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The CPI for use in calculating the rate of inflation is based off of Laspeyres' index, which is essentially the ratio of dot products of the price vector and a quantity vector. What kind of analysis would we be unable to do if we constructed a price index that is just the ratio of the sum of new prices to the sum of old prices?

I ask this because welfare analysis as far as compensating/equivalent variations are concerned looks only at the change in prices.

Of course, looking at prices alone will not allow us to infer substitution effects and so such measure would be a biased measure of welfare. But so too is there such bias if, as with Laspeyres' index, we hold the quantity vector constant. So, the question boils down to: is the Laspeyres' index useful only in how we could couple this with Paasche's to obtain Fisher's ideal index?

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  • $\begingroup$ This question is a little vague, it seems you are asking multiple questions. You should consider separating them out as individual questions or clarify $\endgroup$
    – Brennan
    Dec 15, 2021 at 16:48

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What kind of analysis would we be unable to do if we constructed a price index that is just the ratio of the sum of new prices to the sum of old prices?

You would probably be unable to do meaningful analysis. Such a metric would be unable to detect a change in the prices of staple foods, e.g., bread, as this is purchased frequently and in small quantities. Durable goods such as refrigerators on the other hand are purchased rarely, and in case of larger items usually one at a time. Yet considering just bread and refrigirators: suppose the current price are \$3 per loaf of bread and \$2,000 per fridge. If the price of bread would increase tenfold, while the price of fridges are unchanged this would barely register on your metric: $$2030/2003 \approx 101.35\%$$ On the other hand, a 5% price increase in fridge prices would register as close to 5% even if the price of bread was unchanged. Yet the first kind of price increase would affect most people much more than the second kind.

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