Public Finance, 2nd Edition

environment. Nonetheless, they do have distributional consequences, and

knowing these aids the government in its search for the optimal pattern of

lump-sum redistributions.

If, realistically, governments are assumed to use distorting taxes to

Wnance their expenditures, then the analysis is inherently second best, and

tax and expenditure incidence cannot be separated (unless the expenditures

happen to be self-Wnancing using beneWts-received taxes). As we saw in the

discussion of tax incidence in a many-consumer world, one may have no

choice but to adopt the aggregate-social-welfare approach to have a theoret-

ically sound analysis.

We will not attempt an exhaustive analysis of all possible tax-and-ex-

penditure combinations with all possible incidence measures. Rather, we will

highlight some of the problems involved with introducing speciWc expend-

iture programs into an analysis of incidence. Thus, to keep the discussion

manageable, the numerous possibilities will be limited in three ways:

1. Tax-and-expenditure packages will be evaluated by the income

compensation or loss measure of incidence.

1

Hence, we will assume a one-

consumer-equivalent economy, with an optimal income distribution.

2. Only three expenditure programs will be considered: transfer pay-

ments, decreasing costs services, and nonexclusive Samuelsonian public

goods.

3. We will assume that lump-sum tax revenues Wnance the two resource-

using expenditure programsÐdecreasing cost services and Samuelsonian

public goodsÐand analyze their incidence in a Wrst-best environment. Since

the theory of resource-using public expenditures in a second-best environ-

ment will not be considered until the next chapter, a discussion of second-best

expenditure incidence at this point in the text would be premature. In con-

trast, all the tools necessary for a comprehensive analysis of the incidence of

transfer payments in a second-best environment have already been de-

veloped.

THE INCIDENCE OF GOVERNMENT TRANSFER PAYMENTS

Transfer payments, or subsidies, are analytically equivalent to negative taxes.

Consequently, the theory of tax incidence is fully applicable to government

transfer payments, with the single exception that all signs are reversed. All we

need do, then, is review the major results of the previous chapter as they apply

to subsidies:

1

The many-person social welfare measure of incidence will be discussed in Chapter 22. For

an analysis of expenditure incidence in the Harberger tradition, see C. McClure and W. Thirsk,

``A SimpliWed Exposition of the Harberger Model, II: Expenditure Incidence,'' National Tax

Journal, June 1975.

17. EXPENDITURE INCIDENCE AND ECONOMY-WIDE INCIDENCE STUDIES 575

1. If lump-sum taxes Wnance lump-sum transfers, there is no burden or

incidence in a one-consumer-equivalent economy. In a many-person econ-

omy, the tax paid or transfer received by any one person will be an appropri-

ate income proxy for the welfare gain or loss by that person under either one

of two assumptions: (a) technology is linear so that the taxes and transfers

cannot change the equilibrium vector of consumer and producer prices; or

(b) the policy relevant alternative to a given transfer-tax program is for the

government to completely undo the program, recalling all transfers and

returning all taxes, thereby restoring the original pretax and transfer equilib-

rium. Otherwise the tax-transfer program changes relative prices, and an

individual's gain or loss would be measured by the value of his expenditure

function evaluated at, say, the new prices and original utility level, less the

lump-sum tax paid or transfer received.

2. A set of distorting subsidies oVered to consumers and Wnanced by

lump-sum taxes is formally equivalent to the single-tax incidence problem of

levying a set of distorting taxes and returning the revenues lump sum. The

distorting subsidy-with-lump-sum tax generates a deadweight loss measured,

in the case of linear technology, by:

L

~

sM

~

q;

U

0





P

N

i1

s

i

X

comp

i

(17:1)

where:

~

s  the vector of per-unit subsidies with element s

i

.

~

q  the vector of consumer prices net of subsidy.

The appropriate measure in the case of general technology is:

L

~

sM

~

q;

U

0





P

N

i1

s

i

X

comp

i

 p

~

p (17:2)

The conceptual experiment described by Eq. (17.1) is a comparison between

the lump-sum income necessary to reach the original utility level at the new

lower prices less the amount of the subsidy, which is returned lump sum,

everything measured at the compensated equilibrium. (Eq. (17.2) ) subtracts

the pure proWts available at the compensated income from the required

income.) Hence, Eq. (17.1) measures the payment the consumers are willing

to make as a consequence of the subsidies less the required lump-sum income

payment (the return of the subsidy).

2

2

Since, from the consumer's point of view, goods prices are falling and factor prices are

rising, M(q;

U

0

) measures the income consumers are willing to pay for the subsidies and is a

negative number. Hence, loss is the addition of M(q;

U

0

) and

P

N

i1

s

i

X

comp

i

, where s

i

> 0 for

goods, < 0 for factors. Similarly, good prices are rising and factor prices are falling from the

Wrm's point of view, both of which tend to increase proWts. Hence, p(

~

p) must be subtracted from

the subsidy payment in Eq. (17.2) under general technology. This HCV measure is conceptually

equivalent to the HEV measure for a distorting tax.

576 THE INCIDENCE OF GOVERNMENT TRANSFER PAYMENTS