11 One approach to deriving the weights used is the concept of an underlying social welfare function that links personal utility (or satisfaction) to income.
12 Broadly, the empirical evidence suggests that as income is doubled, the marginal value of consumption to individuals is halved: the utility of a marginal pound is inversely proportional to the income of the recipient. In other words, an extra £1 of consumption received by someone earning £10,000 a year will be worth twice as much as when it is paid to a person earning £20,000 per annum.
BOX 5.1:THE MARGINAL UTILITY OF CONSUMPTION
Welfare Weights, by Cowell and Gardiner (1999) concluded that "most [studies] imply values of the elasticity of marginal utility of just below or just above one".4 Pearce and Ulph (1995), in their survey of the evidence, estimate a range from 0.7 to 1.5, with a value of 1 being defensible.5 Assuming a value of 1 implies a utility function of the form U = log C where C is consumption. The marginal utility of consumption is then given by δU/δC i.e. 1/C. This implies that if consumption doubles, the marginal utility of consumption falls to one half of the previous value. |
13 Box 5.2 provides an example of how distributional weights might be calculated from the equivalised income quintiles in Table 5.1 or Table 5.2.The weights provided are merely illustrative. Despite this uncertainty it is important that appraisers, where deemed appropriate, attempt to adjust explicitly for distributional implications. The assumptions underpinning the chosen distributional weights should be fully explained.
BOX 5.2: DERIVING ILLUSTRATIVE DISTRIBUTIONAL WEIGHTS
The marginal utility of each quintile in Tables 5.1 and 5.2 can be calculated by dividing 1 by the median income of each quintile (U' = 1/C). Distributional weights can then be derived by expressing the marginal utility of each quintile as a percentage of average marginal utility (1 divided by the median income). The table below provides the illustrative weights as ranges, reflecting uncertainty in the utility function and the assumed income quintiles.
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14 It will often be the case that neither net nor gross incomes of those affected by a proposal are known directly, so as to allow the distributional adjustment to be calculated. However, if the family or other circumstances of a group affected are known, an adjustment may be calculable indirectly using whatever is known about the relative incomes of those in the relevant category.
15 For example, it may be that a particular proposal will disproportionately provide additional employment for people on probation in a particular area. If it is known that probationers in that area are predominantly in the lowest income quintile, it will be reasonable to use the adjustment factor calculated for that quintile.
16 The regional impact of policy may assist the analysis: the income impact of a proposal may be estimated indirectly by determining its geographical impact and taking note of small-area indices of deprivation.6 However, care must be taken to assess whether the beneficiaries of a proposal are representative of the geographical area from which they come.
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4 Cowell and Gardiner (1999) page 31
5 Pearce and Ulph (1995) page 14
6 'Where does public spending go? A pilot study to analyse the flows of public expenditures into local areas', by the former DETR (now ODPM).