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Real and Nominal Values and the Price Index

Inflation is what occurs when prices go up over time.

Values that have been adjusted for inflation are called ______values.
GDP that has been adjusted for inflation is called ______GDP.

Real values are calculated using other (old) prices (ones that don't have inflation)
Real values are also called constant values, since they are constructed treating prices as constant over time.

Nominal values are calculated using prices of the current year (including inflation in prices). Because they use prices that are current with the production amounts, nominal values are sometimes called current values.

Notice that nominal values are the ones we get if we don't care about inflation, and just take all the numbers we are given. Real values require someone to correct for inflation or do some kind of reconstruction. Real values are created, while nominal values are just sort of the ones you come across. However, the real values tells us what is really going on under the veil of prices, or under the surface.

How we find real values is to use something called a price index. A price index is a number used to compare sets of prices. We could construct price indexes whenever we have prices to compare, such as when we visit different grocery stores.

Suppose I shop at Basher's and you shop at Allforfun's. We each buy items on a list of groceries, and our list of groceries is the same (no impulse buying, now).
I spend $110 at Basher's, while you spend $100 on the same groceries at Allforfun's.

If the groceries cost $100 at Allforfun’s and $110 at Bashers, we can create a "price index" for each store just by using the totals. We set one of the price index numbers at 100. We'll do that for Allforfun's.
If the "Shopping Price Index" at Allforfun’s is 100, then the "Shopping Price Index" at Bashers is 110. For each list of groceries that costs us $100 at Allforfun's, the same list would cost us $110 at Basher's.

Since the only difference between how much we spent at each store was due to the differences in prices (since the list of groceries was the same), the ratio of spending has to be the same as the ratio of prices (or price index numbers)

This is not much different from the way price index numbers are created by the goverment, but they don't make them to compare grocery stores.

Notice that we can use the relationship between the spending ratio and the price index ratio above to answer other questions about the expense of shopping in the two stores.
Suppose your neighbor spends $200 at Bashers.
How much would those same groceries cost if they were bought at Allforfun’s instead?

Use the relationship

remember, the price index at Basher's is 110 and the price index at Allforfun's is 100

We know the spending at B (Basher's) and want the spending we would do at A (Allforfun's) to buy the same list of groceries, so, solving for the spending at A gives us

or
(^{spending at B}/₁₁₀)x100=
spending at B x (100/110)
$200 x 100/110 = $181.82

If the math gets in your way, you might want to consider that we are taking the spending at B, dividing out the prices of B, and multiplying in the prices of A to get the spending of A.

We could do the same thing for different years rather than for different grocery stores. Suppose
Shopping Price Index 2002 is 110,
Shopping Price Index 2001 is 100.
If someone spends $200 in 2002. How much would those same items have cost in 2001?

The relationship is still the same:

But since the stuff being bought in 2002 is being paid for in 2002 prices, the spending on the (2002) list in 2002 is the "nominal spending" for 2002. And, when we adjust it for 2001 prices, we are constructing real spending. So, we can show the list as

(^{spending 02 (02 prices)} /₁₁₀)x100=
spending 02 (02 prices) x (100/110)
$200 x ¹⁰⁰/₁₁₀ = $181.82 to buy those same groceries in 2001
Here again, we are dividing by the prices we have but want to eliminate (2002 prices) and multiplying by the prices we want to replace them with (2001 prices).

Here' another example: If spent $400 in 2002. How much would it cost to buy that same stuff in 2001?

$400 x (¹⁰⁰/₁₁₀)= $363.64 or
(^$400/₁₁₀)x100=$363.64

Now, some terminology. When price indexes are created the year which is used as a comparison is called the base year. The price index for this year is arbitrarily set at 100 (so, 2001 was the base year in our previous example). If the spending on a list of items in the base year is not a nice $100, we can still create price index numbers for the other year, using the price ratio relationship we established, and setting the price index for the base year to 100.

For example, if the amount spent on a particular list of goods in 1992 is $6.00 trillion, and if we wish this to be the base year, we say that 100 is the price index in 1992 (or "1992=100" for short).
If the amount of money that would have to be spent to buy the same list of goods in 1993 would be $6.12 trillion, we can find the price index for 1993, using the following relationship:

We know everything but the price index for 1993, so we have

or

= 1.02 x 100 = 102
This is how a price index can be found from any two years' of spending.

Once we have that information, we can easily convert the spending in one year to the equivalent in another year....

If year B is the year for which we have some nominal value, this becomes

So, to find the nominal value if you are given a real value, you use the following:

and to find a real value from the nominal, you use the following:

which is the same as

In all of these calculations, to convert from the values of one year to those of another year, you take

Here's an example:
In 1980 your parents made $20,000
In 2001, you made $35,000. What is the real value (in 1980 dollars) of your 2001 income?
CPI (price index) 1980=82.4
CPI (price index) 2001=177.1

Answer
$35,000 x ^82.4/_177.1=$16,284.58
Notice, you made less in 2001 (if you converted it to 1980 dollars) than your parents made in 1980.

You could also do it the other way...
In 1980 your parents made $20,000
In 2001, you made $35,000. What is the real value (in 2001 dollars) of your parents’ 1980 income?
CPI (price index) 1980=82.4
CPI (price index) 2001=177.1
$20,000 x ^177.1/_82.4 = $42,985.44