By Organisation for Economic Co-operation and Development
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Extra resources for Biomass and agriculture : sustainability, markets and policies
Thus, old prices understate marginal valuations while new prices overstate them. Notice how welfare measures are computed here as changes in the value of ﬁnal consumption demand. In other words, as areas underneath the demand schedules. A much more common approach, however, measures welfare changes as areas to the left of demand schedules. This is approximated using the Laspeyres and Paasche price MEASURING WELFARE CHANGESBRIEF OVERVIEW 7 indices to estimate changes in private surplus, where the necessary condition for x1Px0 is obtained from the Paasche price index as: and sufﬁcient condition for x1Px0 from the Laspeyres price index as: The necessary condition tells us that the consumer could not afford the new bundle x1 at old prices q0.
One response is to separate the efﬁciency and equity effects for actual dollar changes in utility so that people can make their own assessments about the ﬁnal welfare changes. Potential welfare changes are frequently referred to as efﬁciency effects because they isolate changes in real income from using resources more efﬁciently, while equity effects identify how these potential welfare effects are distributed across consumers. Hatta (1977) proves an important relationship between the efﬁciency and equity effects for marginal policy changes, and does so in a single (aggregated) consumer economy with constant producer prices.
These differences are determined by the cross-price changes in the compensated demands, where for small price changes, we have: By Shephard's Lemma and Young's Theorem the CVs must be equal, with: Thus, since areas A and B are equal by the symmetry of the cross-price changes in demand the compensated welfare changes are path independent. 3 APPLICATION: MEASURING THE SOCIAL DEADWEIGHT LOSSES FROM DISTORTING TAXATION This section computes the excess burden for a single commodity tax on a consumer facing constant producer prices.