# Real and nominal value interpretation

When price is deflated according to some base year, what does the real value mean? E.g. if we are deflating \$5.000 from year 2000 (base year, deflator=1) to 1980, using the CPI 1.6 from 1980, we get \$3.125.

Is this real value equivalent to $5.000 in 1980? • Simple answer: this example would mean that if you had \$3125 in 1980 then you could afford to buy the same amount of stuff as if you had \$5000 in 2000. – Ubiquitous Jun 23 '15 at 15:04 • @Ubiquitois Actually, it should be 5000 x 1.6 = 8000 dollars in 1980 which is the same as 5000 dollars in 2000 (which seems correct due to 1.6 higher prices in 1980). I have now realized that I also have mistake in the main question where I have divided base period value by deflator, thus causing possible confusion. Instead, nominal value from 1980 (e.g. 5000 dollars) should be divided by deflator which yields 3125 dollars. This seems right because we would buy less in 1980 in this example. Anyway, thanks for your effort. ;) – Quirik Jun 23 '15 at 15:21 ## 1 Answer The formula for calculating the real value of an amount$x$in a given year using dollars from a particular reference year is $$\frac{x_{baseyear}}{x_{current year}}=\frac{CPI_{base year}}{CPI_{current year}}$$ So in your hypothetical example (where the deflator is higher in 1980 than in 2000, which indicates deflation over the period), the value of \$5 in 2000 is equal in 1980 to:

$$x_{current year}=x_{base year}*\frac{CPI_{current year}}{CPI_{base year}}$$

or

$$5*\frac{1.6}{1}=8$$

So in your example, a basket of goods costing \$5 in 2000 would cost \$8 in 1980.

• In other words, the $5 and$3.12 are amounts for which we can buy the same quantity of goods in 2000 and 1980, respectively? – Quirik Jun 23 '15 at 7:38
• @dismalscience It seems im confusing something. Let's go from the begining. I have 5 dollars in 2000 (base, deflator = 1) and 4 dollars in 1980 (deflator = 1.6). The 4/1.6 = 2.5 dollars is the amount from 1980 expressed in 2000 dollars. This means that we can buy more things in 2000 since obviously the prices were higher in 1980. On the other hand, the 4 dollars in 1980 is equal to 4 x 1.6 = 6.4 dollars in 2000, i.e. it is amount for which we can buy the same quantity of goods in 1980 and 2000? Please, correct me if I'm wrong. – Quirik Jun 23 '15 at 8:49
• @dismalscience If I'm not mistaken, 6.4 dollars in 1980 is equal to 4 dollars from 2000, not the other way around as I wrote... It was a mistake that neither you or I noticed until now... – Quirik Jun 23 '15 at 13:55
• @dismalscience Yes, it is only for illustration purposes only I made up, not the real world example. :) – Quirik Jun 23 '15 at 14:26
• @navi — Thanks, I was confused by the deflator being opposite the real-world experience... is the edited version clear? – dismalscience Jun 23 '15 at 15:28