# How to Calculate the Cross Elasticity of Demand. Overview and Explanation

The cross elasticity demand tells you what happens to the demand of one good when there's a change in the price of another good. So basically it can tell you whether two goods are substitutes or whether they're complements. You can calculate the cross elasticity demand by taking the percentage change in quantity demanded of the one good and then dividing it by the percentage change in the price of the other good and if the number that you get is positive then that means that the two goods are substitutes and if the number you get is negative then it means that the two goods are complements.

Let's walk through an example let's pretend that you are the president of a professional baseball team and you decide that you're going to raise the price of hot dogs which are a popular food item sold at baseball games by 20%. Then there's a 25% increase in the quantity of hamburgers that are demanded at the baseball games but there's a 40% decrease in the quantity of beer demanded at the baseball games in response to that 20% increase in the price of hot dogs.

Now we can go and we can calculate the cross elasticity of demand for hamburgers with respect to hotdogs and we can calculate the cross elasticity of demand for beer with respect to hotdogs. When I say with respect to hotdogs I mean that there was a 20% increase in the price of hot dogs and we want to say how does that affect in the end for hamburgers and how does it affect demand for beer. So if we take the 25% increase in the quantity of hamburgers demanded, we say well, what's the percentage change in demand? there's a 25% increase I'll put a little positive sign there. Then we had a 20% increase in the price of hotdogs, so that equals 1.25 and what is relevant here is this is positive so it means that the two goods are substitutes.

Think about it what this is saying is that hotdogs became more expensive and what happened to the demand for hamburgers, it went up. So people substitute and say I'm not going to buy a hotdog I'm going to buy a hamburger and so that's when we say that this cross elasticity demand is positive the two goods are substitutes. Now let's look at the cross elasticity demand for beer, so what happened to the demand for beer when there was a 20% increase in the price of hotdogs? Well, demand for beer went down by 40%. I'm going to say negative 40% divide by what do we have we had a 20% increase in the price of hotdogs. So we've got a negative number and so that means that the two goods are complements.

That means when I see the two goods are complements I mean that hotdogs and beer based on this fact that this cross elasticity number is negative hotdogs and beer are typically consumed together and so if you increase the price of hot dogs by 20% it's leading to a decrease in the quantity of beer demanded. Even though the price of beer hasn't changed, people buy hot dogs and beer together so if you make hot dogs more expensive people are going to buy less beer and so that explains why this number is negative that the goods are complements.