費用便益分析の厚生経済学的基礎

抄録

The objective of this paper is to review the welfare foundations on the ordinal utility theory of cost-benefit analysis (CBA) .
In welfare economics, it is proved that the project of which ΣEV (the aggregated equivalent variation over individuals) is positive, improves society (The individual equivalent variation is the ordinal measure of individual utility changes and can be calculated by a Taylor series expansion using the individual Marshallian demand function) . So far there is a general belief that CBA is given the welfare foundations by this proof. This is true if CBA is defined as the method that compares ex-ante situation with only one ex-post situation. However, CBA practically compares and estimates many alternative projects. In section 4, if CBA is defined as the method that compares many situation (if CBA regards the project as the better, the greater benefit minus cost), it can be proved that CBA can not be given the welfare foundations by the proof.
In figure 1 (for simplification we argue two commodity economy), volume of commodity X is in the horisontal axis. Volume of commodity Y (the numeraire goods) is in the vertical axis. Position I is ex-ante situation and position II and position III are comparable alternative situation. CIC is Scitovsky or community indifference curve. ΣEV_A→B stands for the aggregated equivalent variation over individuals from situation A to situation B.
In figure 1 we find following formulas
ΣEV_I→II=T_IU_I (1)
ΣEV_I→III=T_IV_I (2)
ΣEV_II→III=U_IIV_II (3)
ΣEV_III→II=V_IIIU_III (4)
ΣEV_I→II>ΣEV_I→III (5)
One may feel intuitively from above formulas that situation II is the best of three. However, it is clear from figure 1 that the best of three is undoubtedly situation III.
Therefore it is not true to say better a project of which benefit minus cost is greater than that of another project. This is because CICs (that are not ordinal measures of welfare level of community) intersect unlike individual difference curves.