Public Finance, 2nd Edition

The second point in favor of a socially adjusted MRS is due to Amartya

Sen and Stephen Marglin.

9

They argue that saving has a Samuelsonian public

good aspect to it that the government should take into consideration, just as it

would any intratemporal externality. It is essentially the intertemporal version

of the issue of pareto-optimal redistributions discussed in Chapter 10.

Namely, the beneWts received by future generations from any one individual's

saving are twofold: (1) a direct beneWt arising from the increased income of the

individual's own heirs, plus (2) an external beneWt arising because the returns

are taxed and distributed throughout the population, thereby increasing the

income of others' heirs. To the extent people receive utility from the indirect

eVect, Sen and Marglin show that a social contract in which all are forced to

save for the future is generally pareto superior to the situation of privately

determined savings, from the current generation's point of view. Without

presenting the details, the essence of the proof is identical to that for any

external economy: Subsidizing any activity that generates external economies

yields net beneWts otherwise unexploited by private decision making. In this

instance, the subsidy implies setting MRS

soc

below MRS

priv

for purposes of

project evaluation.

THEORETICAL CONSIDERATIONS FROM NORMATIVE PUBLIC

EXPENDITURE AND TAX THEORY

Before proceeding to a model speciWcally designed to incorporate these three

features, let us brieXy consider the implications of the theoretical models of

public expenditures and taxation developed in Parts II and III. They describe

a number of special cases for which computing the rate of discount would be

relatively straightforward, but the assumptions each time are so stringent that

these results may not have much practical value.

The First-Best Environment

One ``easy'' case occurs if the economic and policy environment can reason-

ably be assumed to be Wrst best. This would greatly simplify computations of

the discount rate because the MRS and MRT between the present and future

would be equal for investments of equal risk. Hence, the consumption±

investment mix would be irrelevant. Optimal income distribution would

render the economy equivalent to a one-consumer economy and, with perfect

markets everywhere, the economy would reach an equilibrium such as point

A in Fig. 24.3, at which the common MRS just equals the common MRT.

9

S. Marglin, ``The Social Rate of Discount and the Optimal Rate of Investment,'' Quarterly

Journal of Economics, February, 1963; A. Sen, ``The Social Time Preference Rate in Relation to

the Market Rate of Interest,'' in R. Layard, Ed., Cost±BeneWt Analysis, Penguin Education,

Penguin Books, Ltd., Middlesex, England, 1972; A. Sen, ``Isolation, Assurance, and the Social

Rate of Discount,'' Quarterly Journal of Economics, February, 1967.

740 THEORETICAL CONSIDERATIONS FROM NORMATIVE PUBLIC EXPENDITURE

A

C

t

C

t +1

I

0

FIGURE 24.3

Hence, the MRS

soc

is the opportunity cost of public funds, so that the two

opposing pragmatic views on the public rate of discount coincide.

10

As usual, the Wrst-best assumptions make life easy, but they are clearly

inappropriate for computing the public rate of discount in any of the de-

veloped market economies. As noted above, the MRS and MRT are driven

far apart by taxation in the United States. Thus, determining the proper

discount rate must fall within the domain of the second best, for which there

is an uncomfortably wide range of possibilities.

The Second-Best Environment

To interpret our previous second-best models intertemporally, think of the

economy as consisting of a single good produced and consumed over N time

periods rather than N goods and factors in a single time period, and let the

good in period N serve as the untaxed numeraire. The good can be consumed

directly or used to produce additional units of the good in future periods. The

objective function is the present value of social welfare, discounted at the

MRS

soc

. The consumers' MRS

priv

equals the ratio of the consumer prices q

j

:

(U

j

/U

j1

 q

j

/q

j1

 1  r

c

). Similarly, the private producers' MRT equals

the ratio of the producer prices p

j

:(f

j

/f

j1

 p

j

/p

j1

 1  r

p

). In addition, the

government's production function Z

N

g(Z

1

, ...,Z

N1

)deWnes the public

sector's rate of transformation over time, with g

Z

j

/g

Z

j1

equal to the one-

period rate of discount for public projects. Finally, all budget constraints

10

I

0

in Fig. 24.3 is meant to be a social indiVerence curve under the Wrst-best assumption of

optimal income distribution. If MRS

priv

> MRS

soc

because of a Sen-Marglin intergenerational

savings externality, the private market MRT is the proper rate of discount, not the private market

MRS. At a Wrst-best optimum, MRS

priv

> MRS

soc

 MRT, with the saving externality incorp-

orated into the social indiVerence curves.

24. THE RATE OF DISCOUNT FOR PUBLIC INVESTMENTS 741