01:21.300 --> 00:01:24.150 But in this film, to keep the analysis simple, we're NOTE CONF {"raw":[100,100,100,90,100,100,100,100,100,94]} 00:01:24.150 --> 00:01:27.720 going to assume that our oligopoly firms are just choosing NOTE CONF {"raw":[100,100,100,100,100,100,99,100,100,100]} 00:01:27.720 --> 00:01:30.150 levels of output to maximise profits. NOTE CONF {"raw":[100,100,100,100,100,97]} 00:01:31.560 --> 00:01:35.730 We can think about an individual firm wanting to choose NOTE CONF {"raw":[100,100,100,100,100,100,100,89,100,100]} 00:01:35.730 --> 00:01:41.010 output level QSI to maximise its profits pie, and we NOTE CONF {"raw":[100,100,30,100,99,100,100,92,100,100]} 00:01:41.010 --> 00:01:45.480 can plot this firm's profit function as a function of NOTE CONF {"raw":[82,52,100,100,100,100,100,99,100,100]} 00:01:45.480 --> 00:01:46.420 its output. NOTE CONF {"raw":[100,100]} 00:01:47.640 --> 00:01:51.900 And we see that initially, as output increases, profits will NOTE CONF {"raw":[100,100,100,100,100,100,91,99,100,100]} 00:01:51.900 --> 00:01:52.500 rise. NOTE CONF {"raw":[100]} 00:01:53.430 --> 00:01:58.350 However, if output continues to rise, eventually profits will start NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]} 00:01:58.350 --> 00:01:58.860 to fall. NOTE CONF {"raw":[100,100]} 00:01:59.700 --> 00:02:03.750 So the challenge facing Funmi is to select the level NOTE CONF {"raw":[100,100,100,100,43,100,100,100,100,100]} 00:02:03.750 --> 00:02:09.210 of output QSI associated with profits being maximised. NOTE CONF {"raw":[100,100,32,100,100,100,100,87]} 00:02:10.289 --> 00:02:13.830 And we see that profits will be maximised where the NOTE CONF {"raw":[100,100,100,100,100,100,100,86,87,100]} 00:02:13.830 --> 00:02:17.070 slope of the profit function is equal to zero. NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100]} 00:02:18.450 --> 00:02:22.380 Now, that may make us think that to identify the NOTE CONF {"raw":[100,100,78,100,99,100,94,100,100,100]} 00:02:22.380 --> 00:02:28.080 profit maximising level of output QSI, we should take the NOTE CONF {"raw":[100,89,100,100,88,24,100,100,100,100]} 00:02:28.080 --> 00:02:33.570 derivative of the profit function pie with respect spectacular AQI, NOTE CONF {"raw":[100,100,100,100,100,89,100,49,43,55]} 00:02:34.020 --> 00:02:37.830 and that will give us the slope of the profit NOTE CONF {"raw":[100,100,100,100,100,100,99,100,100,100]} 00:02:37.830 --> 00:02:40.530 function and set that equal to zero. NOTE CONF {"raw":[100,100,100,100,100,100,100]} 00:02:41.100 --> 00:02:41.730 However. NOTE CONF {"raw":[100]} 00:02:44.160 --> 00:02:47.790 The problem is that the profits of I don't just NOTE CONF {"raw":[100,100,100,100,100,86,72,100,100,100]} 00:02:47.790 --> 00:02:51.690 depend on the outputs of I, but also on the NOTE CONF {"raw":[100,100,100,66,87,34,100,100,100,100]} 00:02:51.690 --> 00:02:53.570 outputs of any other firms. NOTE CONF {"raw":[68,100,100,69,97]} 00:02:54.600 --> 00:02:59.280 So we shouldn't just take an ordinary derivative, which would NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]} 00:02:59.280 --> 00:03:01.830 give us a slope of a profit function and set NOTE CONF {"raw":[100,95,57,100,100,100,100,100,100,100]} 00:03:01.830 --> 00:03:06.750 it equal to zero to identify the outputs associated with NOTE CONF {"raw":[100,100,100,100,100,100,100,76,100,100]} 00:03:06.750 --> 00:03:08.160 profits being maximised. NOTE CONF {"raw":[100,100,80]} 00:03:08.370 --> 00:03:11.820 But instead, if we want to take account of the NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]} 00:03:11.820 --> 00:03:16.470 fact that profits depend on the output of AI and NOTE CONF {"raw":[100,100,100,100,100,100,100,100,97,100]} 00:03:16.920 --> 00:03:22.080 sun, then we need to take a partial derivative of NOTE CONF {"raw":[52,100,100,100,100,100,100,100,100,100]} 00:03:22.080 --> 00:03:25.930 the profit function and set that equal to zero and NOTE CONF {"raw":[100,100,100,100,100,97,100,100,100,100]} 00:03:25.930 --> 00:03:29.130 then the remaining fields in the section you will learn NOTE CONF {"raw":[56,100,100,43,100,64,100,100,100,100]} 00:03:29.130 --> 00:03:31.770 how to calculate such partial derivatives. NOTE CONF {"raw":[100,100,100,92,100,100]} 00:03:32.310 --> 00:03:33.810 OK, thank you. NOTE CONF {"raw":[100,100,100]}