Cross-Price Elasticity
BRIAN BUCKLEY: This is Dr. Brian Buckley, and in this video, we will be talking about cross-price elasticity. We know that when the price of apples goes up, the quantity demanded of apples goes down, and measuring how much the price of apples affects the quantity demanded of apples is what we call own-price elasticity.
But we can think about how other prices might affect the quantity demanded of apples too. When the price of bananas goes up, what will that do to the quantity demanded of apples? And this is what we call cross-price elasticity.
So perhaps the price of bananas goes up by 10% and we by 2% more apples. So we can get a cross-price elasticity, and we'll use a very similar formula to the one we saw in the own-price elasticity of demand.
Here we're just thinking how a change in the price of good x leads to a change in the quantity demanded of good y. So we could put the change on the bottom and the response up top.
So in this example, we have a 10% increase in the price of bananas, leading to a 2% decrease in the quantity demanded of apples. So to calculate the cross-price elasticity, a 10% increase in the price of bananas goes on the bottom, a 2% increase in the quantity demanded of apples goes on top. A positive divided by a positive is a positive. Two divided by 10 is 0.2 and the percent signs cancel out.
So we get positive 0.2 for our cross-price elasticity between bananas and apples. We might try a different thing. We might say that the price of pie crust goes up by 10%, and instead of buying more apples, we actually buy less apples. We might buy 5% less apples.
So we have cross-price elasticity for a different good here. The 10% increase in the price of pie crust leads to a 5% decrease in the quantity demanded of apples. So negative divided by a positive is a negative. 5 divided by a 10 is 0.5, and the percent signs cancel out again. So here, we have a cross-price elasticity between pie crust and apples, and this time it's negative.
So we could put our numbers right next to each other. And we can see that they have very different signs. The cross-price elasticity for bananas was positive, but the cross-price elasticity for pie crusts was negative.
So the positive sign here for bananas implied that they're substitutes, that when bananas went up in price, we bought more apples. So when anything goes up in price, we buy less of it, so the price of bananas goes up, we buy less bananas. And as a result, we actually buy more apples, implying that those two goods are substitutes.
With pie crust, the negative sign is telling us that they're complements. When the price of pie crusts went up, we would buy less pie crusts, and as a result, we might need less apples because of that. So the negative sign tells us that they're complementary.
So again, we can about what sign tells us for an elasticity. A positive sign means they move in the same direction. And for a cross-price elasticity, that means these things are substitutes.
And if you ever get a negative sign, that means these two variables move in opposite directions. And if this is cross-price elasticity, it means that these two goods are complements.
Now, once we get rid of the sign, we can take a look at the size of these numbers. We can see that the number for pie crusts is slightly higher than bananas. They're still relatively small numbers, each of them, but we can compare the size of these.
And once we get rid of the sign, we could think about what the size means. Bigger numbers implies that the good is more responsive to price. So bananas and apples, not great substitutes, so it's not a huge effect on the quantity demanded of apples, when the price of bananas change.
But there may be a slightly bigger change in the quantity demanded of apples when the price of pie crusts change. So those two things might be more complementary.
So up next, we could think about what the sizes of these numbers might mean. So if you want to check that out, take a look at the categories of elasticity. If you need to go back and check out the own-price elasticity of demand to see how the price of apples might affect the quantity demanded of apples, take a look at the elasticity of demand video.
Or if you want to take a look at the other side of the coin, the elasticity of supply, take a look at that video. Also we could take a look at income elasticity to figure out how does changes in income affect the amount of a good we're buying.
Or if you want to get a little bit deeper into the math behind elasticities, go ahead and click on the methods of calculating elasticity.