Income Elasticity of Demand

Now let's talk about another elasticity of demand, The income elasticity of demand. So remember um that income was one of the things that could shift our demand curve. Right? When we studied that in supply and demand. When we were shifting our demand curve, consumer income could affect the demand for goods, Right? And that's when we talked about normal goods and inferior goods. Right? So an increase in income caused an increase in the demand for normal goods. Right? That kind of uh topic. So what we're gonna have here is a similar discussion where the income elasticity of demand is going to help us identify goods as normal goods or inferior goods. Right? So let's go ahead and check out the equation. We've got income elasticity of demand, right? It's gonna answer the question, How does quantity demanded, respond to a change in consumer income? Right. When we're doing price elasticity of demand, it was the same thing, except how does quantity demanded affect uh respond to a change in price. Right. So notice the only thing that's changing with our formula here is first the name. Right Now we're talking about income elasticity of demand. And now, instead of price and the denominator, we've got income in the denominator and you should be able to notice that we've got this pattern going that whatever the name of it income elasticity, income in the denominator quantity is always going to be in the numerator for all of our elasticity ease. Most of them are gonna be quantity demanded. But when we're talking about quantity supplied, we have quantity supplied in the numerator. But here we go income and income. Right, easy peasy. So let's go ahead and use our midpoint method. Right? We're still gonna use that same method that we already know. Um Except we're just gonna update it that it's going to be dealing with income instead of price. Right? So our second variable instead of it being priced now it's gonna be income. But our calculations are gonna stay basically the same. Except for this one added step here where we're gonna notice that positive and negative numbers do matter in this case. This is how we're gonna make our analysis is when we have positive or negative numbers are gonna help us identify normal and inferior goods. So we although all our steps are the same, we're gonna have an added step six where we're gonna analyze the direction of the movement of quantity and the direction of the movement of income uh to get our positives and negatives. Okay so let's go ahead and do an example where we're going to use our same method and then we'll have that added step six notice. I've got that step six here which We're gonna do after. We've gotten our answer. So let's go ahead and use these steps in this example at a price of $75 per serving of caviar. The quantity demanded is 9000. Although price did not change consumer income increased from 950 per week to 1050 per week, causing the quantity demanded to increase to 11,000. What is the income elasticity for demand of caviar? Um so let's go ahead and start by marking off our quantities and our incomes right? We've got quantity demanded of 9000 went to 11,000 And our income right? Not price. This time we're talking about income elasticity. 950-1050. But check it out at the beginning of the problem. They did give us a price. They said price was $75. But they also said price did not change, which is good for us, right? Because we want to hold everything constant. This goes back to that Severus Paradise. The only thing we want to change is the income and see how that affects demand. Right? So the idea here is price did not change. Price doesn't even come up in our formula right up here, percentage change in quantity demanded, divided by percentage change in income. We don't talk about price at all there. So price is irrelevant. Let's go ahead and do our steps, right? So step one is where we do our subtraction. So let me make two columns. We've got our quantity demanded and notice this is one of our small changes. Is that our second column is gonna be income. But notice how similar the steps are. Let's go with Step one. I'm gonna move this over to save some space uh quantity demanded. And right here income. So step one, just like before we're going to subtract the two quantities and it still doesn't matter which one you do first. Just as long as we include that step six where we're gonna analyze the positives and the negatives. So for now I just like to keep the math simple and um just keep all these positive numbers while I do this. So income 10 50 minus 9 50 is going to give us a change of 100. Alright step to just like before we're gonna some them. So now we've got 11,000 plus 9000 equals 20,000. And the same thing for income. Let's sum the incomes 10 50 plus 9 50 is going to give us 2000. Step three is where we divide our answer from step two x 2. So step three right here uh we are going to have 20,000 divided by two which is just 10,000. Um How about income income? We're gonna have 2000 divided by two which is 1000 step four. Just like before is hey that rhymed step four, that's where we just uh divide our answer from step one. And our answer of step three. So we're gonna get 2000 divided by 10,000. And that is going to give us 0.2 right 0.2. That is our percent change in quantity demanded right just like before our answer to step four is is uh the percent change in quantity demanded. And on the other side 100 divided by 1000. Right answer from step one divided by answer from step three is 0.1. And that is our percentage change not in price. This time our percentage change in income, right? Which is the denominator of our income elasticity. So let's go ahead and do step five here. So I'm gonna put step five because we do have a step six now. Um And step five is where we're going to calculate our income elasticity which is gonna be the 0.2 Divided by the 0.1. Right? So 0.2 divided by 0.1. That is equal to the to to our answer here is to but let me get out of the way but we have to see is it a positive two or a negative two? We're not sure yet. We need to go back to the problem and analyze whether the quantity change was positive or negative and whether the income change was positive or negative. Let's start with quantity quantity demanded, started at 9000, then income changed and quantity demanded increased to 11,000. So we saw an increase in quantity demanded that was a positive change. So that is going to be a positive quantity demanded. So it's gonna be a positive in the numerator. Now let's look at the income income was 9 50 it increased to 10 50. So easy enough here we got a positive in the denominator as well. So we are going to have a positive two. Okay so the same thing could have happened if we had a decrease in quantity demanded. Right? Let me just erase these and pretend we had a decrease in quantity demanded from 11,000 to 9000 and a decrease in income from 10 50 to 9 50. We would have gotten the same answer. We would have got a negative on the top, a negative on the bottom, they would have canceled out and we would have got a positive two again. Right? So this is the last step is where you just have to look back in the problem and see whether quantity increased and whether income increased. Right? So an increase is going to be a positive number and a decrease is a negative number. So there we go. We have gotten our, our answer to our income elasticity is to but how do we analyze that? Right. This is how we're gonna analyze our answers. So when we get a positive number that's greater than one, this we call income elastic and this is a normal good. That's a luxury. This is a good that when our income goes up we buy even more of it than our increase in income, our quantity increases more than than our increase in income. Right? And this is because now we have more money to spend, we spend it on luxury items um compared to this one where we have a positive answer but it's less than one. So we get some sort of decimal like 0.5 or 0.7 where it's still positive, it's still a normal good because we made more money and we spent more on it, right? Remember from our demand shifts if consumer income increases, we spend more on normal goods, so we would expect to get a positive income elasticity of demand here. Um But this is in this case a necessity, it's stuff that we were already buying before, so we're not gonna buy much more of it, We're still gonna buy maybe a little more because we have more money but we're not gonna buy as much as we might with a luxury good. Where now we have more money so we have money to play around with this luxury stuff. And when we get a negative answer, that's when we're talking about an inferior good, right? Because that would be where we have an increase in income and a decrease in quantity demanded, or the opposite, a decrease in income and an increase in quantity demanded. So that's the case of inferior goods, just like we discussed in supply and demand, the shifts in demand. Cool. So that's how we're gonna analyze here. So in this situation we got a positive number that was greater than one. Its income elastic, we're gonna say it's a normal good and that it's a luxury good. Alright, so we're able to get that just from our income elasticity of demand that we calculated. Cool, let's go ahead and do some practice problems with income elasticity of demand.

Johnny Clutch just got a raise from $900 per week to $1100 per week. As a result, he decreases the amount of ramen noodles he buys from seven cartons a week to one carton a week. For Johnny, ramen noodles are:

• A. Normal Goods, Necessity
• B. Normal Goods, Luxury
• C. Inferior Goods
• D. Substitute Goods

Johnny Clutch just got a raise from $950 per week to $1,050 per week. As a result, he increases the number of concerts he attends by five percent. His demand for concerts is:

• A. Income elastic
• B. Income inelastic
• C. A horizontal line
• D. A vertical line

A twelve percent increase in consumer income has caused the quantity of orange juice demanded to increase from 24,000 to 26,000. The income elasticity of demand for orange juice is:

• A. 0.25
• B. 0.33
• C. 0.50
• D. 0.67