The Theory of Water and Utility Pricing - Global Drinking Water Management and Conservation - page 72

represent the n-good hyper-indifference surface, along which
utility is held constant. Note that

Let the function U

U can be replaced by any increasing function W of U .

Let the individual budget constraint, after taxes, be
X p i q i ¼ m

; ð where m is money income Þ ð 5 : 4 Þ

Assuming utility maximization, the consumer chooses the highest U , subject to

( 5.4 ).
Suppose q 0 1 ; q 0 2 ; ...; q 0 n were any other set of quantities satisfying ( 5.4 ), so that:

X p i q i ¼ m

ð 5 : 5 Þ

Then:

¼ U þ dU

q 0 1 ; ...; q 0 n

U ¼ U ð

q 1 ; ...;

Þ [ U

q n

Let us consider a system with the imposition of excise taxes and reduction of
income taxes. Of course some of the taxes may be negative. The excise tax may be
called a over and above marginal cost. Now there may

be a redistribution of production and consumption. Let pi, i , q i and m be replaced,
respectively, by

“ toll ” or a “ service user fee ”

p i ¼ p i þ d q i ¼ q i þ d m 0 p i ; q i ; ¼ m þ d m ð 5 : 6 Þ

where the increments can be either positive or negative. The new excise tax revenue
is P q i d p i . The consumer

' is income tax is reduced by d m, and the net increment of

government revenue is

r ¼ X q i d d p i d m ð 5 : 7 Þ

is budget constraint is P p i q i ¼ m 0 , which we can also write as
X ð p i þ d

The consumer '

p i Þ q i þ d ð q i Þ ¼ m þ d m ð 5 : 8 Þ

Subtract the budget Eq. ( 5.4 ) corresponding to the former regime (excise taxes)
and using ( 5.6 )we nd that

d m ¼ X q i d p i þ X p i d q i

ð 5 : 9 Þ