1 00:00:09,404 --> 00:00:13,250 - In our first lecture on the elasticity of demand, we explain the intuitive 2 00:00:13,430 --> 00:00:18,220 meaning of elasticity. It measures the responsiveness of the quantity demanded to 3 00:00:18,400 --> 00:00:22,006 a change in price. More responsive means more elastic. 4 00:00:22,620 --> 00:00:26,910 In this lecture, we're going to show how to create a numeric measure of elasticity. 5 00:00:27,090 --> 00:00:32,820 How to calculate with some data on prices and quantities, what the elasticity is 6 00:00:33,000 --> 00:00:34,817 over a range of the demand curve. 7 00:00:39,715 --> 00:00:42,446 So here's a more precise definition of elasticity. 8 00:00:42,446 --> 00:00:47,920 The elasticity of demand is the percentage change in quantity demanded 9 00:00:48,100 --> 00:00:51,347 divided by the percentage change in price. 10 00:00:51,940 --> 00:00:56,920 So let's write it like this. We have some notation here. The elasticity demand is 11 00:00:57,100 --> 00:01:03,890 equal to the percentage change in. Delta is the symbol for change in, so this is 12 00:01:04,069 --> 00:01:10,040 the percentage change in the quantity demanded divided by the percentage change 13 00:01:10,220 --> 00:01:16,720 in the price. That's the elasticity of demand. Let's give an example or two. 14 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 15 00:01:22,850 --> 00:01:27,603 quantity demanded falls by 5%, then the long run 16 00:01:27,603 --> 00:01:31,221 elasticity of demand for oil is what? 17 00:01:32,710 --> 00:01:39,440 Well, elasticity is the percentage change and the quantity demanded. That's minus 5% 18 00:01:39,620 --> 00:01:44,810 divided by the percentage change in the price. That's 10%. So the elasticity of 19 00:01:44,990 --> 00:01:51,247 demand is minus 5% divided by 10%, or negative 0.5. 20 00:01:52,816 --> 00:01:58,017 Elasticities of demand are always negative because when price goes up, the quantity 21 00:01:58,017 --> 00:02:02,266 demanded goes down. When price goes down, the quantity demanded goes up. 22 00:02:02,850 --> 00:02:06,679 So we often drop the negative sign and write that the elasticity 23 00:02:06,679 --> 00:02:09,638 of demand is 0.5. 24 00:02:11,353 --> 00:02:17,870 Here's some more important notation. If the absolute value of the elasticity of 25 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 26 00:02:23,480 --> 00:02:28,576 the demand curve is inelastic. Elasticity of demand less than one, 27 00:02:28,576 --> 00:02:30,661 the demand curve is inelastic. 28 00:02:31,700 --> 00:02:36,570 If the elasticity demand is greater than one, we say the demand curve is elastic. 29 00:02:36,750 --> 00:02:41,800 And if elasticity of demand is equal to one, that is the knife point case, then 30 00:02:41,980 --> 00:02:44,797 the demand curve is unit elastic. 31 00:02:45,570 --> 00:02:49,460 These terms are going to come back, so just keep them in mind. 32 00:02:49,640 --> 00:02:53,482 Inelastic: less than one. Elastic: greater than one. 33 00:02:53,482 --> 00:02:58,692 So we know that elasticity is the percentage change in quantity divided by 34 00:02:58,692 --> 00:03:00,360 the percentage change in price, 35 00:03:00,360 --> 00:03:02,906 how do we calculate the percentage change in something? 36 00:03:03,640 --> 00:03:06,470 This is not so hard, but it could be a little bit tricky for the following 37 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 38 00:03:10,900 --> 00:03:14,270 recommend this, but let's just imagine that you are. You're going 100 miles per 39 00:03:14,450 --> 00:03:21,090 hour, and now you increase speed by 50%. How fast are you going? 150 miles per 40 00:03:21,090 --> 00:03:26,172 hour, right? Okay, so now you're going 150 miles per hour. Suppose you decrease speed 41 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 42 00:03:32,538 --> 00:03:36,635 you can increase speed by 50% and then decrease by 50% 43 00:03:36,635 --> 00:03:38,925 and not be back to where you started? 44 00:03:39,890 --> 00:03:44,450 Well the answer is, is that intuitively we have changed the base by which we are 45 00:03:44,630 --> 00:03:51,160 calculating the percentage change. And we don't want to have this inconsistency when 46 00:03:51,340 --> 00:03:56,430 we calculate elasticity. We want people to get the same elasticity whether they're 47 00:03:56,610 --> 00:03:59,690 calculating from the lower base or from the higher base. 48 00:03:59,870 --> 00:04:04,610 So because of that, we're going to use the Midpoint Formula. So the elasticity of 49 00:04:04,790 --> 00:04:09,260 demand, percentage change in quantity divided by the percentage change in price, 50 00:04:09,440 --> 00:04:16,070 that's the change in quantity divided by the average quantity times 100. That will 51 00:04:16,250 --> 00:04:22,320 give us the percentage change divided by the change in price divided by the average 52 00:04:22,500 --> 00:04:26,280 price. Again, that times 100. Notice, since we've actually got 100 on top and 53 00:04:26,460 --> 00:04:30,093 100 on the bottom, those 100s we can actually cancel out. 54 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 55 00:04:35,990 --> 00:04:40,190 in quantity? Well, let's suppose we have two quantities. Let's call them after and 56 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 57 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 58 00:04:51,110 --> 00:04:57,230 divided by the average, Q after plus Q before, divided by two, divided by the 59 00:04:57,410 --> 00:05:03,150 change in price, P after minus P before, divided by the average price, b after plus 60 00:05:03,330 --> 00:05:05,115 b before, divide by two. 61 00:05:05,640 --> 00:05:11,120 So that's a little bit of a mouthful, but everything, I think, is fairly simple. 62 00:05:11,300 --> 00:05:18,330 Just remember change in quantity divided by the average quantity and you should 63 00:05:18,510 --> 00:05:23,040 always be able to calculate this. Let's give an example. 64 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 65 00:05:27,600 --> 00:05:33,160 term. At the initial price of $10, the quantity demanded is 100. When the price 66 00:05:33,340 --> 00:05:40,550 rises to $20, the quantity demanded falls to 90. What is the elasticity is, what is 67 00:05:40,730 --> 00:05:43,335 the elasticity over this range of the demand curve? 68 00:05:44,040 --> 00:05:47,710 Well, we always want to begin by writing down what we know, our formula. The 69 00:05:47,890 --> 00:05:50,880 elasticity of demand is the percentage change in quantity divided by the 70 00:05:51,060 --> 00:05:55,460 percentage change in price. Now, let's remember to just expand that. That's Delta 71 00:05:55,640 --> 00:06:00,600 Q over the average Q all divided by Delta P over the average P. 72 00:06:01,040 --> 00:06:08,620 Now, we just start to fill things in. So our quantity after, okay, after the change 73 00:06:08,800 --> 00:06:16,860 is 90. Our quantity before that was 100. So on the top, the percentage change in 74 00:06:17,040 --> 00:06:21,640 quantity is 90 minus 100 divided by 90 plus 100, over two. That is the average 75 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 76 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 77 00:06:33,860 --> 00:06:38,180 the price which is associated with that quantity started off, the same way. So 78 00:06:38,360 --> 00:06:39,996 always just keep it in the same order. 79 00:06:40,610 --> 00:06:45,090 So on the bottom, then, we have the quantity, the price after, which is 20 80 00:06:45,270 --> 00:06:49,430 minus the price before, which is 10, divided by the average price. And now, 81 00:06:49,610 --> 00:06:55,400 just, it's numerics. You plug in the numbers and what you get is the elasticity 82 00:06:55,580 --> 00:07:01,520 of demand is equal to negative 0.158, approximately. We can always drop the 83 00:07:01,700 --> 00:07:04,510 negative sign because these things, elasticity of demands, are always 84 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 85 00:07:11,900 --> 00:07:19,940 this range elastic or inelastic? Inelastic, right? The elasticity of demand 86 00:07:20,120 --> 00:07:24,448 we've just calculated as less than one, so that makes this one inelastic. 87 00:07:24,448 --> 00:07:26,121 There you go. 88 00:07:27,030 --> 00:07:31,070 We need to cover one more important point about the elasticity of demand, and that 89 00:07:31,250 --> 00:07:37,410 is its relationship to total revenue. So a firms revenues are very simply equal to 90 00:07:37,590 --> 00:07:42,860 price times quantity sold. Revenue is equal to price times quantity. 91 00:07:43,040 --> 00:07:47,270 Now, elasticity, it's all about the relationship between price and quantity, 92 00:07:47,450 --> 00:07:52,800 and so it's also going to have implications for revenue. Let's give some 93 00:07:52,980 --> 00:07:57,460 intuition for the relationship between the elasticity and total revenue. So revenue 94 00:07:57,640 --> 00:07:59,324 is price times quantity. 95 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 96 00:08:05,120 --> 00:08:10,310 a little bit. What then is going to be the responsive revenue? Well, if price is 97 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 98 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 99 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 100 00:08:27,990 --> 00:08:30,003 inelastic demand curve. 101 00:08:30,810 --> 00:08:34,650 So what this little thought experiment tells us is that when you have an 102 00:08:34,830 --> 00:08:42,230 inelastic demand curve, when price goes up revenue is also going to go up, and of 103 00:08:42,409 --> 00:08:45,990 course, vice versa. Let's take a look at this with a graph. 104 00:08:46,170 --> 00:08:51,630 So here's our initial demand curve, a very inelastic demand curve, at a price of $10 105 00:08:51,810 --> 00:08:57,640 that quantity demanded is 100 units, so revenue is 1,000. Notice that we can show 106 00:08:57,820 --> 00:09:02,370 revenue in the graph by price times quantity. Now, just looking at the graph, 107 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 108 00:09:08,040 --> 00:09:12,998 just a little bit, in this case to 90, but revenues go up to 1,800. 109 00:09:13,610 --> 00:09:21,460 So you can just see, by sketching the little graph, what happens to revenues 110 00:09:21,640 --> 00:09:25,770 when price goes up when you have an inelastic demand curve. And again, vice 111 00:09:25,950 --> 00:09:30,240 versa. Let's take a look about what happens when you have an elastic demand 112 00:09:30,420 --> 00:09:35,170 curve. So let's do the same kind of little thought experiment, revenue is price times 113 00:09:35,350 --> 00:09:41,110 quantity. Suppose price goes up by a modest amount and quantity goes down by a 114 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 115 00:09:45,870 --> 00:09:51,990 lot, then revenue must also be falling. And what type of demand curve is it when 116 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 117 00:09:56,050 --> 00:09:59,175 is that? That's an elastic demand curve. 118 00:09:59,790 --> 00:10:05,660 So revenues fall as price rises with an elastic demand curve. And again, let's 119 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. 120 00:10:10,963 --> 00:10:16,070 I can never remember, myself, but I always draw these little graphs. So draw a really 121 00:10:16,250 --> 00:10:22,781 flatter, elastic demand curve. In this case, at a price of $10, the quantity 122 00:10:22,781 --> 00:10:29,754 demanded is 250 units. So revenues is 2,500. And see what happens, when price 123 00:10:29,754 --> 00:10:35,552 goes up, price goes up to $20, quantity demanded falls to 50, 124 00:10:35,552 --> 00:10:37,642 so revenue falls to 1,000. 125 00:10:38,025 --> 00:10:44,089 And again, you can just compare the sizes of these revenue rectangles to see which 126 00:10:44,089 --> 00:10:50,147 way the relationship goes. And of course this also implies, going from $20, the 127 00:10:50,147 --> 00:10:56,725 price of $20 to the price of $10, revenues increase. So with an elastic demand curve, 128 00:10:56,725 --> 00:11:00,250 when price goes down revenues go up. 129 00:11:01,296 --> 00:11:04,866 So here's a summary of these relationships. When the elasticity of 130 00:11:04,866 --> 00:11:08,862 demand is less than one, that's an inelastic demand curve and price and 131 00:11:08,862 --> 00:11:11,901 revenue move together. When one goes up the other goes up. 132 00:11:11,901 --> 00:11:13,484 When one goes down, the other goes down. 133 00:11:13,484 --> 00:11:18,796 If the elasticity demand is greater than one, that's an elastic demand curve and 134 00:11:18,796 --> 00:11:23,366 price and revenue move in opposite directions. And could you guess what 135 00:11:23,366 --> 00:11:27,833 happens if the elasticity demand is equal to one, if you have a unit elastic curve? 136 00:11:27,833 --> 00:11:31,986 Well then, when the price changes, revenue stays the same. 137 00:11:32,676 --> 00:11:38,550 Now, if you have to, again, memorize these, but it's really much better to just 138 00:11:38,550 --> 00:11:42,666 sketch some graphs. I never remember them, as I've said myself, I never remember 139 00:11:42,666 --> 00:11:46,987 these relationships, but I can always sketch an inelastic graph and then with a 140 00:11:46,987 --> 00:11:51,767 few changes in price I can see whether the revenue rectangles are getting bigger or 141 00:11:51,767 --> 00:11:57,907 smaller and so I'll be able to recompute all of these relationships pretty easily. 142 00:11:59,330 --> 00:12:03,210 Here's a quick practice question. The elasticity of demand for eggs has been 143 00:12:03,390 --> 00:12:09,280 estimated to be 0.1. If egg producers raise their prices by 10%, what will 144 00:12:09,460 --> 00:12:16,060 happen to their total revenues? Increase? Decrease? Or it won't change? 145 00:12:16,240 --> 00:12:21,980 Okay, how should we approach this problem? If the elasticity of demand is 0.1, what 146 00:12:22,160 --> 00:12:29,280 type of demand curve? Inelastic demand. Now, what's the relationship between an 147 00:12:29,460 --> 00:12:34,780 inelastic demand curve? When price goes up, what happens to revenue? If you're not 148 00:12:34,960 --> 00:12:38,116 sure, if you don't remember, draw some graphs. Draw an inelastic, 149 00:12:38,116 --> 00:12:39,853 draw an elastic, figure it out. 150 00:12:40,530 --> 00:12:45,870 Okay, let's see. What happens? Revenue increases, right? If you have an inelastic 151 00:12:46,050 --> 00:12:50,650 demand curve and price goes up revenue goes up as well. 152 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 153 00:12:57,480 --> 00:13:04,460 typically going to have a fairly inelastic demand curve. What that means is that when 154 00:13:04,640 --> 00:13:09,510 enforcement actions raise the price of drugs, make it more costly to get drugs, 155 00:13:09,690 --> 00:13:15,520 raising the price, that means the total revenue for the drug dealers goes up. So 156 00:13:15,700 --> 00:13:19,830 check out this graph. Here is the price with no prohibition, here's our demand 157 00:13:20,010 --> 00:13:21,871 curve, our inelastic demand curve. 158 00:13:22,350 --> 00:13:27,140 What prohibition does, is it raises the cost of supplying the good. But that 159 00:13:27,320 --> 00:13:31,830 raises the price, which is what it's supposed to do, and that does reduce the 160 00:13:32,010 --> 00:13:37,580 quantity demanded of the drug. But it also has the effect of increasing seller 161 00:13:37,760 --> 00:13:43,300 revenues. And seller revenues may be where many of the problems of drug prohibition 162 00:13:43,480 --> 00:13:49,910 come from. It's the seller revenues which drive the violence, which drive the gun, 163 00:13:50,090 --> 00:13:55,290 which make it look good to be a drug dealer, which encourage people to become 164 00:13:55,470 --> 00:13:57,260 drug dealers, and so forth. 165 00:13:57,670 --> 00:14:02,360 So there's a real difficulty with prohibition, with prohibiting a good, 166 00:14:02,540 --> 00:14:05,416 especially when it has an inelastic demand. 167 00:14:06,000 --> 00:14:09,760 Here's another application of elasticity of demand and how it can be used to 168 00:14:09,940 --> 00:14:14,732 understand our world. This is a quotation from 2012 from 169 00:14:14,732 --> 00:14:16,635 NPRs food blog "The Salt." 170 00:14:17,600 --> 00:14:21,910 "You've all heard a lot about this year's devastating drought in the Midwest, right? 171 00:14:22,090 --> 00:14:26,270 US Department of Agriculture announced last Friday that the average US cornfield 172 00:14:26,450 --> 00:14:33,290 this year will yield less per acre than it has since 1995. Soybean yields are down, 173 00:14:33,470 --> 00:14:38,970 too. So you think that farmers who grow these crops must be really hurting. And 174 00:14:39,150 --> 00:14:44,900 that's certainly the impression you get from media reports. But how's this, for a 175 00:14:45,080 --> 00:14:50,780 surprising fact? On average, corn growers actually will rake in a record amount of 176 00:14:50,960 --> 00:14:53,777 cash from their harvest this year." 177 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 178 00:15:00,550 --> 00:15:05,700 question. This is exactly the type of question you might receive on an exam. But 179 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. 180 00:15:09,440 --> 00:15:14,250 And in particular, what I want you to answer is, what type of demand curve, for 181 00:15:14,430 --> 00:15:20,670 corn, would make exactly this type of outcome perfectly understandable? Not a 182 00:15:20,850 --> 00:15:24,055 secret or surprise, but perfectly understandable. 183 00:15:25,240 --> 00:15:29,560 Okay, that's the elasticity of demand. Next time we'll be taking up the 184 00:15:29,740 --> 00:15:33,440 elasticity of supply, and we'll be able to move through that material much quicker 185 00:15:33,620 --> 00:15:37,410 because it covers many similar concepts. Thanks. 186 00:15:39,432 --> 00:15:42,662 - If you want to test yourself, click Practice Questions 187 00:15:43,363 --> 00:15:46,728 or if you're ready to move on, just click Next Video.