Laspayre's Index: What they don't tell you about the CPI

Here's a doodle from a tutorial.

Vaguely, the tutorial was about Consumer Price Index and alternative measures. The one currently in use in Australia is based on Laspayre's Index.

To calculate how well off you are after a price hike, you compare 2 ratios: Laspayres Index and Money Income. To calculate Laspayre's index, you take this year's prices and multiply that with last years mixture of goods. Divide that by the base year prices and quantity of goods. Next, you compare that ratio with the ratio of money income (simply, take this year's prices X this years goods and divide by base year prices and quantities.)

If it so happens that your Money Income ratio is less than Laspayre's Index that means you're worse off.

The reason why you multiply it with last year's mixture of goods is because people 'prefer' their old consumption patterns and therefore find it hard to change. Its all part of revealed preference theory.

Anyway, to get the analogy across, economists spend a lot of time thinking about how to compensate people with enough income to leave them just as they were last year. They aim to compensate people for the loss in welfare due to a hike in prices.

Now what they don't tell you is that one of the key assumptions is that they've assumed that people are inflexible and rigid in their consumption patterns. Therefore, the goldfish with a frown in a leaky bowl. (See Diagram Left Rectangle.)

Now what if people adapt to higher prices and substitute away from old quantities of goods that have gone up in price and chose new quantities of goods. What happens to our measures of how well off we are after a rise in prices?

The goldfish with the multi level, worm-hole fishbowl has got choices and though water levels may fall (analogy to welfare falling) he can still get by and choose other modes of consumption.

So I wonder if instead of worrying about compensation for loss of welfare with price hikes, why not give a person more choices instead?