CBA lecture 4__weights__2015-1

# CBA lecture 4__weights__2015-1 - ECO5074F Cost Benefit...

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ECO5074F Cost Benefit Analysis Beatrice Conradie [email protected] or directly after the lecture

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DISTRIBUTIONAL WEIGHTS Gines de Rus, 2010. The micro-foundations of CBA. Chapter 11 in: Introduction to cost-benefit analysis: Looking for reasonable shortcuts. Edward Elgar Campbell & Brown, 2003, chapter 11
Which of the following projects is optimal? Project Rich Poor Total NPV Decision A 60 40 100 B 50 30 80 Drop, inefficient C 20 80 100 C is best for the poor Project Rich Poor Total NPV Decision D 60 40 100 Most efficient E 40 50 90 Best for the poor Project Rich Poor Total NPV Decision D 60*1 40*3 180 E 40*1 50*3 190 If the poor is 3x more important than the rich, project E outperforms project D

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Theoretical model for deriving weights If social welfare is constituted by individual welfare, then dW = the sum of variations in individual utility across the m members of society, weighted by the relative importance society attaches to each individual Inter-personal comparisons are hard because U is unobservable and there is no obvious functional form to W
Consumer optimisation First order conditions Rearranged MU of consuming the last unit of good j = price of good j x the MU of money for person i

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Totally differentiate the individual utility function and substituting MU ij with the expression on the previous page, we get The variation in utility of person i depends on the marginal variation in quantities of the n goods consumed by person i, multiplied by their prices j and person i’s MU of money
Indirect utility function expresses individual wellbeing as a function of observable prices and income Differentiating V(.) wrt price (chain rule) and grouping terms FOC=0 when utility is maxed Produces Roy’s identity

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By total differentiation the indirect utility function and using the previous result If income is constant, the last term disappears, therefore Compare The variation in utility of individual i depends on the marginal variation in quantities price of the n goods consumed, multiplied by their price quantity and the marginal utility of income
Measurable impacts on utility The impact is a price or quantity, with the other kept constant Unless we know the value of MU of money at different income levels, it is impossible to convert observable prices and quantities into unobservable utility As utility is not observable, we use monetary measures that reflect changes in the utility of individuals. We do not directly measure the change in utility, but the change in the willingness to pay or accept. The best approximations we have.

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Aggregating individual impacts into social welfare impacts
Two types of weights are needed (together = the social marginal utility of income) ∂U i /∂M i Individual marginal utility of money Depends on the person’s income level (and preferences) Usually assumed to be constant ∂W/∂U i Distributional weight, importance in society Different for different stakeholders/ reference groups A political question For society to improve, ∂W/∂U i must be positive

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