0:00:09.404,0:00:13.250 - In our first lecture on the elasticity[br]of demand, we explain the intuitive 0:00:13.430,0:00:18.220 meaning of elasticity. It measures the[br]responsiveness of the quantity demanded to 0:00:18.400,0:00:22.006 a change in price. More responsive[br]means more elastic. 0:00:22.620,0:00:26.910 In this lecture, we're going to show how[br]to create a numeric measure of elasticity. 0:00:27.090,0:00:32.820 How to calculate with some data on prices[br]and quantities, what the elasticity is 0:00:33.000,0:00:34.817 over a range of the demand curve. 0:00:39.715,0:00:42.446 So here's a more precise definition[br]of elasticity. 0:00:42.446,0:00:47.920 The elasticity of demand is[br]the percentage change in quantity demanded 0:00:48.100,0:00:51.347 divided by the percentage change in price. 0:00:51.940,0:00:56.920 So let's write it like this. We have some[br]notation here. The elasticity demand is 0:00:57.100,0:01:03.890 equal to the percentage change in. Delta[br]is the symbol for change in, so this is 0:01:04.069,0:01:10.040 the percentage change in the quantity[br]demanded divided by the percentage change 0:01:10.220,0:01:16.720 in the price. That's the elasticity of[br]demand. Let's give an example or two. 0:01:16.900,0:01:22.670 So if the price of oil increases by 10%[br]and over a period of several years the 0:01:22.850,0:01:27.603 quantity demanded falls by 5%,[br]then the long run 0:01:27.603,0:01:31.221 elasticity of demand for oil is what? 0:01:32.710,0:01:39.440 Well, elasticity is the percentage change[br]and the quantity demanded. That's minus 5% 0:01:39.620,0:01:44.810 divided by the percentage change in the[br]price. That's 10%. So the elasticity of 0:01:44.990,0:01:51.247 demand is minus 5% divided by 10%, or[br]negative 0.5. 0:01:52.816,0:01:58.017 Elasticities of demand are always negative[br]because when price goes up, the quantity 0:01:58.017,0:02:02.266 demanded goes down. When price goes down,[br]the quantity demanded goes up. 0:02:02.850,0:02:06.679 So we often drop the negative sign and[br]write that the elasticity 0:02:06.679,0:02:09.638 of demand is 0.5. 0:02:11.353,0:02:17.870 Here's some more important notation. If[br]the absolute value of the elasticity of 0:02:18.050,0:02:23.300 demand is less than one, just like the[br]example we just gave for oil, we say that 0:02:23.480,0:02:28.576 the demand curve is inelastic. Elasticity[br]of demand less than one, 0:02:28.576,0:02:30.661 the demand curve is inelastic. 0:02:31.700,0:02:36.570 If the elasticity demand is greater than[br]one, we say the demand curve is elastic. 0:02:36.750,0:02:41.800 And if elasticity of demand is equal to[br]one, that is the knife point case, then 0:02:41.980,0:02:44.797 the demand curve is unit elastic. 0:02:45.570,0:02:49.460 These terms are going to come back, so[br]just keep them in mind. 0:02:49.640,0:02:53.482 Inelastic: less than one.[br]Elastic: greater than one. 0:02:53.482,0:02:58.692 So we know that elasticity is the[br]percentage change in quantity divided by 0:02:58.692,0:03:00.360 the percentage change in price, 0:03:00.360,0:03:02.906 how do we calculate the[br]percentage change in something? 0:03:03.640,0:03:06.470 This is not so hard, but it could be a[br]little bit tricky for the following 0:03:06.650,0:03:10.720 reason. Let's suppose you're driving down[br]the highway at 100 miles per hour. I don't 0:03:10.900,0:03:14.270 recommend this, but let's just imagine[br]that you are. You're going 100 miles per 0:03:14.450,0:03:21.090 hour, and now you increase speed by 50%.[br]How fast are you going? 150 miles per 0:03:21.090,0:03:26.172 hour, right? Okay, so now you're going 150[br]miles per hour. Suppose you decrease speed 0:03:26.172,0:03:32.538 by 50%. Now, how fast are you going? 75[br]miles per hour, right? So how is it that 0:03:32.538,0:03:36.635 you can increase speed by 50% and then[br]decrease by 50% 0:03:36.635,0:03:38.925 and not be back to where you started? 0:03:39.890,0:03:44.450 Well the answer is, is that intuitively we[br]have changed the base by which we are 0:03:44.630,0:03:51.160 calculating the percentage change. And we[br]don't want to have this inconsistency when 0:03:51.340,0:03:56.430 we calculate elasticity. We want people to[br]get the same elasticity whether they're 0:03:56.610,0:03:59.690 calculating from the lower base[br]or from the higher base. 0:03:59.870,0:04:04.610 So because of that, we're going to use the[br]Midpoint Formula. So the elasticity of 0:04:04.790,0:04:09.260 demand, percentage change in quantity[br]divided by the percentage change in price, 0:04:09.440,0:04:16.070 that's the change in quantity divided by[br]the average quantity times 100. That will 0:04:16.250,0:04:22.320 give us the percentage change divided by[br]the change in price divided by the average 0:04:22.500,0:04:26.280 price. Again, that times 100. Notice,[br]since we've actually got 100 on top and 0:04:26.460,0:04:30.093 100 on the bottom, those 100s we can[br]actually cancel out. 0:04:30.980,0:04:35.810 Let's expand this just a little bit more.[br]The change in quantity. What is the change 0:04:35.990,0:04:40.190 in quantity? Well, let's suppose we have[br]two quantities. Let's call them after and 0:04:40.370,0:04:44.330 before. It doesn't matter which one we[br]call after or which one before. So we're 0:04:44.510,0:04:50.930 going to then expand this to the change in[br]quantity. That's Q after minus Q before 0:04:51.110,0:04:57.230 divided by the average, Q after plus Q[br]before, divided by two, divided by the 0:04:57.410,0:05:03.150 change in price, P after minus P before,[br]divided by the average price, b after plus 0:05:03.330,0:05:05.115 b before, divide by two. 0:05:05.640,0:05:11.120 So that's a little bit of a mouthful, but[br]everything, I think, is fairly simple. 0:05:11.300,0:05:18.330 Just remember change in quantity divided[br]by the average quantity and you should 0:05:18.510,0:05:23.040 always be able to calculate this. Let's[br]give an example. 0:05:23.220,0:05:27.420 Okay, here's an example of a type of[br]problem you might see on a quiz or a mid 0:05:27.600,0:05:33.160 term. At the initial price of $10, the[br]quantity demanded is 100. When the price 0:05:33.340,0:05:40.550 rises to $20, the quantity demanded falls[br]to 90. What is the elasticity is, what is 0:05:40.730,0:05:43.335 the elasticity over this range of the[br]demand curve? 0:05:44.040,0:05:47.710 Well, we always want to begin by writing[br]down what we know, our formula. The 0:05:47.890,0:05:50.880 elasticity of demand is the percentage[br]change in quantity divided by the 0:05:51.060,0:05:55.460 percentage change in price. Now, let's[br]remember to just expand that. That's Delta 0:05:55.640,0:06:00.600 Q over the average Q all divided by Delta[br]P over the average P. 0:06:01.040,0:06:08.620 Now, we just start to fill things in. So[br]our quantity after, okay, after the change 0:06:08.800,0:06:16.860 is 90. Our quantity before that was 100.[br]So on the top, the percentage change in 0:06:17.040,0:06:21.640 quantity is 90 minus 100 divided by 90[br]plus 100, over two. That is the average 0:06:21.820,0:06:28.260 quantity. And then on the bottom, and the[br]only trick here is always write it in the 0:06:28.440,0:06:33.680 same order, so if you put the 90 here,[br]then make sure you put the 20, the number 0:06:33.860,0:06:38.180 the price which is associated with that[br]quantity started off, the same way. So 0:06:38.360,0:06:39.996 always just keep it in the same order. 0:06:40.610,0:06:45.090 So on the bottom, then, we have the[br]quantity, the price after, which is 20 0:06:45.270,0:06:49.430 minus the price before, which is 10,[br]divided by the average price. And now, 0:06:49.610,0:06:55.400 just, it's numerics. You plug in the[br]numbers and what you get is the elasticity 0:06:55.580,0:07:01.520 of demand is equal to negative 0.158,[br]approximately. We can always drop the 0:07:01.700,0:07:04.510 negative sign because these things,[br]elasticity of demands, are always 0:07:04.690,0:07:11.720 negative. So it's equal to 0.158. So does[br]this make the elasticity of demand over 0:07:11.900,0:07:19.940 this range elastic or inelastic?[br]Inelastic, right? The elasticity of demand 0:07:20.120,0:07:24.448 we've just calculated as less than one, so[br]that makes this one inelastic. 0:07:24.448,0:07:26.121 There you go. 0:07:27.030,0:07:31.070 We need to cover one more important point[br]about the elasticity of demand, and that 0:07:31.250,0:07:37.410 is its relationship to total revenue. So a[br]firms revenues are very simply equal to 0:07:37.590,0:07:42.860 price times quantity sold. Revenue is[br]equal to price times quantity. 0:07:43.040,0:07:47.270 Now, elasticity, it's all about the[br]relationship between price and quantity, 0:07:47.450,0:07:52.800 and so it's also going to have[br]implications for revenue. Let's give some 0:07:52.980,0:07:57.460 intuition for the relationship between the[br]elasticity and total revenue. So revenue 0:07:57.640,0:07:59.324 is price times quantity. 0:07:59.324,0:08:04.940 Now suppose the price goes up by a lot and[br]then quantity demanded goes down, just by 0:08:05.120,0:08:10.310 a little bit. What then is going to be the[br]responsive revenue? Well, if price is 0:08:10.490,0:08:15.260 going up by a lot and quantity is going[br]down just by a little bit, then revenue is 0:08:15.440,0:08:20.900 also going to be going up. Now, what kind[br]of demand curve do we call that, when 0:08:21.080,0:08:27.810 price goes up by a lot and quantity falls[br]by just a little bit? We call that an 0:08:27.990,0:08:30.003 inelastic demand curve. 0:08:30.810,0:08:34.650 So what this little thought experiment[br]tells us is that when you have an 0:08:34.830,0:08:42.230 inelastic demand curve, when price goes up[br]revenue is also going to go up, and of 0:08:42.409,0:08:45.990 course, vice versa. Let's take a look at[br]this with a graph. 0:08:46.170,0:08:51.630 So here's our initial demand curve, a very[br]inelastic demand curve, at a price of $10 0:08:51.810,0:08:57.640 that quantity demanded is 100 units, so[br]revenue is 1,000. Notice that we can show 0:08:57.820,0:09:02.370 revenue in the graph by price times[br]quantity. Now, just looking at the graph, 0:09:02.550,0:09:07.860 look at what happens when the price goes[br]up to 20. Well, the quantity goes down by 0:09:08.040,0:09:12.998 just a little bit, in this case to 90, but[br]revenues go up to 1,800. 0:09:13.610,0:09:21.460 So you can just see, by sketching the[br]little graph, what happens to revenues 0:09:21.640,0:09:25.770 when price goes up when you have an[br]inelastic demand curve. And again, vice 0:09:25.950,0:09:30.240 versa. Let's take a look about what[br]happens when you have an elastic demand 0:09:30.420,0:09:35.170 curve. So let's do the same kind of little[br]thought experiment, revenue is price times 0:09:35.350,0:09:41.110 quantity. Suppose price goes up by a[br]modest amount and quantity goes down by a 0:09:41.290,0:09:45.690 lot. Well, if price is going up by a[br]little bit and quantity is going down by a 0:09:45.870,0:09:51.990 lot, then revenue must also be falling.[br]And what type of demand curve is it when 0:09:52.170,0:09:55.870 price goes up by a little bit, quantity[br]falls by a lot? What type of demand curve 0:09:56.050,0:09:59.175 is that? That's an elastic demand curve. 0:09:59.790,0:10:05.660 So revenues fall as price rises with an[br]elastic demand curve. And again, let's 0:10:05.840,0:10:10.963 show that. If you're ever confused and you[br]can't quite remember, just draw the graph. 0:10:10.963,0:10:16.070 I can never remember, myself, but I always[br]draw these little graphs. So draw a really 0:10:16.250,0:10:22.781 flatter, elastic demand curve. In this[br]case, at a price of $10, the quantity 0:10:22.781,0:10:29.754 demanded is 250 units. So revenues is[br]2,500. And see what happens, when price 0:10:29.754,0:10:35.552 goes up, price goes up to $20, quantity[br]demanded falls to 50, 0:10:35.552,0:10:37.642 so revenue falls to 1,000. 0:10:38.025,0:10:44.089 And again, you can just compare the sizes[br]of these revenue rectangles to see which 0:10:44.089,0:10:50.147 way the relationship goes. And of course[br]this also implies, going from $20, the 0:10:50.147,0:10:56.725 price of $20 to the price of $10, revenues[br]increase. So with an elastic demand curve, 0:10:56.725,0:11:00.250 when price goes down revenues go up. 0:11:01.296,0:11:04.866 So here's a summary of these[br]relationships. When the elasticity of 0:11:04.866,0:11:08.862 demand is less than one, that's an[br]inelastic demand curve and price and 0:11:08.862,0:11:11.901 revenue move together. When one goes up[br]the other goes up. 0:11:11.901,0:11:13.484 When one goes down, the other goes down. 0:11:13.484,0:11:18.796 If the elasticity demand is greater than[br]one, that's an elastic demand curve and 0:11:18.796,0:11:23.366 price and revenue move in opposite[br]directions. And could you guess what 0:11:23.366,0:11:27.833 happens if the elasticity demand is equal[br]to one, if you have a unit elastic curve? 0:11:27.833,0:11:31.986 Well then, when the price changes,[br]revenue stays the same. 0:11:32.676,0:11:38.550 Now, if you have to, again, memorize[br]these, but it's really much better to just 0:11:38.550,0:11:42.666 sketch some graphs. I never remember them,[br]as I've said myself, I never remember 0:11:42.666,0:11:46.987 these relationships, but I can always[br]sketch an inelastic graph and then with a 0:11:46.987,0:11:51.767 few changes in price I can see whether the[br]revenue rectangles are getting bigger or 0:11:51.767,0:11:57.907 smaller and so I'll be able to recompute[br]all of these relationships pretty easily. 0:11:59.330,0:12:03.210 Here's a quick practice question. The[br]elasticity of demand for eggs has been 0:12:03.390,0:12:09.280 estimated to be 0.1. If egg producers[br]raise their prices by 10%, what will 0:12:09.460,0:12:16.060 happen to their total revenues? Increase?[br]Decrease? Or it won't change? 0:12:16.240,0:12:21.980 Okay, how should we approach this problem?[br]If the elasticity of demand is 0.1, what 0:12:22.160,0:12:29.280 type of demand curve? Inelastic demand.[br]Now, what's the relationship between an 0:12:29.460,0:12:34.780 inelastic demand curve? When price goes[br]up, what happens to revenue? If you're not 0:12:34.960,0:12:38.116 sure, if you don't remember, draw some[br]graphs. Draw an inelastic, 0:12:38.116,0:12:39.853 draw an elastic, figure it out. 0:12:40.530,0:12:45.870 Okay, let's see. What happens? Revenue[br]increases, right? If you have an inelastic 0:12:46.050,0:12:50.650 demand curve and price goes up revenue[br]goes up as well. 0:12:50.830,0:12:57.300 Here's an application. Why is the war on[br]drugs so hard to win? Well, drugs are 0:12:57.480,0:13:04.460 typically going to have a fairly inelastic[br]demand curve. What that means is that when 0:13:04.640,0:13:09.510 enforcement actions raise the price of[br]drugs, make it more costly to get drugs, 0:13:09.690,0:13:15.520 raising the price, that means the total[br]revenue for the drug dealers goes up. So 0:13:15.700,0:13:19.830 check out this graph. Here is the price[br]with no prohibition, here's our demand 0:13:20.010,0:13:21.871 curve, our inelastic demand curve. 0:13:22.350,0:13:27.140 What prohibition does, is it raises the[br]cost of supplying the good. But that 0:13:27.320,0:13:31.830 raises the price, which is what it's[br]supposed to do, and that does reduce the 0:13:32.010,0:13:37.580 quantity demanded of the drug. But it also[br]has the effect of increasing seller 0:13:37.760,0:13:43.300 revenues. And seller revenues may be where[br]many of the problems of drug prohibition 0:13:43.480,0:13:49.910 come from. It's the seller revenues which[br]drive the violence, which drive the gun, 0:13:50.090,0:13:55.290 which make it look good to be a drug[br]dealer, which encourage people to become 0:13:55.470,0:13:57.260 drug dealers, and so forth. 0:13:57.670,0:14:02.360 So there's a real difficulty with[br]prohibition, with prohibiting a good, 0:14:02.540,0:14:05.416 especially when it has an[br]inelastic demand. 0:14:06.000,0:14:09.760 Here's another application of elasticity[br]of demand and how it can be used to 0:14:09.940,0:14:14.732 understand our world. This is a quotation[br]from 2012 from 0:14:14.732,0:14:16.635 NPRs food blog "The Salt." 0:14:17.600,0:14:21.910 "You've all heard a lot about this year's[br]devastating drought in the Midwest, right? 0:14:22.090,0:14:26.270 US Department of Agriculture announced[br]last Friday that the average US cornfield 0:14:26.450,0:14:33.290 this year will yield less per acre than it[br]has since 1995. Soybean yields are down, 0:14:33.470,0:14:38.970 too. So you think that farmers who grow[br]these crops must be really hurting. And 0:14:39.150,0:14:44.900 that's certainly the impression you get[br]from media reports. But how's this, for a 0:14:45.080,0:14:50.780 surprising fact? On average, corn growers[br]actually will rake in a record amount of 0:14:50.960,0:14:53.777 cash from their harvest this year." 0:14:54.500,0:15:00.370 So can you explain this secret side of the[br]drought? I'm not going to answer this 0:15:00.550,0:15:05.700 question. This is exactly the type of[br]question you might receive on an exam. But 0:15:05.880,0:15:09.260 you should be able to answer it by now,[br]with a few sketches on a piece of paper. 0:15:09.440,0:15:14.250 And in particular, what I want you to[br]answer is, what type of demand curve, for 0:15:14.430,0:15:20.670 corn, would make exactly this type of[br]outcome perfectly understandable? Not a 0:15:20.850,0:15:24.055 secret or surprise, but perfectly[br]understandable. 0:15:25.240,0:15:29.560 Okay, that's the elasticity of demand.[br]Next time we'll be taking up the 0:15:29.740,0:15:33.440 elasticity of supply, and we'll be able to[br]move through that material much quicker 0:15:33.620,0:15:37.410 because it covers many similar concepts.[br]Thanks. 0:15:39.432,0:15:42.662 - If you want to test yourself, click[br]Practice Questions 0:15:43.363,0:15:46.728 or if you're ready to move on,[br]just click Next Video.