Nominal Income and Real Income - Online Tutor, Practice Problems & Exam Prep

Nominal income refers to the actual dollar amount received, such as wages or rent, while real income adjusts nominal income for inflation, reflecting purchasing power. To calculate real income, divide nominal income by the Consumer Price Index (CPI). For example, if nominal income is $25,000 and CPI is 1.20, real income is approximately $20,041.33. Understanding these concepts is crucial for analyzing economic conditions and the impact of inflation on financial well-being.

Nominal Income and Real Income

So just like we can talk about nominal interest and real interest, we can discuss nominal income and real income. Just like with interest, the difference between the nominal and the real is going to have to do with inflation. When we're discussing nominal income, nominal income is the actual number of dollars you receive. So when you go to work and they pay you your salary of $10 an hour, that $10 an hour is your nominal income, right? The number of dollars received as wages or salary; rent could be profit. Whatever type of income you have, right? So if you just have a job, we're talking about wages or salary, but if you're a landlord, it's rent; any of this is nominal income.

So when we talk about real income, we're adjusting that nominal income for inflation. It's adjusted for inflation. Remember how inflation affects our income is the same way it affects interest; it's going to make our purchasing power less. Real income measures the amount of goods you can buy. So if you're thinking about what you could buy in one year and what you could buy in another year, that would have to deal with your real income, your purchasing power of that money.

Let's go ahead and use a calculation for real income. We're going to take our nominal income, what we're earning, and we're going to divide it by the price index. This is the CPI. When we're talking about the price index, we're talking about the CPI here, and notice that it's normalized to 100. So if they give you the CPI as, say, 110, we would have to adjust it to be treated as 1.10, more of a decimal rather than a percentage here. A CPI of 110 means that prices are 1.1 times the level of what they were in the base year. So the base year would have had a CPI of 100, and now it's 110. That means we've increased by essentially 10% since the base year.

If nominal income increases at the same rate as the price index, then what happens to the real income? Think about it. If your nominal income is increasing, and the price level is increasing at the same rate, then your real income is going to stay constant because what's happening is if you're earning more money—say, you're getting a raise from $10 to $12 which is a 20% raise—but at the same time, the price of everything goes up by 20%, which is what it's saying here. If nominal income, your $10 wage going to $12 increases at the same rate as the price index, the prices of everything also went up by 20%, you can purchase just the same as before. Your real income is going to stay the same there.

In essence, the main formulas you're going to want to know here are how to calculate real income, which is just taking the nominal income divided by the price index, and you're also going to be able to calculate the change in your real income by noting the change in the nominal income and the change in the price level. We've got an example that we're going to practice using these formulas. Let's do that in the next video.

Nominal Income and Real Income

DJ Money Face is the world's best DJ. In 2017, he earned $20,000 playing the most popular music at nightclubs. He spent many nights practicing, twisting knobs and holding one earphone of the headphones to his ear. Audiences were so thrilled by his iTunes playlist that in 2018, he was able to earn $25,000 selecting the most popular music. Use the following information regarding CPI to answer these questions. So we're going to go through this together. We're going to calculate DJ Money Face's real income in 2017, and we'll take a pause. I want you guys to try and calculate the 2018 income and also use the percentage change formula to calculate the percentage change in his real income. Alright? So let's go ahead. We're going to start here together, and then you guys can try the other ones. So let's start with A, his 2017 real income.

Remember, when we're calculating real income, we just want to take the nominal, and we're going to divide it by the price index, the CPI, and we're going to do it in 100, right, as a decimal. So let's go ahead and do this here. What was his nominal income in 2017? We have it right up here; in 2017, he earned $20,000. So the numerator here is going to be 20,000, and we'll divide it by the CPI in what year? We're going to use the CPI from 2017, right? In 2017, the CPI was 118, so we got to convert that to a decimal. So 118, that's like 118% of the base year prices, so it's gone up by 18%. So we're going to convert it to 1.18. We moved the decimal over two times, and now we've got a decimal instead of a percent. So we're going to divide by 1.18 here, and we'll do the equal sign right down here. So in 2017, what is his real income? So let's see what that is. Come on, calculator. Don't fail me now. Alright, $20,000 divided by 1.18 gives us a real income of $16,949.15, okay? $16,949.15, that is his real income in 2017.

So, what does that mean? What does it mean that that's his real income? That means if we compared it to the base year in 2005, notice 2005 is our base year here. They didn't tell us, but we can gauge that it's the base year because it's around 2005. So the price level was, what we're saying is that if this money was earned in 2005, it was worth $16,949.15. So, what he earned, the $20,000, this is a better explanation, the $20,000 that he earned in 2017 would have been the equivalent of earning $16,949 in 2005, okay? So basically the same purchasing power, right? He's able to purchase the same amount of goods because inflation has taken place since 2005.

Alright. Let's take a pause here, and you guys try to solve the real income in 2018, and then we'll do another video for the final one, question C. Cool.

Nominal Income and Real Income

Alright. Let's see how you guys did with the 2018 real income. So in 2018, his real income, well, we're going to take his nominal income in 2018, which was $25,000, and we'll divide that by the CPI. And which CPI are we going to use? The 2018 CPI. Right? 2018, and that was 1.20. So 1.20 is our denominator here. Let's go ahead and calculate 25,000 divided by 1.20. It's going to give us a real income of $20,833.33. So now what we're talking about is if, in 2018, he earned $20,833.33 in 2005 money, right? It has the same purchasing power as in the base year $20,833 of purchasing power. Cool? Alright. Let's pause here and then let's try question c in the next video.

Nominal Income and Real Income

Alright. Now let's calculate the percentage change in DJ Money Face's real income. Now there's 2 ways we can go about this. We can find the percentage change so if we go above remember the percentage change in real income well that's the percentage change in nominal income minus the percentage change in the price level and that will approximate the percentage change in real income. But we've already calculated the real income, right? So remember, anytime we're doing percentage change, it's just new minus old divided by old. New minus old divided by old. Right? That's how we do percentage change formulas. So, I'll go through both of them just so you see that we get approximately the same answer to 2 decimal places here. So let's go ahead and do let's start by just taking the real income and finding the percentage change between our real incomes. So percentage change in real income. So we would take the new which was 20,000 833.33 minus the old which was 16,949.15, right, the 2018 minus 2017 real income and divided by the old, 16,949.15. Okay. So what's that going to give us here? If we do this math, 20,833.33 minus 16,949.15, and we divide that by 16,949.15, and it gives us approximately 0.23 and that's as a decimal, so that equals 23% approximately. 23% change in real income when we calculate it that way.

Now, let's calculate it the other way where we're going to take the percentage change So remember, in our formula, we had the percentage change in real income, I'll put RI for real income, is equal to the percentage change in nominal income minus the percentage change in CPI, right? The price level, okay? So instead of if we hadn't calculated the real income already, we could have just taken the nominal income and the price level and found the percentage change in each of those. So let's go ahead and do that. Let's start with the nominal income and the nominal income was 25,000 in 2018, 20,000 in 2017 and we'll put 20,000 in the denominator, right? New minus old divided by old and we'll subtract from that this percentage change in CPI. So CPI was 120 in 2018, 118 in 2017, and divided by 118. Right? New minus old divided by old. So let's get each of these numbers. So let's do 25,000 minus 20,000 divided by 20,000. That gives us 0.25. And what about the other one? 120 minus 118 divided by 118. Whoops. Let me try that again. 120 minus 118 divided by 118, it gives us 0.017. We'll round it to there, and what does that give us? So, the percentage change in real income would be the difference of these 2, which is equal to 0.25-0.017=0.233. So again, this is an approximation. This is like when we had our Fisher equation and we got an approximation here. Same thing going on here but to a certain extent gets us approximately to the correct answer. Right? 23% as well. So that's the easy way to do it. Let me get out of the way. When we have just the nominal and the CPI. So if they had given you the percentage change in the nominal income and the percentage change in CPI, well, you would know just to subtract the 2 just like in our equation. If they had just given you those percentage changes in a multiple choice for example, well, you would just subtract them to get an approximate for the percentage change in real income. Cool? Alright. So a bit of math there but nothing too crazy. Just a percentage change formula and putting it to work. Alright. So that's how we calculate real income. Let's go ahead and move on to the next video.

Here’s what students ask on this topic:

What is the difference between nominal income and real income?

Nominal income refers to the actual dollar amount received, such as wages, rent, or profit. It is the face value of income without any adjustments. Real income, on the other hand, adjusts nominal income for inflation, reflecting the purchasing power of the money. This means real income measures the amount of goods and services that can be bought with the nominal income. To calculate real income, you divide the nominal income by the Consumer Price Index (CPI). This adjustment helps understand the true value of income over time, considering the changes in price levels.

How do you calculate real income from nominal income?

To calculate real income from nominal income, you use the formula:

$\frac{\mathrm{Nominal\; Income}}{\mathrm{CPI}}$

For example, if your nominal income is $25,000 and the CPI is 1.20, the calculation would be:

$\frac{25000}{1.20}=\mathrm{20,833.33}$

This means your real income, adjusted for inflation, is approximately $20,833.33. This value represents the purchasing power of your nominal income in terms of the base year's prices.

Why is it important to understand the concept of real income?

Understanding the concept of real income is crucial because it provides a more accurate measure of financial well-being and economic conditions. While nominal income shows the amount of money received, it does not account for inflation, which can erode purchasing power. Real income, adjusted for inflation, reflects the true value of money in terms of what it can buy. This helps individuals and policymakers make informed decisions about wages, investments, and economic policies, ensuring that income growth translates into actual improvements in living standards.

How does inflation affect nominal and real income?

Inflation affects nominal and real income differently. Nominal income is the actual dollar amount received and is not directly impacted by inflation. However, inflation reduces the purchasing power of nominal income, meaning the same amount of money buys fewer goods and services over time. Real income adjusts nominal income for inflation, providing a measure of purchasing power. If nominal income increases at the same rate as inflation, real income remains constant. If nominal income grows faster than inflation, real income increases, indicating an improvement in purchasing power.

What happens to real income if nominal income increases at the same rate as the price index?

If nominal income increases at the same rate as the price index, real income remains constant. This is because the increase in nominal income is offset by the rise in prices, leaving purchasing power unchanged. For example, if your nominal income rises from $10 to $12 per hour (a 20% increase) and the price index also increases by 20%, the real income calculation would show no change in purchasing power. This means you can buy the same amount of goods and services as before, despite the higher nominal income.