Percentage Change

Suppose you have an index with a base year 1990 and the index value is therefore 100.  Compare that the year 2000 which has a value of 164.  This means that inflation grew by how much over the decade?

% change =  [(new year – base year) / base year]

                 =  [(164 – 100) / 100]

                 =  64 / 100

                  = 0.64 or 64.0%

This is the standard method of calculating percentage change.

Nominal and Real Prices
Suppose a gallon of milk and that you have the following data.

 

Year

Nominal Price

CPI[1]

Real Price

1980

$1.29

86.8

 

1990

$1.79

132.4

 

2000

$2.59

167.8

 

 

We want to compare the prices so to net out general inflation we can adjust the 1980 and 1990 nominal prices into real prices in year 2000 dollars.

We should first ask: Which CPI measure should we use?  All Items or Food and Beverages make sense.  Milk is, after all, a beverage. 

How do we do this calculation?  Again, we have to adjust the nominal price.

Real Pricez =  (Nominal Pricez ) x  (Adjustment Factor)

The adjustment factor is formed using the CPI measures

Real Pricez =  (Nominal Pricez ) x  (CPIbase year / CPIz)

Here we use the nominal price of 1980 milk ($1.29) and adjust them to the 2000 dollars in order to allow me to directly compare them.  Remember the data we have:

 

Year

Nominal Price

CPI[2]

Real Price

1980

$1.29

86.7

 

1990

$1.79

132.1

 

2000

$2.59

168.4

 

 

 

Real Price of 1980 milk in year 2000 dollars = 

(Nominal Price1980 ) x  (CPI2000 / CPI1980)

 

Real Price of 1980 milk in year 2000 dollars =  ($1.29) x  (168.4 / 86.7)

 

Real Price of 1980 milk in year 2000 dollars =  ($1.29) x  (1.9423)

 

Real Price of 1980 milk in year 2000 dollars =  $2.51 in year 2000 prices

 

Now I have both prices in terms of year 2000 prices and I can compare.  What has happened to the real price of milk?

 

PRACTICE:  What is the price of milk in 1990 brought to year 2000 cost of living?[i]
Another use of a Price Index

Suppose you make $42,000 a year in Nashville and you are contemplating a move to Atlanta. You investigate and find that your salary in Atlanta would be $49,000.  Are you thrilled?

It depends on the cost-of-living!  Suppose that the CPI in Nashville is 92.5 and the CPI value for Atlanta is 121.8.  What matters is the purchasing power of that salary and we can get some idea about by looking at a cost of living index in each of the cities.  While this is not a perfect measure it is far better than nothing!

Real Salary in ATL  refers to how you would view the salary as a person from Nashville.  You’re essentially putting the Atlanta salary into the Nashville dollars that you understand.  Calculation:

Real Salary in ATL =  (Nominal SalaryATL ) x  (Adjustment Factor)

Real Salary in ATL =  (Nominal SalaryATL ) x  (CPINVILLE / CPIATL)

Real Salary in ATL =  (Nominal SalaryATL) x  (CPINVILLE / CPIATL)

Real Salary in ATL =  ($49,000) x  (92.5 / 121.8)

Real Salaryin ATL =  $37,213

 

Your current salary in Nashville is $42,000 per year, and while the salary in Atlanta is higher in nominal terms in terms of its real purchasing power the amount of goods and services you could buy in Atlanta would be comparable to what one could buy in Nashville for $37,213.   You are actually $4,787 better off in Nashville!  Why? 

Because the cost of living is higher in Atlanta and you have just adjusted to find that out!

Caveats about Price Indexes:

1)      Quality changes over time.  Between 1980 and now we have gone through the death of 8-track tapes, cassette tapes, and we are watching the eclipse of CDs with the advent of MP3 files and players.

2)      The price index measures very specific things.  Be sure that you are using a price index that captures what you want. 

3)      The CPI is often referred to as “cost-of-living” index which is true only if you buy the same basket as the one the CPI is constructed with.  Unlikely!  But sometimes the next best solution is all that you have…



[1] The Economic Report of the President 2007, Table B-60. – Consumer price indexes for major expenditure classes, 1960-2007

[2] The Economic Report of the President 2007, Table B-60. – Consumer price indexes for major expenditure classes, 1960-2007



[i] $2.28