Now let's talk about another elasticity of demand, the income elasticity of demand. So remember 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 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 going to answer the question: how does quantity demanded respond to a change in consumer income, right? When we were doing price elasticity of demand, it was the same thing except how does quantity demanded 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 in 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 is in the denominator. The quantity is always going to be in the numerator for all of our elasticities. Most of them are going to be quantity demanded, but when we're talking about quantity supplied, we'll have quantity supplied in the numerator. But here we go, income in income, right. Easy peasy. So let's go ahead and use our midpoint method, right. We're still going to use that same method that we already know of, except we're just going to update it that it's going to be dealing with income instead of price, right? So our second variable instead of it being price, now it's going to be income, but our calculations are going to basically the same except for this one added step here where we're going to notice that positive and negative numbers do matter in this case. This is how we're going to make our analysis when we have positive or negative numbers, they're going to help us identify normal and inferior goods. So although all our steps are the same, we're going to have an added step 6 where we're going to analyze the direction of the movement of quantity and the direction of the movement of income 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 6. Notice I've got that step 6 here, which we're going to 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 $9,000. Although price did not change, consumer income increased from $9.50 per week to $10.50 per week, causing the quantity demanded to increase to $11,000. What is the income elasticity of demand for caviar? So let's go ahead and start by marking off our quantities and our incomes, right. We've got quantity demanded of $9,000, one to $11,000, and our income, right, not price this time. We're talking about income elasticity, $9.50 to $10.50. But check it out. At the beginning of the problem, they did give us a price. They said the price was $75, but they also said the price did not change, which is good for us, right, because we want to hold everything constant. This goes back to that ceteris paribus; the only thing we want to change is the income and see how that affects demand, right? So the idea here is the price did not change; the 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. Steps. Alright, so step 1 is where we do our subtraction. So let me make 2 columns. We've got our quantity demanded and notice this is one of our small changes is that our second column is going to be income, but notice how similar the steps are.
Let's go with step 1. I'm going to move this over to save some space. Quantity demanded and right here income. So step 1 just like before, we’re going to subtract the 2 quantities and it still doesn't matter which one you do first just as long as we include that step 6 where we're going to analyze the positives and the negatives. So for now, I just like to keep the math simple and just keep all these positive numbers while I do this. So income $10.50 $9.50 is going to give us a change of a $1.00. Alright. Step 2, just like before, we're going to sum them. So now we've got 11,000 plus 9,000 equals 20,000, and the same thing for income. Let's sum the incomes. $10.50 plus $9.50 is going to give us $20.00. Step 3 is where we divide our answer from step 2 by 2. So step 3 right here. We are going to have 20,000 divided by 2 which is just 10,000. How about income? Income, we're going to have $20.00 divided by 2 which is $10.00. Step 4, just like before is hey, that rhymed. Step 4, that's where we just divide our answer from step 1 and our answer of step 3. So we're going to get 2,000 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 4 is the percent change in quantity demanded and on the other side, $1.00 divided by $10.00, right, answer from step 1 divided by the answer from step 3 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 5 here. So I'm going to put step 5 because we do have a step 6 now, and step 5 is where we're going to calculate our income elasticity, which is going to be the 0.2 divided by the 0.1. Right? So 0.2 divided by 0.1, that is equal to 2. Our answer here is 2, but let me get out of the way, but we have to see is it a positive 2 or a negative 2? 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 $9,000 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 going to be a positive in the denominator. Now let's look at the income. Income was $9.50 and 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 2.
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 9,000, and a decrease in income from $10.50 to $9.50. We would have gotten the same answer. We would have gotten a negative on the top, a negative on the bottom, problem, and see whether quantity increased and whether income 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 answer to our income elasticity which is 2, but how do we analyze that right? This is how we're going to analyze our answers. So when we get a positive number that's greater than 1, we call this 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 our increase in income, right? And this is because now we have more money to spend; we spend it on luxury items. Compared to this one where we have a positive answer but it's less than 1, 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, but this is in this case a necessity. It's stuff that we were already buying before, 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 going to analyze here. So in this situation, we got a positive number that was greater than 1; it's income elastic, elastic; we're going to say it's a normal good, and that it's a luxury good. Alright, so we were 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.
