3Can 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 thenSince the original bundle (xb, yb) is still affordable we could buy it but have not. Thus,
4If Pq < 1 thenNo ranking of bundles is possible, xt, yt chosen when xb, yb is not available: so cannot compare.If Lq < 1 then
5(xt, yt) not available when (xb, yb) chosen. If Lq > 1 then(xt, yt) not available when (xb, yb) chosen.Possible Pq < 1 < Lq
6Original 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
7We are not able to rank using the revealed preference. Price IndicesPaasche Price Index weights are quantities:Laspeyres Price Index:We are not able to rank using the revealed preference.
8Need to define expenditure index: If Pp > M thenRearranging gives:pxb xb + pyb yb > pxb xt + pyb ytThus:
9pxt xb + pyt yb < pxt xt + pyt yt If Lp < M thenpxt xb + pyt yb < pxt xt + pyt ytProblems with Price IndicesChoice of ‘representative weights’CPI Base year weights: LaspeyresUsed to index pensions and social security over-estimates effect of price changes as this does not take account of substitution possibilities.
10Overall real income down One price up, other downOverall real income downy0Original Pricesx0
11Income after Pension rise based on CPI/Laspayres So CPI compensation overestimates effect of inflation since does not allow for substitution of y for xy0U1U0x0
12By contrast, the Paasche index under-estimates the effect of price change.