Using a Price Index to Measure Inflation for a Simple Economy with Three Products
Consider a simple economy, Breakfastland, which only produces three products: milk (measured in gallons), bread (measured in loaves), and breakfast cereal (measured in boxes). The following tables contain relevant data for this economy.
Product
Price in 2003
Quantity Produced in 2003
Value of Output in 2003
Milk
$3.00 per gallon
20 gallons
$60.00
Bread
$2.00 per loaf
15 loaves
$30.00
Cereal
$5.00 per box
10 boxes
$50.00
Total Value of all Output produced in 2003 (GDP)
(Valued using 2003 prices)
$140.00
Table 6. Hypothetical data for 2003 in an economy with three products.
Product
Price in 2004
Quantity Produced in 2004
Value of Output in 2004
Milk
$6.00 per gallon
30 gallons
$180.00
Bread
$3.00 per loaf
20 loaves
$60.00
Cereal
$5.50 per box
10 boxes
$55.00
Total Value of all Output produced in 2004 (GDP)
(Valued using 2004 prices)
$295.00
Table 7. Hypothetical data for 2004 in an economy with three products.
Product
Price in 2005
Quantity Produced in 2005
Value of Output in 2005
Milk
$6.60 per gallon
35 gallons
$231.00
Bread
$3.50 per loaf
25 loaves
$87.50
Cereal
$6.00 per box
15 boxes
$90.00
Total Value of all Output produced in 2005 (GDP)
(Valued using 2005 prices)
$408.50
Table 6. Hypothetical data for 2005 in an economy with three products.
There are five steps to follow when using a price index to measure inflation.
Step 1. Choose the base year and determine the basket of goods.
Step 2. Find the price of each good in each year.
Step 3. Compute the cost of the basket of goods in each year.
Step 4. Compute the price index for each year.
Step 5. Use the price index to calculate the inflation rate.
Step 1. Choose the base year and determine the basket of goods.
Let 2003 be the base year. Let the basket of goods be the output in 2003. Thus, the basket of goods contains 20 gallons of milk, 15 loaves of bread, and 10 boxes of cereal. (Note: The basket of goods does not have to be the output in the base year.)
Step 2. Find the price of each good in each year. The prices of milk, bread, and cereal in 2003, 2004, and 2005 are given in the second column of the three tables above.
Step 3. Compute the cost of the basket of goods in each year.
The basket of goods valued at 2003 prices =
(20 gallons of milk)($3 per gallon) +
(15 loaves of bread)($2 per loaf) +
(10 boxes of cereal)($5 per box) = $140.000
The basket of goods valued at 2004 prices =
(20 gallons of milk)($6 per gallon) +
(15 loaves of bread)($3 per loaf) +
(10 boxes of cereal)($5.50 per box) = $220.00
The basket of goods valued at 2005 prices =
(20 gallons of milk)($6.60 per gallon) +
(15 loaves of bread)($3.50 per loaf) +
(10 boxes of cereal)($6.00 per box) = $244.50
Step 4. Compute the price index for each year.
Assume 2003 is the base year.
Thus, the price index for 2003 is 100. The value of an index in the base year is always 100.
Thus, the price index for 2004 is 157.
Thus, the price index for 2005 is 175.
Step 5. Use the price index to calculate the inflation rate.
Calculate the inflation rate between 2003 and 2004
The inflation rate between 2003 and 2004 for this simple economy can be calculated from the price indexes above.
Thus, the rate of inflation between 2003 and 2004 is 57% in Breakfastland.
Calculate the inflation rate between 2003 and 2005
The inflation rate between 2003 and 2005 for this simple economy can be calculated from the price indexes above.
Thus, the rate of inflation between 2003 and 2005 is 75 % in Breakfastland.
Calculate the inflation rate between 2004 and 2005
The inflation rate between 2004 and 2005 for this simple economy can be calculated from the price indexes above.
Thus, the rate of inflation between 2004 and 2005 is 11.46 % in Breakfastland.
