Crafts and Harley have a neat guide to some index number problems.
1. they imagine an economy with
Year o: 10 bricks at 1 (io% of current value added)
5 cakes at i 8 (90%)
Year 2: 20 bricks at 2 (20%) 40 cakes at 4 (8o%)
2. what is growth in this economy?
3. the issue is this
a. we have physically more bricks and more cake. you can see this with the Quantity ratios, 20/10= 2 and 40/5 = 8
b. but the relative prices of each have changed, such that shares in value added has changed.
4. weighting by the year 0 value added shares (2.7% and 97.3%), we have growth of 7.4.
5. weighting by the year 1 value added shares (50% and 50%), we have growth of 0.2.
the former is a Laspeyres, the lattter a Paasche. The Laspeyers is faster.
