Lecture Note 15: Social Cost Benefit Analysis - University of ...

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1. The project has the same impact on the consumption of good x1 and x2 for all consumers, i.e., x h 1 = x1 and x h 2 = x2 for all h: 2. All consumers have the same private marginal value of income, i.e., h = for all h. This, in turn, is satis…ed if (for example) all consumers have the same utility functions (tastes) and the same level of income. 1 3. The social welfare function values utility increments of all consumers in the same way, i.e., @SW F @Uh = @SW F @U for all h: This is, for example, satis…ed by the (unweighted) utilitarian social welfare function where = 1 for all h. @SW F @Uh Under these (su¢ cient) conditions, we can write equation (8) as @SW F NB = H @U [q1 x1 q2 x2] (9) and that takes us back to the scenario considered in Lecture note 13-14. The three conditions are su¢ cient, so we can get away with less. If, for example, we got conditions 2 and 3, but not condition 1 (i.e., the project might deliver di¤erent amounts to di¤erent individuals or cost them di¤erent amounts in forgone consumption), we would get NB = @SW F @U PH [q1 h=1 xh PH 1 q2 h=1 xh2]; (10) which e¤ectively allow us to add the bene…t and cost increments up and then value them at market prices. Another possibility is that conditions 1 and 3 holds but not condition 2. This case we get that NB = @SW F @U q1 PH x1 h=1 h = [q1 x1 q2 x2] @SW F @U @SW F @U q2 x2 P H h=1 h P H h=1 h: (11) Whichever of these we take as the benchmark, it should be clear now that we have to assume a lot for it to be valid to use the simply cost-bene…t rule that the project will increase social welfare if the market value of its output is greater than the market value of the inputs. 2 In fact, one could argue that these 1 Other assumptions can also insure that everybody have the same marginal value of income. For example, if consumers have quasi-linear preferences, then they can have di¤erent preferences over some goods and di¤erent levels of income while preserving a common value of the marginal utility of income (typically assumed to be one). 2 There is, of course, also the issue of whether market values exist and whether they represent the shadow value of the outputs and inputs. 4
conditions are never satis…ed 100% and thus one should always take distribution into account in social cost bene…t analysis. On the other hand, it is also clear that it, from a practical point of view, is a lot more complicated and requires a lot more information about the impact of a project or policy to take distribution into account in a serious manner and some very eminent economists have argued that unless a project or a policy is explicitly designed to distribute income, one should leave distribution to one side and focus on selecting projects and policies that satisfy the simply e¢ ciency criteria embodied in equation (9). Redistribution should, then, be left to tax system or to expenditure programmes designed redistribute. Arnorld Harberger (of the University of Chicago) is perhaps the most famous supporter of this view. The “Harberger principle” can crudely be summarized as follows. Suppose that for a given project, we can divide the net bene…ts into those which have to do with e¢ ciency (i.e., the net bene…ts as they would be if we were to treat those a¤ected by the project as if there were identical) and the additional net bene…ts that have to do with distribution (i.e., the extra net bene…ts we would get when we treat those a¤ected by the project as being di¤erent in some fundamental way and give more weight to the bene…ts and costs of some than to others). Let the former be denoted NB E and the later be denoted NB D where superscript E refers to e¢ ciency and superscript D refers to distribution. The overall net bene…t of the project is NB = NB E + NB D : The “Harberger principle” (Harberger, 1978) is that one should not accept a project if NB E < 0 but NB > 0. Clearly, such a project is only justi…ed because of its distributional implications. Public sector projects are, the argument goes, an ine¢ cient way to achieve distributional ends. They should be dealt with through more direct tax-transfer programmes and scare resources for public projects should be concentrated on programmes which can pass a purely e¢ ciency-based cost-bene…t test. Implicit in this argument is the assumption that the focus is on public sector investment projects and that the tax-bene…t system is designed (approximately) to induce an optimal distribution of income prior to the project. For expenditure programmes, e.g. in the area of education, health and welfare, targeted more directly at distribution, the power of the Harberger argument is clearly a lot weaker. 3 How should distribution be integrated into the SCBA? On balance, there is a case for incorporating distributional considerations into social cost bene…t analysis, although the case is more compelling for some projects and policies than for others. How should it be done in practice? Equation (8) gives us a useful clue: we need to de…ne social welfare weights (or distributional weights) associated with each individual (or, in practice, with 5
Page 1 and 2: Lecture Note 15: Social Cost Bene
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Page 7 and 8: Exercise 1 Suppose an analyst decid
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Page 13 and 14: Exercise 5 Illustrate graphically w
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Page 19 and 20: Glaister (1994) are highly recommen
Page 21: Table 3: The re-scaled social welfa

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