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Income Elasticity Formula

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Source: Image of Income Elasticity Graph for Normal Good created Kate Eskra, Image of Income Elasticity Graph for Luxury Good created by Kate Eskra, Image of Income Elasticity Graph for Inferior Good created by Kate Eskra

Hi. Welcome to economics. This is Kate. This tutorial is Income Elasticity. As always, my key terms are in red and my examples are in green.

So in this tutorial, I'll be teaching you how to calculate income elasticity, and we'll look at the impact on three different kinds of goods. Normal, luxury, and inferior. OK. So you already know the very common sense idea that as we make more money, we tend to buy more. But is there anything that you can actually think that we buy less of when we make more money?

There are a few examples of things. So it's really not the same for all goods. And the idea of elasticity in general is how much do we change our minds? So how much more or how much less do we buy as something is changing? OK. So income elasticity is different than own price or cross price elasticity, because we're talking about our income changing instead of price.

So it's an economic measure of change in relation to income and demand for normal, inferior, and luxury goods. And here is the equation. We were able to simplify this down to the percentage change in quantity divided by the percentage change in income. Now the order is going to matter here, because it's going to matter whether our coefficient is negative or positive. It will be different depending on what type of good it is. And I'll get to that in a few slides.

So we have an initial quantity minus an initial-- I'm sorry, minus our new quantity, and then those two added together. An initial income minus the new income, and then those two added together. So that will matter, the order. So just be careful about that.

OK so the first example I'd like to use is for Nike. So let's see. If our income rises, will we buy more or less Nike apparel? So my example is Tom. Tom's income goes from $20,000 up to $40,000. He used to buy two pair of Nike running shoes. Now he can afford three.

OK. So notice this demand curve looks different than a normal demand curve that you're used to seeing, but that's because the axes are different. This is the same. It's the quantity of Nike shoes. But since we're not talking about the relationship between quantity and price for income elasticity, I replaced price with Tom's income. So notice these two points just represent exactly what the example showed. At $20,000 he bought two pair of shoes. When his income rose, he's buying three.

So notice that there's a positive relationship between Tom's income and the number of shoes he buys. And that is-- you're seeing that here by the positive slope of the demand curve. OK. So here's our equation again. What we're going to do is we're going to be looking at the percentage change in the quantity of Nike he's buying, and in the denominator we'll be looking at his income.

So if we put those number in-- again, carefully keeping in mind we have to remember that we're doing the initial quantity minus the new quantity, and then they're adding together here. The initial income of Tom minus his new income divided by them added together. Notice both the numerator and denominator are going to be negative, which will cancel out giving us a positive 0.61.

But what exactly does this tell us? Well, here it is. So with own price or cross price elasticity, we look at price in relationship to quantity. So we know that as the price of Nike goes up, people tend to buy less of it. But that's not what this tutorial's on. It's on income elasticity, which is percentage change in quantity divided by percentage change in income.

So if like in our Nike example the coefficient is positive, that tells us that these two move in the same direction. As income rises, we buy more. As income falls, we buy less. Most goods are normal. Most goods we behave this way. And Nike, it turns out in Tom's example, is a normal good.

If the coefficient were to be negative, then the good would be inferior because that would suggest that as our income rises-- the denominator would be positive-- our percentage change in quantity, we would buy less of it. So 1-- the numerator would be negative and the denominator would be positive. Or in the opposite example, as our income fell, we would buy more of an inferior product. And I'll give you an example of one of those in a little bit.

So a normal good is defined simply as goods for which demand increases as income increases. Again, these are most goods. Now let's look at a special kind of normal good. I'm using the example here of a vacation. So here notice that when our income is $40,000, we actually can afford to go on vacation not at all. We go on no vacations in a year. As our income doubles to $80,000, now we're going on vacation three times in a year.

So again, we're looking at our income on the y-axis and the quantity on the x. There's a positive relationship between income and vacations purchased, just as there was with Nike shoes. So this is going to be a normal good. But it's a special kind of normal good, and let me talk about that.

So again here, we have the quantity vacations, our income. We have to be very careful on both the numerator and denominator to do initial quantity minus new quantity. Initial income minus new income. And again, we get two negatives which cancel out and will give us a positive number, right?

But our last positive number was a decimal. It was 0.61. This is a lot larger. With the elasticity of 3, we are going to classify this, though, as a luxury good. Coefficients that are greater than 1 tell us that when our income increases let's say by 1%, our purchases of the good increase by more than 1%. So actually, we weren't able to afford any vacations at all before our income changed. And now all of a sudden, we're able to afford three.

So that's what's considered a luxury good. Other examples would be things like high end luxury cars and artwork. Things that you're not purchasing anything of before your income increases. OK. So luxury goods are defined as a good that offers better quality and features which is consumed when income rises.

All right. Let's look at our last example. So let's talk about a generic cereal for this example. Here we'll be graphing the quantity on the x-axis and our income, again, on the y-axis. Now this curve is downward sloping. This is showing that when our income is $40,000, we buy, let's say, 50 boxes of generic cereal a year.

When our income rises to $60,000, we actually don't buy any generic cereal anymore. OK. So there's a negative relationship between our income and how much generic cereal we're purchasing. So as we make more money, we stop buying generic products and we're going to opt for name brands.

Same formula that I'm using here. The order is going to matter again. So if we take Qa and Qb and plug in the numbers, here now we get a positive numerator but we get a negative denominator. So that's going to leave us with a negative number. And remember, a negative number tells us that it's an inferior good, because there's a negative relationship between income and our consumption. As our incomes rise, we buy less of these. As our income falls, we would buy more. So inferior goods are goods for which demand decreases as income increases.

All right. So in this tutorial, we talked about how income elasticity measures how consumers respond to an income change by buying more or less of certain goods. And the coefficient tells us how much consumers are responding and it also tells us by the sign of it whether the goods are normal, luxury, or inferior. Thank you so much for listening. Have a great day.