The price elasticity of demand is basically just a fraction, it's just a ratio that tells us how responsive the customers or people demanding a good is to a change in the price of that good or service. So for example let's say that we're talking about ice cream and I was to tell you that if there was a 10% decrease in the price of ice cream then people would increase the quantity that they're demanding of ice cream by 50%.
So then what you do is you just take the 50% divided by the 10% and ignore the sign you just say 50% divided by 10% then you've got five. Now you might be thinking "Ok, what does this number tell us?" Well, a number greater than one we would say is very elastic demand. That means that if it's greater than one then the consumers are really responsive, they're really responsive to a change in the price of the good. If there's a decrease in the price it really going to increase the quantity demanded.
If it's inelastic, so if it is less than one for example in elastic that means that customers aren't as responsive maybe it's something like a gallon of milk and they say you know I really really need milk so you know even if the price goes up I'm not going to change how much I demand and so forth.
The nice thing about price elasticity of demand is that it's a unit free measure, so let's say if the ice cream was measured in dollars and if you're trying to think about it in terms of the slope of the ice cream, if instead of measuring ice cream in dollars now we are measuring it in cents. So then that would change the slope. So this is not calculating slop, it's not measured in any kind of units it's just a unit-free measure. We just take the ratio of two percentages and then that tells us whether how elastic the demand is for this good.
Let me give you a more little more complicated example to show you how you calculate this in the real world. So let's say that you run a movie theater and the current price of a ticket is $9 and that price people want to buy 20000 movie tickets but you're considering a price change, you're wanting to know "What would happen if I increase the price by $2?" Let's say you talked to somebody who really knows the movie theater industry and they say "Look if you increase the price to $11 which is that $2 increase then that is going to decrease the number of tickets that are demanded to 15000 tickets." So an increase of two dollars is going to lead to a decrease of five thousand tickets. Now you want to know how is this going to affect business and so forth. So you could just look nine dollars times twenty thousand (9 x 20000) you originally had 180,000 in sales and now you've got eleven times fifteen thousand (11 x 15000) and you've got 165000 in sales.
So you might even be thinking "I increase the price by $2 and yet somehow my sales ended up going down." Let's just say you're thinking about all these things and you want to calculate the price elasticity of demand. We already talked about the ratio but it's a little bit more complicated than that because not always you're just going to be told what is the percentage of change in quantity demanded or the percentage change in price. If I just tell you those things then it's pretty straightforward to calculate but here we've got to use these numbers to figure it out.
For the percentage change of quantity demanded, we're going to have our change in quantity divided by the average quantity I'm going to explain what that means. So if we go to change in quantity (20000 - 15,000) that was our change in quantity. Now we divide the answer by the average quantity during the period. The average is (20,000 + 15000) divided by 2. That gives us 17,500 in our denominator 5,000 in the numerator. Divide them and we get 0.286 rounded. Multiply it by 100 so we convert it to a percentage, we would have 28.6% is our percent change in quantity demanded.
Now we've got to calculate the denominator which is the percentage change in price. So it's the same idea that we take the change in price divided by the average price. So the change in price we say it was (11 - 9) divided by and the average price. We just take the original price of $9 then the new price of 11, it's (11 + 9) and then we divide that by 2. That's our average price so this will give us 2 over 10 which is equal to 0.2. If we multiply that by 100 to get a percentage we'd have 20%. So that means that our denominator the percentage change in price is 20%.
Now if we want to know our price elasticity of demand for these movie tickets at a $2 price increase we would say is 28.6% divided by 20%. So I'm just going to call it price elasticity of demand (PEOD) 28.6% divided by 20% and I'm rounding this all that comes to 1.43.
Now, remember we had said that if the number was greater than one so we would say that demand for these movie tickets at least within this price range when we're talking about a change of nine dollars to $11 we would say that the demand is relatively elastic which means that the consumers these movie is very responsive to a change in the price.
