Show that the following data that Fisher’s ideal index satisfies the Time Reversal Test and Factor Reversal Test:
| Commodity | Price | No. of Units | ||||
| 2005 | 2018 | 2005 | 2018 | |||
| I | 6 | 10 | 50 | 60 | ||
| II | 2 | 2 | 100 | 100 | ||
| III | 4 | 6 | 60 | 60 | ||
| IV | 10 | 12 | 30 | 30 | ||
| V | 8 | 12 | 40 | 40 | ||
Fisher's ideal index is given by:
I = ∏(P2Q1/P1Q2)^(wi)
Where P1, P2 are the prices of the commodity in the base year and current year respectively, Q1, Q2 are the quantities consumed in the base year and current year respectively, and wi is the weight of the ith commodity.
To show that Fisher's ideal index satisfies the time reversal test, we need to show that if we reverse the _________ _____ ______ ____ __________ _____ _________ ___.
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