[Music] hi folks this is Professor Watts coming at you with a short tutorial that shows you how to calculate elasticities of demand and Supply first off we'll do a brief review of definitions the basic concept of elasticity now if you feel that you're um comfortable with the definitions you can feel free to skip right ahead to the sample problems towards the end of the video elasticity simply refers to the responsiveness to change and when we're talking about demand elasticity or technically speaking the price elasticity of demand we're talking about how responsive is quantity demanded to a given change in price we know because the demand curve slopes down that when price goes up quantity goes down but we want to know how much and elasticities of demand can be labeled elastic or strongly responsive that means the quantity changes proportionately more than the price so if the price goes up by let's say 50% quantity might go down by something like uh 90% that would be elastic strongly responsive unit elastic where price and quantity changes are equally responsive they change by the same proportion so if price goes up 20% quantity goes down by 20% and then in elastic quantity is weekly responsive to changes in price quantity changes proportionately less than the change in price so if the price doubles increases by 100% quantity might only go down by something like 5 or 10% and when we get into the problems we'll talk about different kinds of goods that have different elasticities we're talking about elasticity which is responsiveness to change or you can think about it in terms of the responsiveness to a force that's acting on an object in the case of demand for product the force is the price change but let's take something that is elastic that we that we know about a rubber band and the force acting on it will be my hands pulling it apart so I apply a given force and the rubber band easily moves This is highly elastic I'm applying a very light force with my hands probably you know maybe a pound worth of pull and this thing stretches quite a bit so that's elastic it moves a lot in response to a given Force now something that's not elastic my ruler I'm applying the same force in fact I'm I'm pulling probably even a little harder but I apply the same force and this thing doesn't move at all this is very inelastic so it's not responsive to being acted on by a force so here's something that's inelastic doesn't really move or change in response to that Force just something that's elastic moves a lot in response to the force what something in between couldn't find something that moves just a little bit but my tie the fabric will move if I pull on my tie same force it moves a little bit so this is uh slightly elastic but it would will have a a low elasticity coefficient the rubber band would have a high elasticity coefficient and my ruler would have a very low to zero elasticity coefficient okay so hopefully have a good intuitive understanding of what this concept of elasticity means and let me know before we move on that uh demand and Supply elasticity are completely analogous Concepts so if I jump to the definition Supply elasticity everything's the same and notice I've just changed I've just notice I've just replaced the word Demand with Supply Here price elasticity of supply is how responsive quantity Supply it is to give a change in price and we can say whether it's elastic or inelastic okay one more quick definitional item the concept of measuring elasticity with elasticity coefficients which we'll start doing in some sample problems in a moment that's indicated with the Greek Epsilon and it can be either greater than one which will'll label as elastic officially uh it's equal to one that's unit elastic or it's less than one being in elastic let's talk about the formula for elasticity and we'll notice here that there's a problem that could skew the result so we'll need to make a a refinement of our formula before we can actually apply it to some problems the basic formula is really simple it's just a percentage change in quantity demanded divided by the percentage change in price so we're looking at a a typical demand curve price goes up quantity goes down price elasticity therefore is always negative price is going up quantity is going down that means the numerator is negative or if price is going down quantity is going up that means the denominator negative so price elasticity is always negative we typically will'll talk about the elasticity coefficient just in absolute value terms we know it's negative so we just want we just want to look at the magnitude of it okay and here's a an example using that that really simple formula price of oil increases by 10% the quantity demanded Falls by 5% then the price elasticity is with that minus 5% that's the percentage change in Q divided by the plus 10% change in P minus5 or just 0.5 as I mentioned will use absolute value okay now there a problem let's say this let's say you uh run a website design company and you know that at a price of $250 you could sell eight units per month at a price of 200 you could produce 12 websites per month now how do we calculate elasticity here well as we'll notice it's going to depend on whether price is going up or down and therefore quantity going up or down now the problem is that percent change is going to be different depending on where we start if we start at a and the price goes up we'll get one set of percentages but if we start at B and have the price go down the quantity up we'll get a different set of percentages specifically if we're if the price is rising from 200 to 250 that would be a change of 50 divided by the base of 200 so that's a plus 25% increase in price quantity is going from 12 to 8 that's a change of four divided by the base of 12 so that's- 33 so our elasticity in that case is 1.3 which we would label as elastic because the elasticity coefficient is greater than one however if we start at B and go to a price is going down we see the price change is uh 50 over 250 which is just 20% now and the quantity change is plus 4 divided by 8 which is now 50% so now our elasticity coefficient is much higher 2.5 it's almost twice as large in fact so we're going to get a skewed result depending on where we start here so we want a better method that kind of evens out that effect so what we're going to do is use What's called the midpoint method and to calculate these percent changes now we're going to take the difference in price or the difference in quantity and instead of dividing it by one or the other end point we're going to divide it by the midpoint or the average value doesn't matter what end value and start value we use because we're only taking the difference so we'll get the same result either way so whether the price is going up quantity down or the price down quantity up we'll get the same elasticity result so we're going to focus on this midpoint method when we calculate elasticities and for our little examp Le problem here our percent change in quantity now is the difference 12 - 8 or 8 - 12 if you will which is four divided by the average 8 + 12 divided 2 which is 10 or you can just visually think about the midpoint here right between 8 and 12 halfway between 8 and 12 would be 10 okay so our midpoint percent change in quantity the difference 12 - 8 divided by the midpoint which is um 4 ided 10 40% okay now our percent change in P likewise the difference which is 50 whether we're going up or down it's $50 change and the midpoint between 200 and 250 is 225 or if you prefer the average 200 plus 250 550 divided 2 it's 225 okay so now we've got our midpoint percent change in price and that's going to work out to 22.2% now we calculate our elasticity of demand our percent change in quantity 40 divided by our percent change in price 22 2.2 we got a nice midpoint elasticity value of 1.8 okay so just to summarize the formulas our basic elasticity of demand is simply the percent change in quantity divided by the percent change in price our midpoint elasticity is the change in quantity divided by the average quantity divided by the change in price divided by the average price likewise with Supply same exact calculations except on the supply Cur so when we're calculating elasticity of Supply we're just looking at the percent change in quantity supplied divided by the average quantity supplied percent change in price divided by the average price okay let's work some example problems now okay so we're starting off with uh Naval oranges and um you'll notice first off that my price is always in dollars per unit and the P unit here would be pounds my quantity is always in units per time period pounds per week and I did make up these numbers but they they'll be somewhat close to the prices we would actually observe in real markets so I'm going to start us at a dollar per pound and at a dollar per pound we're going to say that this Market buys 10,000 lounds per week just label that 10K then we'll have the price fall to 85 cents per pound and at that price the sales go up to 16,000 pounds okay now we we have a segment of our demand curve here we could kind of draw a demand curve in here we don't need to but that's fine now let's bring in our equation percent Delta Del Q over percent Delta p and remember using the midpoint formula it's Delta Q over average Q / Delta p over average P so it's simply a matter of plug and chug now our Delta Q is six our average Q is just the midpoint between 10 and 16 or 10 + 16 divided 2 it's going to be 13 and I don't need to write the zeros in there I can't I could if I needed to but either way the division problem will be the same my Delta p is 15 cents and my average p is going to be the midpoint between those or the Aver average .925 simply perform the calculations so the the numerator is 6 by 1346 we can round this and the denominator is5 / 92516 do that and we work out to uh elasticity coefficient of 2.875 let's call that 2.88 and of course that registers on our elasticity spect as highly elastic and as we might expect with oranges you know you've got a lot of good substitutes other fruits and other food products so you're not necessarily going to buy you're not going to get excited about buying oranges until there's a significant uh decrease in the price okay now another demand elasticity problem let's look at the demand for household electricity and this time we'll make the price go up it starts at 6.8 cents per kilowatt hour and at that price we have uh 300 kilowatt hours per month demanded this is maybe for an individual household the price Rises to 8 cents per kilowatt hour and demand only Falls slightly to 290 kilowatt hours per month and once again we could kind of sketch in our demand curve there but what we're interested in is elasticity so once again we just want to plug and chug into the formula the Delta Q is uh change of 10 kilowatt hours the average Q would be the Mido 295 the Delta p is 1.2 cents and the average Q here simply 8 + 6.8 / 2 8 + 6.8 that's 14.8 over 2 7.4 okay then we work out all this math we get 034 ided by .16 and that works out to I'm rounding. 21 elasticity coefficient of 0. 21 well less than one so we would label this as inelastic and this would be quite inelastic and it might make sense when you think about home electricity there's not many good substitutes and people are going to be willing to pay higher prices to keep their homes lighted and heated and and not necessarily cut back that much on electricity use in the short run even when the price goes up by the way I want you to notice that uh my percent change in price 16% here and back in my oranges example 16% so I I did exert the same Force if you will the same price change and here we see a rather large quantity change 46% for a large elasticity coefficient and here with the electricity with the with the same price change 16% we saw a very small quantity change just 3.4% for a very small elasticity coefficient okay now let's think about Supply elasticity I'll stay in the agricultural Market let's think about potatoes and it's dollars per pound pounds for week and I'll start us off at a price of 25 cents per pound and a quantity purchased at that price of5 million pounds and price goes up to 30 cents now suppliers of course will supply more at higher prices because they can cover higher cost of production and let's surmise that the quantity goes up to 10 million pounds per week okay we can maybe sketch in our supply curve here but remember it's the same formula so we just need Delta Q over over average Q the Delta Q is 5 million the average Q is 7.5 Delta P here is 5 cents and the average Q the midpoint between 25 and 30 would be 27 A5 or0 275 okay so we work all of this out we get uh 67 on top divided by8 on the bottom and that's going to be approximately 3.6 so that's much larger than one so we can label this as elastic Supply okay let's do one more Supply elasticity now I'm looking at the supply of three-bedroom apartments in Springfield so price now is dollars per month that's the rent and quantity is in the units offered per month by landlords and apartment complexes and we'll say that the price starts at $1,000 a month and at that price in this town landlords offer 2,000 units and the price goes up to say 1,200 and because in the short run the supply of Apartments is relatively fixed it's pretty difficult for them to increase Supply they might be able to maybe get some units that are being cleaned or repaired and kind of hurry that along and and get the supply up just a little bit so let's say it only goes up to to 250 and then we have a supply cover that looks something like that okay and we're working with our same formula hopefully this is getting pretty routine by now change in quantity is just 50 average quantity would be halfway between 2,000 and 250 that would be 2,25 change in price is $200 average is going to be the midpoint between here 1100 and this works out to you do this on a calculator 02 4 7 over. 187 and when we solve that we get .1 36 which is well less than one a very low coefficient so we would label this as in elastic Supply and again if you think about the the constraints on increasing the supply of Apartments uh it makes sense it's even if landlords wanted to in the short run it's difficult for them to build more buildings now in the long long run we might surmise that the the supply curve is much flatter and the same increase in price here would yield a much bigger increase in quantity so we could think about long run elasticity versus short run okay but for now we're just focusing on calculating that coefficient and uh getting this formula down and that's really about it now sometimes you might be asked to find the change in consumer or producer Surplus given a change in price and quantity and uh let's go back to our oranges example and I'll quickly show you how to do that it's pretty uh it's pretty straightforward so we don't know what the overall we don't know what the overall consumer surplus is because we really don't know the shape of this demand curve above this point so the existing consumer surplus before the price change was all this in here and again we just we have no way of calculating that without knowing this demand cve but we do know the change in consumer surplus when we move from when the price goes down from a do to 85 because what we're doing is adding this area right here of consumer surplus and that area consists of a rectangle right here and if we just take the area of that rectangle which is length time width and then this triangle this extra triangle of consumer surplus here which the angle of the area of course is 1 12 base time height and we can calculate those because we know the magnitude of them and then we can uh add those up and find the change in consumer surplus so the area of the extra rectangle worth of consumer surplus is 15 cents times the 10,000 units here and then the area of our extra triangle of consumer surplus is 12 times a a base which is the extra 6,000 units times a height of 15 cents so we'll work all that on the calculator first the rectangle 15 cents time 10,000 get extra, 1500 of consumer surplus and that's dollars $1,500 worth of value for the consumers and for the triangle we're going to get 0.5 or 1 12 time the 6,000 time the 15 C height that's 450 so when I sum these up I get a grand total of an increase of 1,950 okay so it's pretty straightforward to to find the change in consumer surplus likewise we'll do the same thing with producer Surplus we can quickly do that in my potatoes problem and the change in consumer surplus again we don't know the pre-existing consumer surplus that's this area here because we don't know the shape of the supply curve but we do know that when we went from 25 to 30 cents we added this area here and this area consists again of a rectangle and a triangle the rectangle measuring a height of 5 cents times the 5 million units and the triangle area is going to be 1/2 times the base of 5 million units times the height of 5 cents and we'll just work this out in the calculator extra $250,000 of consumer surplus there an extra 125,000 worth here we add those up we get a total increase we'll call it Delta producer Surplus equals $375,000 so it's quite easy to calculate a change in producer consumer surplus with this method and I should briefly note here that um if we're given a price and quantity change on the supply curve we're only able to calculate elasticity of supply and a change in producer Surplus cannot calculate a demand elasticity or a change in consumer surplus because we know nothing about the shapes of the presumptive demand curves presumably in this situation demand did something like this D1 to D2 We had a rightward shift of demand which gave us that increase in the price likewise up in my oranges example we presumably had an a shift in Supply something like this S1 shifted out to S2 which brought us the reduction in price we cannot calculate a supply elasticity here or a change in producer Surplus because we don't know what the shape of the supply curves was it could have been like this or it could have been like this now just to wrap things up ticity of demand captures sensitivity or responsiveness of quantity demanded to changes in price and it's very useful to think about two demand curves that go through the same point is when we look at the same change in price so here we're going from 40 to 50 in price and you can you can see that the inelastic demand curve the quantity doesn't change much at all it only changes by five so it's a relatively small uh quantity response to a given change in price whereas the elastic demand curve has a significant change quantity goes from 80 all the way down to 20 okay much more responsive quantity change to a given change in price and hence that's elastic one one good way to remember what's elastic and inelastic is when we're looking at the the just the shape of a demand curve the more inelastic demand curve is steeper and it looks kind of more like a capital I for in elastic and a more elastic demand curve is much flatter and it you can kind of see that that looks more like an e for elastic so there's a kind of Handy way to remember what's in elastic versus elastic hope you found this video useful please check back on my YouTube channel for more tutorials and reviews trying to help you understand [Music] economics [Music]