Public Finance, 2nd Edition

THREE PRINCIPLES OF COST±BENEFIT ANALYSIS

The Limits of Analytical Rigor

The Wrst principle merely reaYrms the notion that cost±beneWt analysis is as

much an art as a science, for which reasoned judgment is every bit as

important as strict analytical rigor. Our theoretical knowledge of project

costs and beneWts comes from two sources: (1) Wrst-best models, in which

all markets are perfectly competitive and government policy responses to

particular problems are totally unrestricted; and (2) second-best models,

which have taken only the smallest steps in accounting for the vast array of

real-world imperfections and complexities. Second-best theory has also

shown us just how sensitive normative policy prescriptions are to both the

form and the number of restrictions added to the basic Wrst-best general

equilibrium framework. Consequently, analytical rigor cannot be the sole

arbiter in practical policy deliberations. At best, these theoretical models

provide a consistent analytical framework for thinking about practical prob-

lems, with their results serving as guidelines to the policymaker.

The essence of any cost±beneWt study derives from the assumptions it

chooses. To this end, the most important prior consideration is whether or

not Wrst-best assumptions are reasonable for analyzing a given investment

project and, if not, what speciWc second-best assumptions are appropriate

to the analysis. As might be expected, the Wrst-best assumptions greatly

simplify the analysis in most instances, but there is no sense using them if

they are clearly unreasonable. To give but one example, can the policymaker

reasonably assume that the distribution of income is (approximately)

optimal? The answer to this one question is central to a whole host of

practical issues.

One of the main goals of Part IV is to indicate how the choice between

Wrst- and second-best assumptions dictates the approach to each of the

practical problems being considered. For the most part, we will simply be

recalling theoretical results from Parts II and III and reXecting upon their

application to speciWc problems. It makes little sense to push forward with

new second-best models in our view unless absolutely necessary, especially

since no new second-best theoretical model can capture all the elements of

reality in any event. Of course, no such modeling decision arises if the Wrst-

best assumptions are deemed appropriate because Wrst-best theory oVers a

single, well-deWned set of policy guidelines for any given problem. There is

only one possible set of Wrst-best assumptions.

Quantifying the Present Value Formula

The second principle is that a cost±beneWt analysis of government invest-

ments proceeds exactly as the analysis of private investments undertaken by

720 THREE PRINCIPLES OF COST±BENEFIT ANALYSIS

Wrms. Both analyses center around the present value formula, which is

necessary to render all beneWts and costs commensurate over time. Let the

present value of a government project be deWned as:

PV I

0



P

N

n1

R

n

1  r

n

(23:1)

where:

PV  the present value of the investment,

I

0

 initial investments costs,

R

n

 a measure of net beneWts (beneWts  costs) in period n,

r  the appropriate rate of discount (assumed constant over time),

N  the endpoint of the planning horizon,

exactly as for private sector investments.

1

The same decision rules apply for

the government as well:

1. The government should accept all investments, and only those

investments, that have a positive present value. This is the meaning of

a ``worthwhile'' project.

2

2. If funds are limited for some reason, the goal is to select the subset of

projects that maximizes aggregate present value subject to the budget

constraint. The solution to this problem requires programming

techniques and may leave some of the funds unexpended, depending

on the size of each individual project.

Ideally, the government should subject all potential investments to these

present value tests regardless of their purpose.

The present value formula, Eq. (23.1), represents an addition to the

theoretical tools developed in Parts II and III which ignored the investment

aspect of government expenditures entirely by adopting a one-period, static,

general equilibrium framework, but it is only a trivial addition in and of itself.

Our previous models can easily be modiWed to incorporate government

investments by appropriately time-subscripting all variables and writing all

budget constraints (proWt functions) in present value form.

The underlying analytical framework for cost±beneWt analysis, then, is

perfectly straightforward. All the interesting issues lie in trying to quantify

each element in the present value formula. The same can be said of private

investment analysis.

1

If the one-year discount rate varies over time, the formula is PV I

0



P

N

n1

R

n

P

n

i1

1

1r

i



, where r

i

is the appropriate rate of discount for year i.

2

If a subset of these investments contains mutually exclusive projects, the project with the

highest present value within the subset should be chosen.

23. INTRODUCTION: THE ISSUES OF COST±BENEFIT ANALYSIS 721