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 P q > 1 then Since the original bundle (x b, y b ) is still affordable we could buy it but have not. Thus,
If P q < 1 then No ranking of bundles is possible, x t, y t chosen when x b, y b is not available: so cannot compare. If L q < 1 then
If L q > 1 then (x t, y t ) not available when (x b, y b ) chosen. Possible P q < 1 < L q
Original Budget Constraint: P x b x b + P y b y b = M b In time t, Prices, Income and Quantities have changed. We want to know if we are better or worse off when P x t x t + P y t y t = M t
Price Indices Paasche Price Index weights are quantities: Laspeyres Price Index: We are not able to rank using the revealed preference.
Need to define expenditure index: If P p > M then Rearranging gives: p x b x b + p y b y b > p x b x t + p y b y t Thus:
If L p < M then p x t x b + p y t y b < p x t x t + p y t y t 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.
x0x0 y0y0 One price up, other down Overall real income down Original Prices
x0x0 y0y0 U0U0 U1U1 So CPI compensation overestimates effect of inflation since does not allow for substitution of y for x Income after Pension rise based on CPI/Laspayres
By contrast, the Paasche index under-estimates the effect of price change.