WEBVTT 00:00.590 --> 00:03.450 We've already talked about linear demand functions that 00:03.450 --> 00:08.980 actually have changing price elasticity as we go down 00:08.980 --> 00:09.970 the curve. 00:09.970 --> 00:11.940 And we've shown the extremes. 00:11.940 --> 00:15.060 We've shown things that are perfectly inelastic 00:15.060 --> 00:17.406 and things that are perfectly elastic. 00:17.406 --> 00:18.780 What I want to do in this video-- 00:18.780 --> 00:21.070 and it'll be a quick little video-- is think about can we 00:21.070 --> 00:23.690 construct a demand curve, or at least understand what it looks 00:23.690 --> 00:27.650 like, that has a constant elasticity across the curve? 00:27.650 --> 00:31.640 And just for fun, let's make it a constant elasticity of 1. 00:31.640 --> 00:34.847 So it has constant unit elasticity of demand. 00:34.847 --> 00:36.680 So let's think about how we can create that. 00:36.680 --> 00:38.805 And hopefully, it will give us a bit more intuition 00:38.805 --> 00:40.910 on how this elasticity business even works. 00:40.910 --> 00:43.480 So let's draw our axes. 00:43.480 --> 00:49.730 So there you go, that is price. 00:49.730 --> 00:54.700 And that right there is quantity. 00:54.700 --> 00:59.894 And let me put quantity. 00:59.894 --> 01:01.560 Now let's put some numbers there that'll 01:01.560 --> 01:05.459 just help us draw this demand curve that 01:05.459 --> 01:09.100 has unit elasticity at every point, at every price, 01:09.100 --> 01:10.119 in every quantity. 01:10.119 --> 01:11.910 So I'm just going to put some numbers here. 01:11.910 --> 01:14.300 So let's say that that right over there is 10. 01:14.300 --> 01:16.750 So that's $10 or whatever we're doing. 01:16.750 --> 01:20.150 And then this is 10 units per time period, 10 units per week, 01:20.150 --> 01:22.440 or 10 units per month, or whatever else. 01:22.440 --> 01:27.910 Now, we want the absolute value of the elasticity of demand 01:27.910 --> 01:30.010 to be equal to 1 at all points. 01:30.010 --> 01:32.990 And we're going to assume that this curve meets 01:32.990 --> 01:36.540 the law of demand, which means as price goes down, 01:36.540 --> 01:39.265 quantity demanded goes up. 01:39.265 --> 01:39.890 So let's think. 01:39.890 --> 01:41.410 This is going to be a downward sloping, 01:41.410 --> 01:43.920 so really we're going to say that the elasticity of demand 01:43.920 --> 01:46.700 is going to be equal to negative 1. 01:46.700 --> 01:49.970 If we have a 1% decrease in price, 01:49.970 --> 01:53.260 we're going to have a 1% increase in quantity, 01:53.260 --> 01:54.730 and vice versa. 01:54.730 --> 01:56.280 So let's think about it. 01:56.280 --> 02:01.230 If we're up here, where the price is near $10, 02:01.230 --> 02:04.600 and maybe where the quantity is closer to $1, 02:04.600 --> 02:07.750 let's think about what a 10% movement in price 02:07.750 --> 02:10.150 would look like, a 10% movement down. 02:10.150 --> 02:11.930 It would be roughly about this size. 02:11.930 --> 02:14.272 A 10% movement would be roughly there. 02:14.272 --> 02:16.730 And I'm just trying to get the general shape of this curve. 02:16.730 --> 02:18.605 I'm not going to go into the deep mathematics 02:18.605 --> 02:20.060 or the calculus of it. 02:20.060 --> 02:23.090 So that is a 10% price movement down. 02:23.090 --> 02:26.670 And we also want to 10% quantity movement up. 02:26.670 --> 02:29.010 But remember, our quantity is only at 1. 02:29.010 --> 02:34.660 So a 10% quantity movement up would only be 10% of 1. 02:34.660 --> 02:37.810 So if we're moving 10% in price downwards, 02:37.810 --> 02:41.390 this is a 10% upwards in quantity. 02:41.390 --> 02:44.480 So our curve up here would look something like this. 02:44.480 --> 02:46.674 It would actually have to be quite steep. 02:46.674 --> 02:49.090 Now let's think about what the curve would look over here. 02:49.090 --> 02:51.900 Once again, we want 10% for both of them, 02:51.900 --> 02:55.380 because we want the price elasticity of demand 02:55.380 --> 02:58.690 to be 1 throughout the curve. 02:58.690 --> 03:02.380 So if we go over here, a 10% movement in price-- 03:02.380 --> 03:07.130 so let's say we're down here, where price is close to 1-- 03:07.130 --> 03:10.790 a 10% movement in price is going to be very small. 03:10.790 --> 03:13.520 So a 10% movement in price is going to be like that. 03:13.520 --> 03:17.480 It's going to be roughly a tenth of a movement. 03:17.480 --> 03:19.490 So that's a 10% movement in price. 03:19.490 --> 03:22.760 But a 10% movement in quantity demanded over here, 03:22.760 --> 03:24.116 it's going to be much larger. 03:24.116 --> 03:25.740 It's going to look something like that, 03:25.740 --> 03:28.930 because the quantity is approaching 10, so 10% of that 03:28.930 --> 03:31.630 is about 1 unit just like that. 03:31.630 --> 03:33.320 So at this point in the graph, it 03:33.320 --> 03:34.740 would look something like this. 03:34.740 --> 03:37.510 It would flatten out a good bit, just like that. 03:37.510 --> 03:40.640 And then when the price and the quantity is about the same, 03:40.640 --> 03:42.550 so let's say this point right over here, 03:42.550 --> 03:45.810 where the price and the quantity is about the same-- 03:45.810 --> 03:51.020 so let's say that that is 2, this is 3, this is 2, 03:51.020 --> 03:54.859 this is 3 right over here-- your percent movements 03:54.859 --> 03:55.900 are going to be the same. 03:55.900 --> 03:57.816 But since the price and quantity are the same, 03:57.816 --> 04:00.380 the absolute movements are also going to be the same. 04:00.380 --> 04:02.640 So at that point, our curve should look something 04:02.640 --> 04:03.140 like that. 04:03.140 --> 04:04.802 It should have a slope of 1. 04:04.802 --> 04:06.260 And so if you connect the dots, you 04:06.260 --> 04:08.740 get the general shape of a demand 04:08.740 --> 04:12.360 curve that has a price elasticity of demand 04:12.360 --> 04:14.030 at negative 1 throughout the curve, 04:14.030 --> 04:16.959 or whose absolute value of the price elasticity of demand 04:16.959 --> 04:17.670 is 1. 04:17.670 --> 04:18.985 So let's just do that. 04:18.985 --> 04:20.360 So the curve would look something 04:20.360 --> 04:22.290 like-- I'll just draw a dotted line; 04:22.290 --> 04:25.990 it's easier to do-- so it'll look something like that. 04:25.990 --> 04:28.780 It'll keep getting steeper as we get the quantity closer to 0, 04:28.780 --> 04:32.160 and it'll keep flattening out as the quantity grows and grows 04:32.160 --> 04:33.270 and grows. 04:33.270 --> 1193:02:47.296 Anyway, hopefully you found that interesting.