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

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This is simply telling us that the utility cost of the project is that C = R units of private income have to be given up. Since this happens by levying the distortionary tax t2, the social welfare cost per unit of revenue collected is SW F= t2 SW F R= = t2 R . Let us now link this to the marginal cost of public funds (or what Boardman et al. calls the marginal excess burden of taxation). The (social) marginal cost of public funds (SMCF) is de…ned as SMCF = 1 SW F= t2 R= t2 (38) where = 1 P4 4 h=1 h is the average marginal utility of income for the (entire) population (in our example the four individuals). We divide by this parameter in the de…nition in order to convert the welfare cost measured in utils into a welfare cost in units of income. With this in mind, we can do the …nal substitution into the cost di¤erential: SW F = (SMCF ) C = (SMCF ) C 4 Let us now make the critical assumption: assume that the marginal utility of income is the same for all consumers (i.e., h = for all h). This allows us to write the cost di¤erential as and the bene…t di¤erential as The net bene…t is NB = q1 4X h=1 SW F = (SMCF ) C (39) SW F + = 4X h=1 4X q1 x h 1: (40) h=1 x h 1 (SMCF ) C: (41) We can link the social marginal cost of public funds (SMCF ) to the marginal excess tax burden as follows: SMCF = 1 + MET B; (42) which then gives us the formula that Boardman et al. recommends in chapter 4. In short, this tells us that we should adjust the total …nancial cost of the project using an estimate of the marginal cost of public funds and, more generally, that we should adjust all project e¤ects on government revenues and costs by the factor 1 + MET B. This method is widely used in the US. It has intuitive appeal and is easy to apply in practice. However, the main point of going through the derivations above was to make it clear that it is based on two critical assumptions. The …rst of these we already discussed: namely that the 16 h:
marginal value of income is the same for everyone. The second, which we did not stress in calculations because we assumed a utilitarian social welfare function from the beginning, is that all individuals must have the same weight in social welfare function (which is true for the utilitarian social welfare function). Both of these assumptions seriously undermine the case for redistribution in general. If all individuals have the same private marginal value of income, then were the case, then the main reason for any government to get involved with distribution is void (remember that one key reason a social planner would want to distributive income is precisely that the marginal value of income is di¤erent for di¤erent people). If on top of that the social welfare function puts equal weight on everyone, then there is not case for distribution left. If is as if the government thinks that everyone is the same. This makes it clear, on the one hand, that the marginal cost of public funds approach is really about e¢ ciency: it provides a systematic way to integrate into the SCBA the fact that public funds must be raised through distortionary taxation and in situations where the control area of the analyst is such that the broader tax system must simply be taken as given, it makes sense to adjust the …scal implications of a project or programme for the e¢ ciency cost of raising the extra revenue with the preexisting tax instruments (or if the project generates public revenue to take into account that this will then reduce the pressure on other sources of revenue). On the other hand, the two assumption required to make the approach theoretically valid clearly make it hard to justify the approach as a way to take distribution into account. At the surface is may seem intuitive that projects that distribute from the general taxpayer who must pay higher taxes as a consequence of a project to the groups of individuals that bene…ts from the project (who typically constitute a small subset of all taxpayers). But if we think (assume) that the marginal value of income is the same for everyone, then we should not be very concerned with distribution in the …rst place and we could as well raise the required funds using a poll tax. This would avoid any distortions but then there is no need to make any adjustment in the …rst place. In practice, however, it is clear that poll taxes are not being levied on a large scale (and the experience in the UK in the 1980s suggests that they may not be entirely non-distortionary if we count the social cost of the tax rebellion that was triggered). Accordingly, many cost-bene…t analysts take the view that adjusting the e¤ects on the governments budget of projects for the marginal cost of public funds is a sensible way to proceed in particular when the analyst is not able to re-design the entire tax system and thus must take whatever taxes are levied as given. So, if we take that line, we are only left with one question: which value should be using for the adjustment. Boardman suggests that the Marginal Excess Tax Burden per unit of revenue raised is between 0:33 and 0:46 for all taxes taking together, from 0:11 to 0:39 for the sales tax and from 0:31 to 0:65 for the income tax. These estimates apply to the USA; for other countries, see Klever and Kreiner (2006). They estimate that the marginal cost of public funds for the UK is about 1:26. Exercise 6 Can the fact that the marginal excess tax burden di¤ers by tax base 17
Page 1 and 2: Lecture Note 15: Social Cost Bene
Page 3 and 4: of x2 by x h 2 for consumer h. Unde
Page 5 and 6: conditions are never satis…ed 100
Page 7 and 8: Exercise 1 Suppose an analyst decid
Page 9 and 10: In this case, the social welfare fu
Page 11 and 12: where the social weight attached to
Page 13 and 14: Exercise 5 Illustrate graphically w
Page 15: suppose that the cost is covered by
Page 19 and 20: Glaister (1994) are highly recommen
Page 21: Table 3: The re-scaled social welfa

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

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