How to calculate the income elasticity of demand? So income elasticity of demand measures how your demand for a good or service changes as your income goes up or down. As you become wealthy or poor what happens for example, to your demand for candy. We can calculate it with a simple formula here where we take the percentage change in the quantity demanded, let’s say the percentage change in the quantity of candy that you demand divided by the percentage change in your income that occurs.
So let’s say for example that your income was to go up 10% and you had a corresponding percentage change in the quantity demanded of candy of 50%. So we’d say your income elasticity of demand is five. If you’re wondering how do we calculate the numerator and the denominator. Well, to get the percentage change in quantity demanded we take the change in the quantity demanded, so the change in the quantity of candy that you’re demanding is divided by the average quantity demanded. Again to get the denominator which is the percentage change in income, we take the actual change in your income divided by your average income.
I know it’s a little abstract, so let’s go into an example and I’ll show you some actual numbers. Let’s say that you make $200 a month. So your income is $200 a month that you get from working as a clown at children’s parties but then a YouTube video of you getting hit by a car while wearing your clown suit goes viral. People feel bad that this clown was just out walking and got hit by a car, people feel bad for you, they send you donations they set up a GoFundMe site and now your income is increased to $350 a month. Now you have become wealthier you’ve got more income and so that’s going to change how you demand certain items.
Let’s think about the food that you eat. Let’s say that you eat rice, you eat pasta and you eat chocolate bars. So when your income was $200 a month you demanded let’s say 10 bags of rice, 8 boxes of pasta, and 2 chocolate bars. That was what your demand was but now that your income is $350 a month you’re only demanding 5 bags of rice. So your demand for rice is actually going down, you’re eating less rice but 2 additional boxes of pasta you’re demanding and you’re demanding 13 more bars of chocolate.
So we can calculate the income elasticity of demand for each of the items. Again remember that what is the income elasticity of demand? We can think of it as the percentage change in the quantity demanded divided by the percentage change in income. Now, remember the formula was given at the beginning of the article. So what we had to do to calculate the percentage change in quantity demanded is we have to do the actual change in demand which is we went from ten to five. So it was negative 5. Then we need to divide that by the average quantity demanded, which is ten plus five divided by two, that’s 7.5. So that’s going to be the numerator, that’s going to give us the percentage change in quantity demanded. I’ll just calculate that and it’s negative 60.7%. Actually, this is negative five divided by seven point five times 100. So we’re going to multiply everything here by a hundred to get it to a percentage from a proportion.
Now in our denominator, we got the percentage change in income. We had $200 to $350 so we went up by $150 that’s our actual change in income then we have to divide it by the average income is 200 plus 350 divided by 2 which is 275 and that’s going to be the same this percentage change in income which is 54.5%.
That’s going to be the same for each of these items because your income change is the same for every item. What’s going to change is the percent of change in quantity demanded. So now let’s think about and we can go ahead and let me just finish this out here, so that is going to give you a negative 1.2. So we will say that the demand for this good, we will call that inferior demand and an inferior good means that as your income goes up you actually buy less of these goods that’s what I mean when we say that this is an inferior good.
Now with pasta we had an increase, so we can tell right away it’s not going to be an inferior good but now we need to calculate out using our formula. So the percentage change in quantity demanded is going to be our change in demand divided by our average demand. So 8 + 10 is 18 divided by 2, which gives us 9. Now in the denominator again we have the exact same thing 150 divided by 275 because the income has not changed. So we have 22.2% remember, we multiply everything by a hundred to get a percentage. Then we are going to divide that by 54.5% and that’s going to give us 0.41 and so we would say that this is a normal good and when we think normal good what we mean is if your income goes up you become wealthier you buy more of the goods. So it’s a normal good and we’d say normal and inelastic good because a 1% increase in your income increases demand for the good but by less than 1% it’s a 0.41. We talked about it in another article.
Now with the chocolate, we see that Wow chocolate went from 2 to 15, so you’re a clown that really likes chocolate so we’re going to have a big change here. We’re going to have 13 as our actual change in the chocolate bars and the change in demand divided by the average demand which is 8. Then for the denominator, again we take the 150 divided by 275. So what do we have 152.9% increase in the numerator and then we have 54.5% in the denominator and so if we calculate that out that gives us 2.8 income elasticity of demand. So it is a normal good it is in normal good but it’s an elastic good.
So let’s just do a quick review so for the rice we said that it is an inferior good and even if you didn’t know that people buy less rice’s when they become wealthier they start buying all fancy things like chocolate, even if you didn’t know that if you just look at the income elasticity of demand it’s negative anytime the income elasticity of demand is a negative number that means that it is an inferior good. Now with the pasta, the pasta is a normal good because the income elasticity demand is positive but it’s inelastic because it’s positive and less than 1. So if income elasticity demand is positive but less than 1 then you say the good is normal and inelastic. Chocolate is different, a 1% increase in income brings more than a 1% increase in the quantity demanded for chocolate. Your income goes up a little bit your demand for chocolate goes up a lot and so, therefore, we say chocolate is a normal elastic good.