Question

The total price of purchasing a basket of goods in the United Kingdom over four years is: year 1=£840, year 2=£870, year 3=£900, and year 4=£970. Calculate two price indices, one using year 1 as the base year (set equal to 100) and the other using year 4 as the base year (set equal to 100). Round to the nearest 100th. Then, calculate the inflation rate between year1 and year 4 based on the first price index series. If you had used the other price index series, would you get a different inflation rate? If you are unsure, do the calculation and find out.

Answer 1

Price index using Year 1 as base year -

The price index in base year is always 100.

So,

Price index in year 1 is 100.

Price index in year 2 = (Cost of goods basket in year 2/Cost of goods basket in year 1) * 100

Price index in year 2 = (870/840) * 100 = 103.57

So,

Price index in year 2 is 103.57

Price index in year 3 = (Cost of goods basket in year 3/Cost of goods basket in year 1) * 100

Price index in year 3 = (900/840) * 100 = 107.14

So,

Price index in year 3 is 107.14

Price index in year 4 = (Cost of goods basket in year 4/Cost of goods basket in year 1) * 100

Price index in year 4 = (970/840) * 100 = 115.47

So,

Price index in year 4 is 115.47

Price index using Year 4 as base year -

The price index in base year is always 100.

So,

Price index in Year 4 is 100.

Price index in year 1 = (Cost of goods basket in year 1/Cost of goods basket in year 4) * 100

Price index in year 1 = (840/970) * 100 = 86.59

So,

Price index in year 1 is 86.59

Price index in year 2 = (Cost of goods basket in year 2/Cost of goods basket in year 4) * 100

Price index in year 2 = (870/970) * 100 = 89.69

So,

Price index in year 2 is 89.69

Price index in year 3 = (Cost of goods basket in year 3/Cost of goods basket in year 4) * 100

Price index in year 3 = (900/970) * 100 = 92.78

So,

Price index in year 3 is 92.78

Calculate the inflation rate between Year 1 and Year 4 using first index series -

Inflation rate = [(Price index in year 4 - Pprice index in year 1)/Price index in year 1] * 100

Inflation rate = [(115.47 - 100)/100] * 100 = 15.47%

The inflation rate between Year 1 and Year 4 using first index series is 15.47%.

Calculate the inflation rate between Year 1 and Year 4 using second index series -

Inflation rate = [(Price index in year 4 - Pprice index in year 1)/Price index in year 1] * 100

Inflation rate = [(100 - 86.59)/86.59] * 100 = 15.47%

The inflation rate between Year 1 and Year 4 using second index series is 15.47%.

Same result is being achieved by using either of the price indexes.