Indices

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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 gt 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 lt 1 then
No ranking of bundles is possible, xt, yt chosen
when xb, yb is not available so cannot compare.
If Lq lt 1 then
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(xt, yt) not available when (xb, yb) chosen.
Possible Pq lt 1 lt Lq
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(No Transcript)
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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 Pp gt M then
Rearranging gives pxb xb pyb yb gt pxb xt
pyb yt Thus
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If Lp lt M then pxt xb pyt yb lt 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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y0
x0
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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.