# Chain Fisher volume index - Methodology

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## Example 1: A wine and cheese economy

In an insular economy where only wine and cheese are produced, we find the following portrait of production for the last four quarters:

Q1 Q2 Q3 Q4
Cheese (kilos) q 100 105 108 112
p 15 16 18 20
v 1,500 1,680 1,944 2,240
Wine (litres) q 25 30 38 50
p 22 20 16 12
v 550 600 608 600
Total GDP v 2,050 2,280 2,552 2,840

In this economy, the quantity of cheese produced rises regularly, as well as its price. However, the quantity of wine produced raises very quickly as its price drops significantly.

What would the growth of the nominal GDP be between, say, Q1 and Q3? The calculation of the index defined by the equation (1) gives the answer:

The growth of the economy, in nominal terms, will therefore be 24.5% between Q1 and Q3 (we get the percentage growth by subtracting 1 from the ratio given by the index and by multiplying the result by 100).

This calculation can be done for all the periods relatively to Q1. At the end, we obtain an index that covers the four periods:

Q1 Q2 Q3 Q4
GDP

i

1.000 1.090 1.245 1.385

What would the growth be between periods Q3 and Q4? Here, the ratio of the indexes in Q3 and Q4 gives the answer:

The growth will therefore be 11.2% between periods Q3 and Q4.