where qðR 1 ,m 1Þ is the uncompensated demand for land in
the core.
We now want to examine an optimal allocation that is
consistent with equilibrium. To do this we formulate a mixed-
regime problem in which the social planner chooses fiscal instru-
ments to maximize the expected maximum utility, while main-
taining fiscal balance.
Maximizing expected utility is appropriate and reasonable for
two reasons: (i) the planner cannot detect the idiosyncratic tastes
of individual workers, hence the planner cannot set individual
specific instruments and transfers and can only be directly con-
cerned with the expected maximized utility; (ii) the maximum
utilities are distributed with variance s 2 which does not change as
long as the planner’s instruments affect only the common utilities.
Planning action which does not affect the statistical variance of
utility among the consumers appears appealing.
Maximizing average achieved utility is not going to result in an
allocation that is Pareto optimal. We should expect that the
solution we get will deviate from the properties that we saw in
the case of identical individuals. We will, however, continue to
maintain fiscal balance. So the key question is how the allocation
which maximizes the average achieved utility will deviate from
marginal cost pricing and from the Henry George Theorem. To see
the results we specify the disposable incomes as: