WEBVTT 00:00:09.404 --> 00:00:13.250 - In our first lecture on the elasticity of demand, we explain the intuitive 00:00:13.430 --> 00:00:18.220 meaning of elasticity. It measures the responsiveness of the quantity demanded to 00:00:18.400 --> 00:00:22.006 a change in price. More responsive means more elastic. 00:00:22.620 --> 00:00:26.910 In this lecture, we're going to show how to create a numeric measure of elasticity. 00:00:27.090 --> 00:00:32.820 How to calculate with some data on prices and quantities, what the elasticity is 00:00:33.000 --> 00:00:34.817 over a range of the demand curve. 00:00:39.715 --> 00:00:42.446 So here's a more precise definition of elasticity. 00:00:42.446 --> 00:00:47.920 The elasticity of demand is the percentage change in quantity demanded 00:00:48.100 --> 00:00:51.347 divided by the percentage change in price. 00:00:51.940 --> 00:00:56.920 So let's write it like this. We have some notation here. The elasticity demand is 00:00:57.100 --> 00:01:03.890 equal to the percentage change in. Delta is the symbol for change in, so this is 00:01:04.069 --> 00:01:10.040 the percentage change in the quantity demanded divided by the percentage change 00:01:10.220 --> 00:01:16.720 in the price. That's the elasticity of demand. Let's give an example or two. 00:01:16.900 --> 00:01:22.670 So if the price of oil increases by 10% and over a period of several years the 00:01:22.850 --> 00:01:27.603 quantity demanded falls by 5%, then the long run 00:01:27.603 --> 00:01:31.221 elasticity of demand for oil is what? 00:01:32.710 --> 00:01:39.440 Well, elasticity is the percentage change and the quantity demanded. That's minus 5% 00:01:39.620 --> 00:01:44.810 divided by the percentage change in the price. That's 10%. So the elasticity of 00:01:44.990 --> 00:01:51.247 demand is minus 5% divided by 10%, or negative 0.5. 00:01:52.816 --> 00:01:58.017 Elasticities of demand are always negative because when price goes up, the quantity 00:01:58.017 --> 00:02:02.266 demanded goes down. When price goes down, the quantity demanded goes up. 00:02:02.850 --> 00:02:06.679 So we often drop the negative sign and write that the elasticity 00:02:06.679 --> 00:02:09.638 of demand is 0.5. 00:02:11.353 --> 00:02:17.870 Here's some more important notation. If the absolute value of the elasticity of 00:02:18.050 --> 00:02:23.300 demand is less than one, just like the example we just gave for oil, we say that 00:02:23.480 --> 00:02:28.576 the demand curve is inelastic. Elasticity of demand less than one, 00:02:28.576 --> 00:02:30.661 the demand curve is inelastic. 00:02:31.700 --> 00:02:36.570 If the elasticity demand is greater than one, we say the demand curve is elastic. 00:02:36.750 --> 00:02:41.800 And if elasticity of demand is equal to one, that is the knife point case, then 00:02:41.980 --> 00:02:44.797 the demand curve is unit elastic. 00:02:45.570 --> 00:02:49.460 These terms are going to come back, so just keep them in mind. 00:02:49.640 --> 00:02:53.482 Inelastic: less than one. Elastic: greater than one. 00:02:53.482 --> 00:02:58.692 So we know that elasticity is the percentage change in quantity divided by 00:02:58.692 --> 00:03:00.360 the percentage change in price, 00:03:00.360 --> 00:03:02.906 how do we calculate the percentage change in something? 00:03:03.640 --> 00:03:06.470 This is not so hard, but it could be a little bit tricky for the following 00:03:06.650 --> 00:03:10.720 reason. Let's suppose you're driving down the highway at 100 miles per hour. I don't 00:03:10.900 --> 00:03:14.270 recommend this, but let's just imagine that you are. You're going 100 miles per 00:03:14.450 --> 00:03:21.090 hour, and now you increase speed by 50%. How fast are you going? 150 miles per 00:03:21.090 --> 00:03:26.172 hour, right? Okay, so now you're going 150 miles per hour. Suppose you decrease speed 00:03:26.172 --> 00:03:32.538 by 50%. Now, how fast are you going? 75 miles per hour, right? So how is it that 00:03:32.538 --> 00:03:36.635 you can increase speed by 50% and then decrease by 50% 00:03:36.635 --> 00:03:38.925 and not be back to where you started? 00:03:39.890 --> 00:03:44.450 Well the answer is, is that intuitively we have changed the base by which we are 00:03:44.630 --> 00:03:51.160 calculating the percentage change. And we don't want to have this inconsistency when 00:03:51.340 --> 00:03:56.430 we calculate elasticity. We want people to get the same elasticity whether they're 00:03:56.610 --> 00:03:59.690 calculating from the lower base or from the higher base. 00:03:59.870 --> 00:04:04.610 So because of that, we're going to use the Midpoint Formula. So the elasticity of 00:04:04.790 --> 00:04:09.260 demand, percentage change in quantity divided by the percentage change in price, 00:04:09.440 --> 00:04:16.070 that's the change in quantity divided by the average quantity times 100. That will 00:04:16.250 --> 00:04:22.320 give us the percentage change divided by the change in price divided by the average 00:04:22.500 --> 00:04:26.280 price. Again, that times 100. Notice, since we've actually got 100 on top and 00:04:26.460 --> 00:04:30.093 100 on the bottom, those 100s we can actually cancel out. 00:04:30.980 --> 00:04:35.810 Let's expand this just a little bit more. The change in quantity. What is the change 00:04:35.990 --> 00:04:40.190 in quantity? Well, let's suppose we have two quantities. Let's call them after and 00:04:40.370 --> 00:04:44.330 before. It doesn't matter which one we call after or which one before. So we're 00:04:44.510 --> 00:04:50.930 going to then expand this to the change in quantity. That's Q after minus Q before 00:04:51.110 --> 00:04:57.230 divided by the average, Q after plus Q before, divided by two, divided by the 00:04:57.410 --> 00:05:03.150 change in price, P after minus P before, divided by the average price, b after plus 00:05:03.330 --> 00:05:05.115 b before, divide by two. 00:05:05.640 --> 00:05:11.120 So that's a little bit of a mouthful, but everything, I think, is fairly simple. 00:05:11.300 --> 00:05:18.330 Just remember change in quantity divided by the average quantity and you should 00:05:18.510 --> 00:05:23.040 always be able to calculate this. Let's give an example. 00:05:23.220 --> 00:05:27.420 Okay, here's an example of a type of problem you might see on a quiz or a mid 00:05:27.600 --> 00:05:33.160 term. At the initial price of $10, the quantity demanded is 100. When the price 00:05:33.340 --> 00:05:40.550 rises to $20, the quantity demanded falls to 90. What is the elasticity is, what is 00:05:40.730 --> 00:05:43.335 the elasticity over this range of the demand curve? 00:05:44.040 --> 00:05:47.710 Well, we always want to begin by writing down what we know, our formula. The 00:05:47.890 --> 00:05:50.880 elasticity of demand is the percentage change in quantity divided by the 00:05:51.060 --> 00:05:55.460 percentage change in price. Now, let's remember to just expand that. That's Delta 00:05:55.640 --> 00:06:00.600 Q over the average Q all divided by Delta P over the average P. 00:06:01.040 --> 00:06:08.620 Now, we just start to fill things in. So our quantity after, okay, after the change 00:06:08.800 --> 00:06:16.860 is 90. Our quantity before that was 100. So on the top, the percentage change in 00:06:17.040 --> 00:06:21.640 quantity is 90 minus 100 divided by 90 plus 100, over two. That is the average 00:06:21.820 --> 00:06:28.260 quantity. And then on the bottom, and the only trick here is always write it in the 00:06:28.440 --> 00:06:33.680 same order, so if you put the 90 here, then make sure you put the 20, the number 00:06:33.860 --> 00:06:38.180 the price which is associated with that quantity started off, the same way. So 00:06:38.360 --> 00:06:39.996 always just keep it in the same order. 00:06:40.610 --> 00:06:45.090 So on the bottom, then, we have the quantity, the price after, which is 20 00:06:45.270 --> 00:06:49.430 minus the price before, which is 10, divided by the average price. And now, 00:06:49.610 --> 00:06:55.400 just, it's numerics. You plug in the numbers and what you get is the elasticity 00:06:55.580 --> 00:07:01.520 of demand is equal to negative 0.158, approximately. We can always drop the 00:07:01.700 --> 00:07:04.510 negative sign because these things, elasticity of demands, are always 00:07:04.690 --> 00:07:11.720 negative. So it's equal to 0.158. So does this make the elasticity of demand over 00:07:11.900 --> 00:07:19.940 this range elastic or inelastic? Inelastic, right? The elasticity of demand 00:07:20.120 --> 00:07:24.448 we've just calculated as less than one, so that makes this one inelastic. 00:07:24.448 --> 00:07:26.121 There you go. 00:07:27.030 --> 00:07:31.070 We need to cover one more important point about the elasticity of demand, and that 00:07:31.250 --> 00:07:37.410 is its relationship to total revenue. So a firms revenues are very simply equal to 00:07:37.590 --> 00:07:42.860 price times quantity sold. Revenue is equal to price times quantity. 00:07:43.040 --> 00:07:47.270 Now, elasticity, it's all about the relationship between price and quantity, 00:07:47.450 --> 00:07:52.800 and so it's also going to have implications for revenue. Let's give some 00:07:52.980 --> 00:07:57.460 intuition for the relationship between the elasticity and total revenue. So revenue 00:07:57.640 --> 00:07:59.324 is price times quantity. 00:07:59.324 --> 00:08:04.940 Now suppose the price goes up by a lot and then quantity demanded goes down, just by 00:08:05.120 --> 00:08:10.310 a little bit. What then is going to be the responsive revenue? Well, if price is 00:08:10.490 --> 00:08:15.260 going up by a lot and quantity is going down just by a little bit, then revenue is 00:08:15.440 --> 00:08:20.900 also going to be going up. Now, what kind of demand curve do we call that, when 00:08:21.080 --> 00:08:27.810 price goes up by a lot and quantity falls by just a little bit? We call that an 00:08:27.990 --> 00:08:30.003 inelastic demand curve. 00:08:30.810 --> 00:08:34.650 So what this little thought experiment tells us is that when you have an 00:08:34.830 --> 00:08:42.230 inelastic demand curve, when price goes up revenue is also going to go up, and of 00:08:42.409 --> 00:08:45.990 course, vice versa. Let's take a look at this with a graph. 00:08:46.170 --> 00:08:51.630 So here's our initial demand curve, a very inelastic demand curve, at a price of $10 00:08:51.810 --> 00:08:57.640 that quantity demanded is 100 units, so revenue is 1,000. Notice that we can show 00:08:57.820 --> 00:09:02.370 revenue in the graph by price times quantity. Now, just looking at the graph, 00:09:02.550 --> 00:09:07.860 look at what happens when the price goes up to 20. Well, the quantity goes down by 00:09:08.040 --> 00:09:12.998 just a little bit, in this case to 90, but revenues go up to 1,800. 00:09:13.610 --> 00:09:21.460 So you can just see, by sketching the little graph, what happens to revenues 00:09:21.640 --> 00:09:25.770 when price goes up when you have an inelastic demand curve. And again, vice 00:09:25.950 --> 00:09:30.240 versa. Let's take a look about what happens when you have an elastic demand 00:09:30.420 --> 00:09:35.170 curve. So let's do the same kind of little thought experiment, revenue is price times 00:09:35.350 --> 00:09:41.110 quantity. Suppose price goes up by a modest amount and quantity goes down by a 00:09:41.290 --> 00:09:45.690 lot. Well, if price is going up by a little bit and quantity is going down by a 00:09:45.870 --> 00:09:51.990 lot, then revenue must also be falling. And what type of demand curve is it when 00:09:52.170 --> 00:09:55.870 price goes up by a little bit, quantity falls by a lot? What type of demand curve 00:09:56.050 --> 00:09:59.175 is that? That's an elastic demand curve. 00:09:59.790 --> 00:10:05.660 So revenues fall as price rises with an elastic demand curve. And again, let's 00:10:05.840 --> 00:10:10.963 show that. If you're ever confused and you can't quite remember, just draw the graph. 00:10:10.963 --> 00:10:16.070 I can never remember, myself, but I always draw these little graphs. So draw a really 00:10:16.250 --> 00:10:22.781 flatter, elastic demand curve. In this case, at a price of $10, the quantity 00:10:22.781 --> 00:10:29.754 demanded is 250 units. So revenues is 2,500. And see what happens, when price 00:10:29.754 --> 00:10:35.552 goes up, price goes up to $20, quantity demanded falls to 50, 00:10:35.552 --> 00:10:37.642 so revenue falls to 1,000. 00:10:38.025 --> 00:10:44.089 And again, you can just compare the sizes of these revenue rectangles to see which 00:10:44.089 --> 00:10:50.147 way the relationship goes. And of course this also implies, going from $20, the 00:10:50.147 --> 00:10:56.725 price of $20 to the price of $10, revenues increase. So with an elastic demand curve, 00:10:56.725 --> 00:11:00.250 when price goes down revenues go up. 00:11:01.296 --> 00:11:04.866 So here's a summary of these relationships. When the elasticity of 00:11:04.866 --> 00:11:08.862 demand is less than one, that's an inelastic demand curve and price and 00:11:08.862 --> 00:11:11.901 revenue move together. When one goes up the other goes up. 00:11:11.901 --> 00:11:13.484 When one goes down, the other goes down. 00:11:13.484 --> 00:11:18.796 If the elasticity demand is greater than one, that's an elastic demand curve and 00:11:18.796 --> 00:11:23.366 price and revenue move in opposite directions. And could you guess what 00:11:23.366 --> 00:11:27.833 happens if the elasticity demand is equal to one, if you have a unit elastic curve? 00:11:27.833 --> 00:11:31.986 Well then, when the price changes, revenue stays the same. 00:11:32.676 --> 00:11:38.550 Now, if you have to, again, memorize these, but it's really much better to just 00:11:38.550 --> 00:11:42.666 sketch some graphs. I never remember them, as I've said myself, I never remember 00:11:42.666 --> 00:11:46.987 these relationships, but I can always sketch an inelastic graph and then with a 00:11:46.987 --> 00:11:51.767 few changes in price I can see whether the revenue rectangles are getting bigger or 00:11:51.767 --> 00:11:57.907 smaller and so I'll be able to recompute all of these relationships pretty easily. 00:11:59.330 --> 00:12:03.210 Here's a quick practice question. The elasticity of demand for eggs has been 00:12:03.390 --> 00:12:09.280 estimated to be 0.1. If egg producers raise their prices by 10%, what will 00:12:09.460 --> 00:12:16.060 happen to their total revenues? Increase? Decrease? Or it won't change? 00:12:16.240 --> 00:12:21.980 Okay, how should we approach this problem? If the elasticity of demand is 0.1, what 00:12:22.160 --> 00:12:29.280 type of demand curve? Inelastic demand. Now, what's the relationship between an 00:12:29.460 --> 00:12:34.780 inelastic demand curve? When price goes up, what happens to revenue? If you're not 00:12:34.960 --> 00:12:38.116 sure, if you don't remember, draw some graphs. Draw an inelastic, 00:12:38.116 --> 00:12:39.853 draw an elastic, figure it out. 00:12:40.530 --> 00:12:45.870 Okay, let's see. What happens? Revenue increases, right? If you have an inelastic 00:12:46.050 --> 00:12:50.650 demand curve and price goes up revenue goes up as well. 00:12:50.830 --> 00:12:57.300 Here's an application. Why is the war on drugs so hard to win? Well, drugs are 00:12:57.480 --> 00:13:04.460 typically going to have a fairly inelastic demand curve. What that means is that when 00:13:04.640 --> 00:13:09.510 enforcement actions raise the price of drugs, make it more costly to get drugs, 00:13:09.690 --> 00:13:15.520 raising the price, that means the total revenue for the drug dealers goes up. So 00:13:15.700 --> 00:13:19.830 check out this graph. Here is the price with no prohibition, here's our demand 00:13:20.010 --> 00:13:21.871 curve, our inelastic demand curve. 00:13:22.350 --> 00:13:27.140 What prohibition does, is it raises the cost of supplying the good. But that 00:13:27.320 --> 00:13:31.830 raises the price, which is what it's supposed to do, and that does reduce the 00:13:32.010 --> 00:13:37.580 quantity demanded of the drug. But it also has the effect of increasing seller 00:13:37.760 --> 00:13:43.300 revenues. And seller revenues may be where many of the problems of drug prohibition 00:13:43.480 --> 00:13:49.910 come from. It's the seller revenues which drive the violence, which drive the gun, 00:13:50.090 --> 00:13:55.290 which make it look good to be a drug dealer, which encourage people to become 00:13:55.470 --> 00:13:57.260 drug dealers, and so forth. 00:13:57.670 --> 00:14:02.360 So there's a real difficulty with prohibition, with prohibiting a good, 00:14:02.540 --> 00:14:05.416 especially when it has an inelastic demand. 00:14:06.000 --> 00:14:09.760 Here's another application of elasticity of demand and how it can be used to 00:14:09.940 --> 00:14:14.732 understand our world. This is a quotation from 2012 from 00:14:14.732 --> 00:14:16.635 NPRs food blog "The Salt." 00:14:17.600 --> 00:14:21.910 "You've all heard a lot about this year's devastating drought in the Midwest, right? 00:14:22.090 --> 00:14:26.270 US Department of Agriculture announced last Friday that the average US cornfield 00:14:26.450 --> 00:14:33.290 this year will yield less per acre than it has since 1995. Soybean yields are down, 00:14:33.470 --> 00:14:38.970 too. So you think that farmers who grow these crops must be really hurting. And 00:14:39.150 --> 00:14:44.900 that's certainly the impression you get from media reports. But how's this, for a 00:14:45.080 --> 00:14:50.780 surprising fact? On average, corn growers actually will rake in a record amount of 00:14:50.960 --> 00:14:53.777 cash from their harvest this year." 00:14:54.500 --> 00:15:00.370 So can you explain this secret side of the drought? I'm not going to answer this 00:15:00.550 --> 00:15:05.700 question. This is exactly the type of question you might receive on an exam. But 00:15:05.880 --> 00:15:09.260 you should be able to answer it by now, with a few sketches on a piece of paper. 00:15:09.440 --> 00:15:14.250 And in particular, what I want you to answer is, what type of demand curve, for 00:15:14.430 --> 00:15:20.670 corn, would make exactly this type of outcome perfectly understandable? Not a 00:15:20.850 --> 00:15:24.055 secret or surprise, but perfectly understandable. 00:15:25.240 --> 00:15:29.560 Okay, that's the elasticity of demand. Next time we'll be taking up the 00:15:29.740 --> 00:15:33.440 elasticity of supply, and we'll be able to move through that material much quicker 00:15:33.620 --> 00:15:37.410 because it covers many similar concepts. Thanks. 00:15:39.432 --> 00:15:42.662 - If you want to test yourself, click Practice Questions 00:15:43.363 --> 00:15:46.728 or if you're ready to move on, just click Next Video.