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Published byCaleb McDermott Modified over 2 years ago

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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 P q > 1 then Since the original bundle (x b, y b ) is still affordable we could buy it but have not. Thus,

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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

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If L q > 1 then (x t, y t ) not available when (x b, y b ) chosen. Possible P q < 1 < L q

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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

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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 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:

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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.

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x0x0 y0y0 One price up, other down Overall real income down Original Prices

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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

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

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