Cross-price Elasticity of Demand helps us identify substitutes and complements.
Cross-Price Elasticity of Demand
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Now let's talk about another elasticity of demand. The cross price elasticity of demand. So the cross price elasticity of demand helps us gauge whether goods are gonna be substitutes or complements or just completely unrelated. Right? So remember when we were talking about substitutes and complements in the demand shifts um The idea was that the price change in one good would've the demand of another, right? And that's exactly what we see in our formula here. Right? Look at our formula for cross price elasticity of demand. We've got the quantity demanded of one good in the numerator right? Notice how quantity demanded is still in the numerator just like always. But we've got the price of a different good here good. Why? Right? So quantity demanded of one good price of another good. Right. So the idea here is we're gonna see how quantity demanded of one good reacts to the change in price of another good. And you can imagine that it's gonna help us find substitutes and complements. Right? So still, just like before we're going to keep using our midpoint method and luckily again the steps stay 99% the same except in this case we're using the price of a different good rather than the price of our own good. Um just like with the income elasticity to the only thing that changes, we were using income instead of price. Now we're using price of another good instead of price of our good. And once again you can tell right here price and price in the denominator, they all kind of follow this flow, whatever the name of it is, that's what's in the denominator. But it's also easy to just remember that quantity is always going to be in the numerator for all of our elasticity ease. Alright, so let's go ahead and do an example here for cross price elasticity. You're gonna see how similar our steps are. And again with this one we do have the positive and negative uh differences. Right? So we're gonna end up making our conclusion based on it being positive or negative. So that's going to matter in this case as well. So let's go ahead and do an example where we can use our steps which are basically the same as we've been using. So let's go ahead And do this one. When the price, when the price of tennis rackets increased from $45 to $55. The quantity demanded of tennis balls dropped from 21,000 to 19,000. What is the cross price elasticity of demand? So notice they gave us two quantities. Right? But those are quantities of tennis balls and they gave us two prices. But those are prices of tennis rackets, right? So um you can imagine that these are going to be compliments. Like I picked things that sound like compliments just for the sake of it, but we can make sure by doing this calculation but the idea here is we're seeing a price increase in one product and a quantity demanded decrease in the other product, Right? So remember from from demand shifts, that's exactly what happens with a compliment if the price goes up of a compliment, the quantity demanded of the compliment goes down. Right? So um so in this case that's exactly what we're seeing. Let's do our steps and do the analysis with elasticity. So we'll make two columns quantity demanded and that's quantity demanded of tennis balls and p that's our price column for the price of tennis rackets. And let's go ahead and do this. So first we subtract 21,000 -19000 equals 2000 and price. The same thing 55 -45 -45 equals 10. Step two. We're gonna add 21,000 plus 19,000 equals 40,000. And on the other side the same 55 plus 45 equals 100. Now, step three is where we're gonna divide. Step two by 2 40,000, divided by two equals 20,000. And on the other side we've got 100 divided by two equals 50. Step four. This is where we're gonna get our actual percentage changes in each. So step one divided by step 3, 2000 divided by 20,000. That's going to equal 0.1. That's our percentage change in quantity demanded. Let's do the same thing with price. So we've got 10 divided by 50 and we're gonna have 0.2 is our percentage change in price. Right now we haven't dealt with the positives or negatives yet. I always leave that for the last step where I go back to the problem. So first let's get the number of our cross price elasticity, which is just gonna be this quantity demanded 0.1, right? This is Uh quantity divided by price uh which was the 0.2. And we are going to get an answer of 0.5 right there, right half. So now we just have to check is it positive or negative? So let's see for for the prices we had a price increase. So the price is a positive. And for tennis balls, the quantity decrease, right? dropped from 21 to 19 so that Negative right there, so we have a negative and a positive, that means it's a negative, we have a negative 0.5 for our answer. So now how do we analyze this answer that we just got negative 0.5. Well, right down here we've got our answers. So if we get this one's pretty easy because we don't have to think about is it elastic, is it any elastic this or that we just want to know if it ends up being positive or negative. Right? So if it's positive then we know they're substitutes. If it's negative their compliments and if it's zero then you know they're unrelated. Okay, so in this case we got a negative number which tells us that they are compliments. But remember we can use some logic to kind of come to the same conclusion, right? We saw the price of tennis rackets go up and the quantity demanded of tennis balls go down. Right? So the idea is if you remember from the demand shifts when the price of one product goes up, causing the other quantity demanded to go down, that means that they're gonna be compliments. Now, if the price had gone up and the quant demanded of the other one went up, that's when we're talking about substitutes, and that's why you would see a positive answer in this case. Up and up. Right. Um So really in this case you can make a lot of conclusions just from the problem without doing any math. All right. So let's go ahead and do some practice problems about cross price elasticity.
An increase in the demand for chicken, from 8,000 to 12,000, was caused by an increase in the price of beef from $4.50 to $5.50. Therefore, the cross-price elasticity for these two products is:
The cross-price elasticity of demand between apples and oranges is defined as
The price elasticity of demand for apples divided by the price elasticity of demand for oranges
The change in the quantity of apples demanded divided by the change in the quantity of oranges demanded
The percentage change in the quantity of apples demanded divided by the percentage change in the price of oranges
The percentage change in the quantity of apples demanded divided by the percentage change in the quantity of oranges demanded