Contrary to the established, frequently repeated proposition that its
budget surplus cannot be distributed to taxpayers without disturbing t
he incentive compatibility of the demand-revealing process (DRP), the
surplus can be distributed by reapplying the key concept of the DRP. T
here will remain an aggregate refund error that in a Bayesian sense is
random with zero mean, and which vanishes O(1/N)(2) as the economy be
comes large through replication. To deal with income effects, when one
does not restrict the domain of the mechanism to separable utility fu
nctions, I suggest a variation of the DRP that preserves its incentive
compatibility when N is finite.