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Indices

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Definitions Paasche Quantity Index: Laspeyres Quantity Index:

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Can we make any welfare statement if we know that the Paasche Quantity Index or the Laspeyres Quantity Index has gone up or down? This depends on: If Pq > 1 then Since the original bundle (xb, yb) is still affordable we could buy it but have not. Thus,

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If Pq < 1 then No ranking of bundles is possible, xt, yt chosen when xb, yb is not available: so cannot compare. If Lq < 1 then

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**(xt, yt) not available when (xb, yb) chosen. **

If Lq > 1 then (xt, yt) not available when (xb, yb) chosen. Possible Pq < 1 < Lq

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**Original Budget Constraint: Pxb xb + Pyb yb = Mb**

In time t, Prices, Income and Quantities have changed. We want to know if we are better or worse off when Pxt xt + Pyt yt = Mt

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**We are not able to rank using the revealed preference.**

Price Indices Paasche Price Index weights are quantities: Laspeyres Price Index: We are not able to rank using the revealed preference.

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**Need to define expenditure index:**

If Pp > M then Rearranging gives: pxb xb + pyb yb > pxb xt + pyb yt Thus:

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**pxt xb + pyt yb < pxt xt + pyt yt**

If Lp < M then pxt xb + pyt yb < pxt xt + pyt yt Problems with Price Indices Choice of ‘representative weights’ CPI Base year weights: Laspeyres Used to index pensions and social security over-estimates effect of price changes as this does not take account of substitution possibilities.

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**Overall real income down**

One price up, other down Overall real income down y0 Original Prices x0

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**Income after Pension rise based on CPI/Laspayres**

So CPI compensation overestimates effect of inflation since does not allow for substitution of y for x y0 U1 U0 x0

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**By contrast, the Paasche index under-estimates the effect of price change.**

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