Public Finance, 2nd Edition

3. One set of distorting subsidies may be substituted for another while

holding the total subsidy constant, a case of diVerential expenditure analysis.

This is exactly analogous to diVerential tax incidence. Here, the substitution

is viewed as removing one set of subsidies, returning the tax savings lump

sum, and then instituting a second set of subsidies, paid for by lump-sum

taxes. As in the tax case, the Wrst step involves totally diVerentiating the

government's budget constraint:

P

N

i1

s

i

X

comp

i

 S(17:5)

with dS  0, to determine the changes in the s

i

necessary to maintain a

balanced budget. The resulting changes are then substituted into Eq. (17.3)

to evaluate the change in loss (for linear technologies). Finally, the practical

diYculties of applying these compensated measures, especially for general

technologies, which were discussed in Chapter 16, apply to transfer incidence

as well. Recall that an important issue was whether production is constant

returns to scale.

TAX AND EXPENDITURE INCIDENCE WITH DECREASING-

COST SERVICES

As long as decreasing-cost services are being analyzed within the context of

Wrst-best theory, the government is assumed to charge a price equal to the

marginal cost of providing the service and to Wnance with lump-sum taxes

the deWcits arising because MC < AC. The appropriate comparison is an all-

or-none test in which having the service with these characteristics is compared

to not having the service at all. Marginal incidence analysis is not relevant for

decreasing-cost services.

The income-compensation measure of incidence was developed in Chap-

ter 9. Assuming linear or constant-returns-to-scale (CRS) general production

technology elsewhere in the economy, the net beneWt of providing the de-

creasing-cost service with lump-sum Wnancing of its deWcit is

4

B M

~

q; U

0



 T (17:6)

where:

~

q  vector of consumer prices with the service.

U

0

 the utility level without the service.

4

Alternatively,

B  M

~

q

0

; U

0



 M

~

q;

U

0

hi

 T, with M

~

q

0

; U

0



 0(17:6N)

The term in brackets is Hicks' Compensating Variation measure of the willingness to pay for the

price change, where

~

q

0

 the vector of consumer prices without the service.

578 TAX AND EXPENDITURE INCIDENCE WITH DECREASING-COST SERVICES