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

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3.2 The adjusted social weights approach This approach is used in the UK and forms part of the Green Book 4 (the government’s manual for how to conduct social cost bene…t analysis). It uses a particular normalization to calculate the social welfare weights attached to the bene…ts of a project or a policy proposal. The approach, as well as the general pitfalls associated with the task of de…ning social welfare weights in a sensible way, can be illustrated through an example. 5 The example is based on the following assumptions: 1. We consider a society with four individuals, h = 1; 2; 3; 4. 2. The individuals’utility functions are Uh = log(x h 1). This is a special case of the utility function with constant inequality aversion considered above (with = 1). 3. The pre-project consumption levels of the four individuals are 6 x 1 1 = x 2 1 = $1000 per month x 3 1 = x 4 1 = $2000 per month 4. The social welfare function is utilitarian, i.e., SW F + = P 4 h=1 Uh, where we use the superscript + to indicate that this is net net of the monetary cost of the project. 5. The (expected) impact of the project under consideration is to increase consumption of good x1 for each of the four individuals. We denote the extra consumption of individual h by x h 1 > 0. 6. The monetary cost of the project is $C. Given this information, we want to evaluate if the project is socially desirable or not, i.e., we want to know if the net social bene…t NB = 4X @SW F + h=1 @Uh @Uh @x h 1 is positive. Using the assumptions that individuals’utility functions are logarithmic and the SWF is utilitarian, we can write this as NB = 4X x h=1 h 1 4 See Chapter 5 of the Green Book. 5 I am greatful to Dr Tom Crossley for providing this example. 6 We assume that the price of good 1 is una¤ected by the project. This allows us to measure pre- and post-project consumption levels in pounds, but we could as well have speci…ed the consumption levels in physical units. 1 10 x h 1 x h 1 C; C
where the social weight attached to the bene…ts of individual h is simply h = . Since marginal utility is falling with the level of consumption, we put 1 x h 1 less weight on individuals 3 and 4 (1=2000) who consume a lot of the project output to begin with and higher weight on individuals 1 and 2 (1=1000) who consume less of the project output initially. Table 1 shows what happens when we apply these weights to a project that takes $1 of uncommitted public funds and distribute it equally across the four individuals (through a non-distortionary lump sum transfer). The last column shows the welfare increments ( 1 xh x 1 h 1) for each consumer. We see that the sum of these bene…ts adds up to a very small amount, namely 0:00075. This is a lot less than the $1 cost of the project, so it should be rejected. But this does not seem to make any sense. We got a pound of uncommitted funds, how can dividing it equally amongst individuals be such a bad idea? The issue is that we have (without saying it out load..) chosen to use public funds as the numeraire, i.e., as the unit in which we measure the cost of the project ($1 of public funds is worth $1). The bene…ts, however, 1 xh x 1 h 1, are measured in units of utility. So the problem is that we are not comparing like with like. More fundamentally, the problem is that the choice of the utility functions must in practice be understood as the choice of ordinal utility functions. This means that we can subject it to any positive transformation and it will still represent the same underlying preferences over consumption. To see what this implies more clearly, let us transform the utility function and represent the individuals’preferences by the function e Uh = 10000 log(xh 1). Table 2 shows the re-calculated bene…ts of the divided-a-pound-equally project. Now, they add up to 7:5 and we conclude that the project is a good idea after all. Exercise 2 Does this logic strengthen or weaken Harberger’s case for not applying welfare weights at all? Clearly, to reach a sensible decision and avoid leaving the analysis wide open to manipulation by special interests, we need a principle that can tell us how to normalize or anchor the social welfare weights so that the costs and bene…ts become comparable. The Green Book suggests the following normalization. Begin by de…ning as the benchmark the social value of a uniform lump sum transfer, i.e., the social value of dividing $1 of uncommitted public funds equally amongst all citizens. This benchmark de…nes the opportunity cost of spending a pound on some other project or programme. The logic is that any project or programme would have to be better than simply spending the funds on a uniform lump sum transfer in order to be socially justi…ed. How does one implement this principle? What we need to do is to normalize the welfare weights of the four individuals in such a way that a project that divides $1 equally amongst them breaks even, i.e., yields a social bene…t equal to the cost of $1. Formally, we want the normalized social weights –denoted 11
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Page 7 and 8: Exercise 1 Suppose an analyst decid
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Lecture Note 15: Social Cost Benefit Analysis - University of ...

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