WEBVTT

00:00:00.720 --> 00:00:03.450
<v Speaker 0>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
<v Speaker 0>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
<v Speaker 0>for economists.

NOTE CONF {"raw":[100,100]}

00:00:08.430 --> 00:00:09.970
<v Speaker 0>Most specifically, I'll explain.

NOTE CONF {"raw":[94,100,91,100]}

00:00:09.970 --> 00:00:14.370
<v Speaker 0>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
<v Speaker 0>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
<v Speaker 0>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
<v Speaker 0>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
<v Speaker 0>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
<v Speaker 0>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
<v Speaker 0>decisions of rivals as well.

NOTE CONF {"raw":[100,100,99,100,100]}

00:00:37.450 --> 00:00:39.920
<v Speaker 0>So firms decisions are interdependent.

NOTE CONF {"raw":[100,54,100,100,99]}

00:00:41.170 --> 00:00:44.230
<v Speaker 0>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
<v Speaker 0>real world.

NOTE CONF {"raw":[100,100]}

00:00:45.400 --> 00:00:48.790
<v Speaker 0>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
<v Speaker 0>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
<v Speaker 0>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
<v Speaker 0>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
<v Speaker 0>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
<v Speaker 0>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
<v Speaker 0>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
<v Speaker 0>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
<v Speaker 0>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
<v Speaker 0>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
<v Speaker 0>levels of output to maximise profits.

NOTE CONF {"raw":[100,100,100,100,100,97]}

00:01:31.560 --> 00:01:35.730
<v Speaker 0>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
<v Speaker 0>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
<v Speaker 0>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
<v Speaker 0>its output.

NOTE CONF {"raw":[100,100]}

00:01:47.640 --> 00:01:51.900
<v Speaker 0>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
<v Speaker 0>rise.

NOTE CONF {"raw":[100]}

00:01:53.430 --> 00:01:58.350
<v Speaker 0>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
<v Speaker 0>to fall.

NOTE CONF {"raw":[100,100]}

00:01:59.700 --> 00:02:03.750
<v Speaker 0>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
<v Speaker 0>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
<v Speaker 0>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
<v Speaker 0>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
<v Speaker 0>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
<v Speaker 0>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
<v Speaker 0>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
<v Speaker 0>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
<v Speaker 0>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
<v Speaker 0>However.

NOTE CONF {"raw":[100]}

00:02:44.160 --> 00:02:47.790
<v Speaker 0>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
<v Speaker 0>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
<v Speaker 0>outputs of any other firms.

NOTE CONF {"raw":[68,100,100,69,97]}

00:02:54.600 --> 00:02:59.280
<v Speaker 0>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
<v Speaker 0>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
<v Speaker 0>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
<v Speaker 0>profits being maximised.

NOTE CONF {"raw":[100,100,80]}

00:03:08.370 --> 00:03:11.820
<v Speaker 0>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
<v Speaker 0>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
<v Speaker 0>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
<v Speaker 0>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
<v Speaker 0>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
<v Speaker 0>how to calculate such partial derivatives.

NOTE CONF {"raw":[100,100,100,92,100,100]}

00:03:32.310 --> 00:03:33.810
<v Speaker 0>OK, thank you.

NOTE CONF {"raw":[100,100,100]}