Transcription
How's it class? So today, we are doing chapter 19. Chapter 19 has to do with the concept of elasticity. The first type of elasticity we're going to be dealing with is price elasticity of demand, and the symbol we'll be using for that is E for the concept of elasticity and P for price. So, EP. So, the responsiveness of quantity demanded of a commodity to changes in its price. And essentially, it's defined as the percentage change in the quantity demanded divided by the percentage change in price. So, here we see this formula: EP equals percentage change in quantity demanded over the percentage change in price. Keep in mind, let's see, that when we're talking about quantity demanded, that is your dependent variable, and then price, that's going to be your independent variable. Okay? So, we're looking at the change in quantity demanded with respect to our independent variable, change in price.
So, the thing about this concept of elasticity, everywhere you see this concept of elasticity, you should just be kind of thinking of this word: responsiveness. How does something respond?
So, for thinking elasticity equals responsiveness, let's have a general look in terms of how it would be graphically. So, if we're talking about price elasticity, the one that we just introduced, we're looking at price and quantity. And essentially, the varying responsiveness has to do with this demand curve and sort of this slope of the demand curve. In other words, remember our independent variable, price, can change. And so, let's say we have P1, and then the price goes down to P2. And with P1, we have associated Q1, and with P2, we have associated Q2. So, as price changes, how much does quantity demanded change? So, we can see various levels of responsiveness based on the slope of this demand curve. If we have something like that where we have a small change in price from P1 to P2, based on this really gentle slope, I exaggerate, it's obviously not perfectly drawn to scale, but we can see Q1 to Q2. Relative to this small change, we have a large change, a high responsiveness, a high level of elasticity. On the other hand, if we have another diagram with a different slope, a very steep slope, negative slope, such as this, where we can have a very big change in price, but based on the slope of the demand curve, a relatively small change or small elasticity in terms of quantity change. So, this is a big change in price with a small response. So, that would be a more inelastic demand curve. So, that's this concept of elasticity. So, that's the price elasticity. And so, this price elasticity would be looking at a demand curve that might be like D1, that might be like D2, that might be like D3. So, different elasticities.
But we're also going to see a different type of elasticity that is not just the shape, happens to do the shape of the demand curve, but how responsive something changes, for example, to a non-price determinant such as income. So, you're going to see something called income elasticity that uses this symbol right here. And instead of this situation like this, where we have varying degrees of slopes, it'll look more something like this, where, for example, we're going to hold price constant, and then we're going to see Q1. And then if, for example, if someone's income changes quite a bit, then the demand for a product might increase significantly or a little. Or it actually might go this way if it's an inferior good. So, these are the different types of elasticities that we're going to be looking at on the demand side. We're going to be looking at the various price elasticities. Oops, not going to go backwards like this one, sorry. Or like the one we see right above.
Now, going back to the price elasticity, it's always going to be negative. Increases in price decrease the quantity demanded, ceteris paribus. And oftentimes, the minus sign is ignored when you calculate it. It can be there, but oftentimes you're going to see in the textbook and the homework problems, it's just an implied negativity that we sometimes leave out the sign. I'm not a big fan of that, I prefer to have the sign in, but the textbook and many textbooks tend to just overlook it, assuming that you know that there's a negative relationship between price and quantity demanded.
So, here's the elasticity formula. This is called the midpoint method. And we're looking at the change in quantity with respect to the average of the two quantities in question, divided by the change in price with respect to the average of the prices in question.
So, actually, I tend to write it like this. So, I'll write Q2 minus Q1 over Q1 plus Q2 over 2, all over P2. I'm going to run out of space. Minus P1 over P1 plus P2 over 2. So, essentially, that's what the above formula looks like when I write it out, for example, if I was doing something on the board.
So, an example for the price elasticity of demand for oranges. We have two different quantities in 2006, 2007, dollar 56.91 a pound. Total of quantity orange consumed declined. What is the price elasticity of demand? So, using that formula. Okay, so now you have the amounts, the quantities, and the respective prices. Plug it in. You got 0.85. So, that 0.85 what you calculated is a percentage. So, when you calculated this 0.85, it's always squashed the result is always squashed into this format of an answer. So, what's implied is a one percent increase in price generated, and this is what you calculated, a 0.85 decrease in the quantity demanded of oranges. So, if you calculated a 1.85 up above, it would be a one increase in price generated a 1.85 percent decrease in the quantity demanded of oranges. And whenever you calculate the elasticity just straight up as we just did, then that is the interpretation. It's a one percent increase relative to whatever you calculated, or one percent decrease, whichever way the change occurred.
So, talking about our price elasticity ranges. There's an elastic demand where percentage change in the quantity demanded is larger than the percentage change in price. So, that means the total expenditures in price are inversely related in the elastic region of the demand curve. And essentially, you calculated a price elasticity that's going to be greater than one if you are elastic. Anything greater than one deems an elastic demand.
Now, there's also an area on the demand curve that's a unit elasticity of demand. That's a percentage change in quantity demanded is equal to the percentage change in price. And so, that's EP is equal to one. So, not greater than one, but equal to one. So, when you calculate one, that's saying a one percent increase in price led to a one percent decrease in quantity demanded. And then likewise, there's an inelastic demand, and that's when percentage change in quantity demanded is smaller than the percentage change in price. So, if you have an EP is less than one, then, so if you had 0.85, then a one increase in price yielded a 0.85 percent decrease in quantity demanded. So, there was a lack of response to that price change. And there was. So, every time you think of this word elasticity, just swap it out with the word responsiveness. That will probably help with the understanding of that concept. So, here we have a basic summary of what we just looked at for price elasticity ranges.
Now, there's extreme elasticities. We have perfectly inelastic demand. Perfectly inelastic means there's no response. Remember elasticity, responsiveness. So, inelastic means there's no response to a price change. A demand curve that is a vertical line. It has only one quantity demanded for each price. No matter what the price, quantity demanded does not change. And a demand that it exhibits zero responsiveness to price changes. So, here we have a zero elasticity. Price may jump by a thousand percent, quantity demanded will not respond. It's inelastic. It'll stay at what we see here is eight.
On the other hand, there's a perfectly elastic demand curve. A demand curve that is a horizontal line. It has only one price for every quantity. The slightest increase in price leads to zero quantity demanded. When price goes up, consumers don't like that. They can completely respond to that price increase and purchase nothing. And there we have a perfectly elastic or infinitely elastic demand curve, perfectly horizontal.
So, the policy example. What we may ask is, who pays higher taxes? Whether it be the households or the firms? Well, the answer is, who pays it depends on the elasticity or the slope of the curves, whether it be supply curve or demand curve. So, here I attempted to draw a demand curve with a pretty steep negative slope, so relatively inelastic demand curve. And here we'll have a supply curve that looks to be about a 45. I tried to make it a 45-degree line. So, here we have a situation. So, let's just say that a tax is imposed. And from the last chapter, we know that essentially it will reduce quantity. Now, I'm not going to talk about who is who is the tax imposed upon and which curve shifts. Let's just look at that new situation here where we have, kind of hard to see, but if you can kind of look at who has the bigger space between the original equilibrium price. Here we have a situation above the equilibrium price that is smaller. That is larger than this smaller range here. This point here, smaller versus this area up here, which is larger. So, this was the inelastic, the inability to respond. So, this inelastic, steeper curve, the lack of ability to respond to the tax situation means that the consumers, the households, will pay a greater portion of the tax. So, here this is the greater portion. I'll just use the word G, letter G for greater, and L for the lesser portion of the tax paid by the suppliers, the firms. So, the firms pay less, the consumers pay more. Here I drew another situation where we have the firms, the supply curve is inelastic, very steep, and the demand curve is elastic, not very steep. So, they have the ability to respond. And so, going from Q1 down to Q2 due to a tax, here you can see that, I hope you can see that, this distance here, which is the portion paid by the suppliers, is greater than this portion here, which is the portion paid by the consumers. So, again, who pays the higher taxes? It depends on the elasticity of the curves.
Now, we're also going to be looking at the concept of elasticity and how it relates to this concept of total revenues. Now, if you recall, total revenues, oh, we haven't really talked about it too much, actually. Total revenues is simply price times quantity. So, TR is going to equal to total revenues, and it's going to be price times quantity. So, when demand is elastic, a negative relationship exists between changes in price and changes in total revenues. When demand is unit elastic, changes in price do not change total revenues. And when demand is inelastic, a positive relationship exists between changes in price and total revenues.
Okay, so this example is a little dated. We're looking at price here in the column on on the first column up here, various prices, 11 cents, 10 cents, all the way down to one cent. And this is something that you're probably not familiar with. This is in the day when you used to be charged per minute of cellular phone use. Now it's on, everyone thinks unlimited, but back in the old days, you used to get charged per minute that you use your phone. So, that the various prices per minute, you see the quantity demanded in billions of minutes. And if you take the price times quantity, you'll get the total revenue here. So, looking at the elasticity, price elasticity, using this equation, you get to see the elasticities in terms of the responses. It's responsiveness. Remember, we talk about a one percent change and how it responds to a 21 percent change, a 6.3 percent change, a three point four percent change in quantity demanded, or a one percent change in price results in a one percent change in quantity demanded. That's a unit elastic situation. And then so forth and so on into our inelastic zone.
So, anyway, um, taking a look at this, we'll actually see it related to our demand curve. Okay, so we have our demand curve. What's not is labeled here, we have price, quantity, our downward sloping demand curve. And then we're going to have another curve, which is our total revenue. So, the thing here is that the horizontal axis is still the quantity terms, like just like the quantity demanded. But on the vertical axis, it's no longer price, it is now total revenue. Okay? And so, we can see it. What helps is if we can see it stacked up relative to each other. There we have it. So, here we have quantity on the horizontal axis, and quantity on the horizontal axis here. And then we have total revenue on the vertical axis, but price on the vertical axis. So, what we're looking at here is essentially this blue area on the curve is the elastic range of the demand curve. So, as price goes down, say we're at 10 cents, 10 cents here, and it goes down to 9 cents, the question you should ask yourself, do consumers like that? Do they like a price decrease? Yes. So, how do consumers tend to respond? Elasticity, responsiveness, remember that relationship between the two words. How do they tend to respond? They want more. Well, if it's elastic, that means they can truly really respond to this price decrease, and they increased their quantity demanded so much that total revenues to the firm will increase. So, therefore, we are in that elastic range. Now, in the unit elastic range, that's this going down from six cents to five cents, or up from five cents to six cents. It doesn't matter what we do either way, the total revenue is going to be the same because it's in the unit elastic range. Now, when we go below that, when we go below that, let's just say to four cents, to three cents. Again, how do consumers respond? They like that price decrease. So, they will increase quantity demanded. But remember, we're relating this elasticity concept to total revenues, which is the firm's concern, the business is concerned. So, they lower the price from four cents to three cents. They they might be happy because consumers will consume more. But the question is, did they consume more enough? Did they respond enough to that price reduction? Well, as we can see here, the total revenues in this portion here goes down. So, if they didn't respond enough, therefore, we can consider this the inelastic, this the inelastic range of the demand curve. So, when we're looking at, when we're looking at elasticity and how it relates to total revenues, we're really looking at how price changes affect total revenues in terms of this negative parabolic curve on the bottom.
So, to summarize that, in an inelastic range, when there's a price decrease, total revenue decreases. When there's a price increase, total revenue increases. Going to the bottom, the elastic range, a price decrease will see total revenue increase, but a price increase, we'll see total revenue decrease. So, I hope that kind of concept kind of makes sense as we discussed it.
So, now we're going to discuss the determinants of the price elasticity of demand. The price elasticity of demand for a particular commodity at any price depends on the following factors. Number one, the existence of substitutes. So, the closer the substitutes and the more substitutes there are, the more elastic is demand because there's going to be more responsiveness to price changes because there are more options as substitutes for the households. Share of budget. The greater the share of the consumer's total budget spent on a good, the greater is the price elasticity. You're going to respond to a price change if it's a good portion of your income. If it's a really small portion of your income, then it probably doesn't matter to you. And if someone doubles the price of something that costs two cents to you, so it goes from two cents to four cents, that's probably a very small portion of your income, you're probably not going to care and you probably won't change your behavior. But if it's a big share of your budget, if someone doubles the price, it's definitely going to change your habits, your responsiveness to that price change. And then finally, the length of time allowed for adjustment. The longer any price change persists, the greater is the elasticity of demand. Price elasticity is greater in the long run than in the short run. In the short run, people cannot respond because they cannot find appropriate substitutes for them. In the shorter run, but in the longer run, they have time to do shopping, they can find suitable substitutes, even if it's not the same good, they can find something to replace the good that is just too high priced, even if it's not exactly the same.
So, next, we're going to want to define how to define the short run and the long run. The short run is a time period too short for consumers to fully adjust to a price change. And the long run is a time period long enough for consumers to fully adjust to a change in price, ceteris paribus, other things being constant. So, short run and long run price elasticity of demand. Given a demand curve, here we have a very inelastic demand curve. So, remember, as price changes, consumers can't respond. So, is that a long run or short run situation? Well, it means they don't have time to find appropriate substitutes. So, here's a situation where in the short run, quantity demanded falls slightly when the price changes, when the price goes up, because it's the short run. But in the long run, we're going to see their ability to respond to find alternatives. They will respond to the price change at a greater amount. So, with more time for adjustment, the demand curve becomes more elastic, and quantity demanded falls by a greater amount. So, for some real-world data, this is estimated elasticities looking at short run versus long run. So, we have air travel for business. We had short run elasticity of 0.4. That meant a one percent increase in the price resulted in a 0.40 percent decrease in quantity demanded for air business air travel. But in the long run, a one percent increase in price resulted in a 1.2 decrease in quantity demanded for business air traffic. Or vice versa, we could have said price decrease. And then of course, you can see for air travel for vacation, food products, electricity, gasoline, and so forth. These are the various changes.
Now, there's another elasticity of demand. We looked at price elasticity of demand. Now we're going to look at cross-price elasticity of demand. So, this is the percentage change in the demand for one good, holding its price constant, divided by the percentage change in the price of a related good. Now, to tie it back to chapter three, we're talking about non-price determinants. So, if we're talking about price determinants, it's really EP. That's EP is looking at the demand curve and how is it sloped like this. But when we talked about a non-price determinant, remember we had non-price determinants like income, taste and preferences, price of related goods, expectations, number of consumers in the marketplace. These were the five non-price determinants. Now we're looking at a situation where price and quantity, something like price of a related good. If this is for plate lunches, market for plate lunches, and that's the demand for plate lunches, we want to see what happens if price of plate lunches is held constant. What happens if a related good price changes? So, let's just say price of subway sandwiches, a related good to plate lunches. If price of subway sandwiches doubled, what's going to happen? Well, we know that price of subway sandwiches doubled, people are going to buy less subway sandwiches and substitute plate lunches. So, demand will shift to the right. Now, the question is, how much to the right? How much will this go from Q1 to Q2? So, this is cross-price elasticity of demand. It's no longer price elasticity. Now we're looking at a non-price determinant for a given good.
So, the formula for computing cross-price elasticity of demand between good X and good Y. This time we have EXY. We have two letters there because this represents, suppose that could be plate lunches, and Y could represent subway sandwiches. I'll just say SS for subway sandwiches. And so, we're looking at the change in the price of one good, for example, subway sandwiches, and how it affects the demand for plate lunches. Now, for cross-price elasticities, you should pay attention to the signs. Because remember, like we last one, we earlier on, we calculated something like 0.85. So, 0.85 for price elasticity, we said there was always an implied negative relationship between price and quantity demanded. So, we just said, just drop, just drop this negative sign, and we're just going to use 0.85 because everyone understands it's a negative relationship. But now that it's cross-price elasticity, we should really pay attention. For substitute goods, the value is going to be positive. So, an increase in the price of X would increase the quantity of Y demanded at each price. Whereas for complements, EXY, the value would be negative. So, you might be given values to calculate, and you might not be told what the value, what the goods are. You might not be told that you're looking, oops, you might not be told that you're looking at subway sandwiches and plate lunches where you can look at that and figure that, well, if I know what goods they are, I can assume they're substitutes. You might just be given good X and good Y and asked to determine, are they substitutes or complements? You're going to be using this or this to determine what the goods are. So, let's just suppose we're looking at a situation where the market in question will be again plate lunches, but we're looking at a price change in subway sandwiches. So, essentially, we're looking at the change in the quantity of plate lunches with respect to the change in prices of subway sandwiches.
Okay, so if we were to write out the formula or the midpoint method, then we're going to be looking at the quantity of plate lunches, the change in that. So, be we're going from Q2 minus Q1 over Q1 plus Q2 over 2, with respect to, and this is all for plate lunches, PL, PL, and so forth and so on. But now we're looking at the price change of sub, so price of subway sandwiches, P2 minus P1, a subway sandwich, divided by P1 plus P2, subway sandwich, divided by 2. Okay, so that's how you would go about calculating your cross-price elasticity.
So, here's an example of determining values and whether or not things are substitutes or complements. The US Postal Service has raised rates on first-class mail, which aims to deliver more speedily than second-class mail, several times in the past few years. Each time it does so, it must take into account the cross-price elasticity of demand between first-class mail and second-class mail. The estimated cross-price elasticity of demand between first-class mail and second-class mail is about plus 0.3. So, with that positive sign, you can recall from what we saw, first-class mail and second-class mail are substitutes. If you came out with a negative 0.3, then they are complement goods. But we have two types of goods, first-class mail versus second-class mail, and they happen to be substitutes, as shown by the positive value. And plus also, just the understanding of what they represent.
Next, we have another non-price determinant of demand. Therefore, we again are looking at an elasticity, not of varying slopes, not like this, but rather what happens like this, the responsiveness in quantity based on a change in a non-price determinant. In this case, that non-price determinant is income. So, income elasticity of demand. The percentage change in demand for any good, holding its price constant, divided by the percentage change in income. The responsiveness of demand to changes in income, holding the good's relative price constant. So, here we're looking at EI, the percentage change in demand with respect to the percentage change in income. And again, the format of the formula is going to be the same, where we have percentage change in demand with respect to the change in income. So, again, we're looking at the quantity, Q2 minus Q1 over Q1 plus Q2 divided by 2, all over now we're going to have the income, income 2 minus income 1 over I1 plus I2 divided by 2. And you're going to be plugging it into this midpoint method formula.
And finally, we're going to be looking at price elasticity of supply. This time, we're switching up, going away from the demand curve, but we're still going to put a price and quantity. But this time, we're looking at either a supply curve that looks like this or like this. So, price elasticity of supply is the responsiveness of the quantity supplied of a commodity to a change in its own price. The percentage change in quantity supplied divided by the percentage change in price. The formula for computing price elasticity of supply is percentage change in quantity supplied over a percentage change in price. Using the same midpoint method, I think it should be pretty straightforward based on already what we've covered.
Classifying supply elasticities. We have perfectly elastic supply, where quantity supplied falls to zero when there is the slightest decrease in price. If the price falls, firms don't like that, and they will respond completely by supplying zero. The supply curve is horizontal at a given price. When we have perfectly inelastic supply, quantity supplied is constant, no matter what happens to price. The supply curve is vertical at a given price. So, there we have the look at the two different extreme supply curve elasticities.
Okay, now, the price elasticity of supply and the length of time for adjustment. Well, these are the thoughts to consider. The longer the time allowed for adjustment, the more resources can flow into or out of an industry through expansion or contraction of existing firms. The second one, the longer the time allowed for adjustment, the entry or exit of firms increases or decreases production in an industry. So, here we have, as time passes, the supply curve rotates from S1 to S2, going from the short run to the long run, and quantity supplied rises to Q1. As more time passes, the supply curve rotates further from S2 to S3, and the quantity supplied rises from Q1 to Q2.
So, that wraps up this lecture for chapter 19, elasticities. Um, hope everyone's doing well and stay healthy, and I will look forward to talking to you guys again soon. Aloha.