The effects of road pricing - Feweb - Vrije Universiteit Amsterdam

to maximise social rather than private welfare. This may take the form of price
regulation, or taxing firms so that their prices become socially optimal. This will be
explained below.
Deriving optimal prices needs an objective function. The most general form of this
function is a social welfare function. Formally, a social welfare function
1 n
i
W = W ( V ... V ) has as its arguments the indirect utility functions V of individuals
i , i = 1...
N (Varian, 1999). These indirect utility functions indicate the maximum
utility levels of the individuals. The utility levels depend on prices, income, and the
magnitude of externalities such as congestion and pollution. The social welfare
function incorporates welfare judgements with respect to the distribution of economic
resources. These value judgements are reflected in the policy prescriptions based on
the welfare function.
Several alternatives can be used as a target. These include: the search for local
improvements to welfare (rather than a global optimum); Pareto improvements;
potential Pareto improvements; compensating and equivalent variation; and social
surplus. This last one is the most commonly used for applied welfare analysis. Social
surplus is defined to be the sum of producers’ surplus and consumers’ surplus (CS).
Consumers’ surplus represents the benefit to consumers, as expressed by their
willingness to pay, in excess of the cost of providing a particular quantity or level of
output. Producers’ surplus represents the revenue in excess of the cost of providing
that level of output, i.e. profit. The principal advantage is that CS can be calculated
using uncompensated aggregate demand curves. On the other hand, CS makes the
implicit welfare judgement that welfare distributional concerns do not matter, by
giving equal weight to the surplus of all individuals. Another drawback is that CS is
not an exact measure of welfare when the utility function is not quasilinear.
Despite these disadvantages, the considerable practical advantages of CS make it
attractive. CS is most commonly used to measure welfare changes associated with the
change in the price of a good. Willig (1976) has shown that CS serves as a good
approximation to the compensating and equivalent variation, which are exact
measures of changes in welfare, as long as any one of three conditions hold:
1. the price change is not large;
2. expenditure on the commodity is not a large fraction of income;
3. the income elasticity of demand is not large.
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