Guide to COST-BENEFIT ANALYSIS of investment projects - Ramiri

Another exhaustive way to include distributive effects and concerns in the economic analysis is to adopt a set of‘explicit welfare weights’.When there is socially undesirable income distribution, one Euro at the margin does not have the same value forindividuals with different incomes. Public redistributive preferences in this case are expressed by weighting theaggregated per-capita consumption for the various consumer groups. To define the welfare weights we can refer tothe declining marginal utility of income or consumption: utility increases with a rise in consumption but incrementsget smaller the more we consume 114 . The elasticity of marginal utility of income, which we have already dealt with inappendix B in relation to the social discount rate, measures this particular effect.Under some assumptions 115 the welfare weights normalized to the average household are structured as follows:W⎛= ⎜⎝CC i⎞⎟⎠ewhere C is the average consumption level, C i is the per capita consumption in the group, and e is the constantelasticity of marginal utility of income 116 .Table E.1 Example of welfare weightsClasses Consumption C / C ) e=0 e=0.3 e=0.7 e=1.2(iHigh income 3,000 0.75 1 0.9173 0.8176 0.7081Medium income 2,500 0.90 1 0.9689 0.9289 0.8812Low income 1,250 1.80 1 1.1928 1.5090 2.0245Average 2,250 1 1 1 1 1Thus, expressing the effect of adopting welfare weights with an example, let us suppose there are in a region thefollowing per capita income groups: 3,000, 2,500 and 1,250 with an average of 2,250, see Table E.1.From the tax schedule we can obtain an estimate of the elasticity of marginal utility of income with the same methodused for the SDR. We can easily see from Table E1 that from the same revenue distribution, weights differ greatlydepending on the value of e.The elasticity parameter is a planning signal that in principle should be given to the project analyst by the managingauthority at a national level. Roughly speaking, we can say that zero elasticity implies unitary welfare weights; hence,one Euro is one Euro in welfare terms whoever the ‘winner’ or ‘loser’ of the project adoption. Values between zeroand one will fit with moderate inequality-aversion; e above one will be adopted by more egalitarian social planners.Table E.2 Example of weights for the distributional impactClasses Net benefits Elasticity 0.7 Distributional impactHigh income 60 0.8176 49.06Medium income 100 0.9289 92.89Low income 140 1.5090 211.26Total 300 353.21Let us suppose, as in Table E.2, that the marginal utility of income is equal to 0.7 and the total net benefits of aproject reach ENPV=300. These benefits would mainly be for the disadvantaged households and the use of welfareweights allows us to give more importance to these benefits. In particular, the amount of net benefits (140) obtainedby the low income class is, with our weights, worth 211.26 and the entire project is worth 353.21.114In the case of the commonly assumed iso-elastic social utility function, the expression for marginal utility is as follows: MUy = Y -e .If e were to take a unitary value, for which there is some empirical support, then we have: MUy = Y -1 = 1/Y.115The most important assumption is that an iso-elastic social utility function applies and is relevant over the complete range of incomes, so thatthe same value of e holds for all income classes.116 See Evans, Kula and Sezer (2005) for further elaboration and the measurement of welfare weights in a regional context.216