A Student’s Guide to Cost Benefit Analysis for Natural Resources

 

Lesson 3 - Cost-Benefit Analysis in Theory and Application

 

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I. Introduction

 

Cost-benefit analysis (CBA) is the principal analytical framework used to evaluate public expenditure decisions. CBA said to have had its origins in the 1930s with the WPA water projects (dams) in the western U.S. There was a need to justify these projects to the taxpayers and Congress, hence CBA.

 

A greater demand for CBA is initiated by Executive Order 12291 issued by Reagan in 1981 requiring CBA on all government projects costing $100 million or more. Also, the need for CBA is illustrated by the fact that nearly all western countries require CBA and have developed protocols for CBA. CBA is a very common form of analysis for governments.

 

II. CBA and Economic Efficiency

 

Purpose of CBA: The general purpose of CBA is to help government & society better allocate their scarce productive resources.

 

CBA's Social Goal: The societal goal behind CBA is to achieve maximum economic efficiency.

What is economic efficiency?: economic efficiency requires that B>C. Efficiency is concerned about economic inputs vs. economic outputs.

 

CBA Rules: Thus, CBA analyses adheres to the following 2 simple rules:

 

1. If there are no constraints on inputs, adopt all projects that have positive net benefits (i.e., NPV).

2. If there are constraints (e.g., budgets) which limit the number of projects you can choose; then choose the combination of projects that maximizes net benefits (i.e., NPV).

 

3. Corollary: never adopt a project with negative net benefits.

 

III. Applying the Fundamental Rules

 

Next we will illustrate the application of the fundamental rules with 4 examples.

 

Example 1: Accepting or rejecting a single project.

 

This is simple. Remember, in the single project choice situation, adopt the project if the NPV > 0. If NPV is negative, reject the project.

 

But what about the alternative of no project?

No project is always implied by your analysis. CBA compares the additional benefits and costs with the project to benefits and costs without the project. CBA examines only the incremental costs, benefits, damages due to the project, not those that would occur anyway given a passage of time.

 

Thus, the proper comparison is:

1) costs and benefits with the project vs.

2) cost and benefits without the project.

With vs. without always insures a no project comparison.

 

The potential pitfall is that you will make a before vs. after comparison rather than with vs. without. In the future outputs will be different than they are now even w/o the project. So, you always have to take care to compare the situation with vs. without the project. Never analyze before vs. after.

 

Example 2: Choosing from one project from a number of mutually exclusive alternatives.

 

Solution: chose the one project that will "max net benefits."

 

Example 3: Choosing the appropriate scale of a project

 

Rather than a discreet choice set, as with the previous problem, this is a continuous choice set. Example: application of fertilizer or insect control to agricultural fields. You can apply varying amount of control. What is the optimal level of the application?

 

This is, in practice, a very difficult sort of problem, because you must know the continuous range of response to a range of treatments. Requires lots of production information. Here we simplify greatly.

 

We normally use a graphical solution to illustrate this problem. [See example with fig.1.1, p. 14 in Boardman.] In real practice, quantitative information would be developed.

 

Problem: Farmer want to know how much fertilizer to apply to his crops. Fertilizer costs are rising continuously in a nonlinear rate; indicates increasing costs.   Total cost = the cost of fertilizer.

 

The value of growth response (benefits) is non-linear ($ value of increased crops. production). This curved TB line exhibits decreasing marginal returns from fertilization.

 

Choice Rule: expand the project until MC=MB; also the same as MNB=0. In doing this, you are maximizing net benefits; this is the greatest distance, hence difference, between total costs and total benefits.

Calculus rules: equate first derivatives equal dTB/dQ = dTC/dQ;

Or, alternatively, set dNB/dQ=0

The fertilizer solution: Optimal amount (cost) of fertilizer is inferred from the Y axis.

 

Example 4: Accepting or rejecting a number of projects when initial cost is a constraint.

 

The first rule said accept all projects with a positive net benefit if there were no constraints on inputs. But now we have constraints on initial capital. How do we choose among the many projects?

 

The situation: The Wildlife Commission is considering a number of investment projects. Each is desirable, however, the Commission has a constraint on the initial (i.e., current year) investment capital it can spend. It can probably choose more than one project, but probably not all of them.

Solution: compute B/C ratio and array project in descending order of B/C ratios. Select projects until capital is exhausted.

 

Our objective is still to max net benefits. But with a constraint on initial investment, we will need some help from B/C ratio in finding a solution. B/C ratio can show us where we get the greatest benefits relative to initial investment.

 

IV. The Benefit/Cost Ratio

 

We introduced B/C ratio in the last example to help rank projects in order to max net benefits.

 

What about B/C ratio itself as a criteria for choosing mutually exclusive projects?

You have heard about B/C ratio and the adage accept the project if B/C ratio > 1,

meaning that the benefits are greater than the costs. It has historically been a very popular measure of investment performance for govt. projects.

 

Key Question: are B-C and B/C consistent when choosing one project from among mutually exclusive projects? Will the 2 criteria always lead to the same conclusion regarding the one best project?

 

The answer is no. The results may be conflicting. Thus: If projects are mutually exclusive (you must choose only one), B/C and B-C could give inconsistent, conflicting results.

 

What to do? Maximize net benefits is the favored criterion.

 

Another characteristic of B/C ratios.

Benefits are an algebraically positive entry in our accounting system. And costs are negative. But what about accounting for environmental damages like those stemming from air pollution?

 

For example, suppose the government wants to build a coal-fired power generation plant and they anticipate some air pollution damage to the surrounding environment.

It is possible in CBA to account for these environmental damages as either:

1) a positive cost, or 2) a negative benefit. There are great debates about which is appropriate.

Q: Will this accounting decision affect the analysis?

A: Not with max net benefits as the criterion. If you use max net benefits criterion; damages net-out either way you choose to classify damages (whether as a positive cost or negative benefit).

 

Conclude: if max net benefits is the criterion, it does not matter if damages are counted as a negative benefit or a positive cost. However, if you use B/C ratio, you must be careful.

Example: Cost=$1; benefits=$4; damage=$2. Make the B/C and B-C calculations first with damages as a positive cost then as a negative benefit and compare.

   

V. Theoretical Foundations of CBA

As we said, the goal of CBA is to determine economic efficiency (i.e., if B>C?).

 

Q: Is there any rational basis for saying that B>C is, in fact, the proper criterion for selecting public projects?

 

Gainers and losers: Decisions regarding public policies can create economic losers and gainers. Almost every alternative to be judged by CBA will have favorable effects on some people and unfavorable effects on others. Almost any project asks one part of society to sacrifice in order to provide for another part of society.

 

Because social welfare depends upon the satisfaction of all of society: Does the simple standard - benefits must be greater than costs - adequately deal with this issue of gainers compensating losers?

In a nutshell, B>C does deal with gainers and losers in that B>C at least assures that economic surplus could permit gainers to compensate losers. Follow the logic:

 

From 19^th century economist Vilfredo Pareto, we derive the notion of Pareto Efficiency:

a state such that resources cannot be reallocated in order to improve the utility of at least one person without decreasing the utility of others.

 

Pareto Efficiency requires that gainers must compensation losers. "cannot be reallocated"... is the key phrase.

 

Thus, if Pareto Efficiency is our rationale, then any government project must assure that gainers compensation losers.

 

But, it is argued that:

1. B>C alone doesn't provide specific guidance for compensation

2. compensation involves interpersonal comparisons about utility that economists cannot make, and

3. administration of actual, full compensation is too costly to consider.

 

Thus, the Pareto Efficiency, because it says compensation must take place, seems not to justify B>C.

 

An alternative rationale:

The Kaldor-Hicks Compensation Principle says: a policy should be adopted only if those who will gain could compensate those who will lose and still be better off. K-H does not say (as does Pareto Efficiency) that compensation must take place, only that it could take place. Thus, K-H says that B>C is valid because it creates enough economic surplus (i.e., B>C ) such that compensation of losers by gainers potentially can occur. Thus B>C leads to a potential Pareto improvement.

So equity (i.e., the distributional issue) is not important; CBA is not concerned with equity.

Or is it?

A quote to contemplate: Economic welfare analysis of policies which do not look at impacts on individual groups in effect usurps the policymaker's authority to make such judgements.

 

VI. Ex ante vs. ex post CBA:

There are 2 general types of CBA analyses: ex ante and ex post. Ex ante means coming before. Ex ante CBA precedes a project. Ex ante helps to make a goor no-go decision on a single project, or to select the best one of several project before it actually begins.

Strength: Ex ante studies can contribute a lot to the optimal resource allocation question (because this type of CBA precedes the project.)

 Weakness: Ex ante studies, because they are based on future benefits and costs, may be based on weak information and may involve a high degree of uncertainty.

 

Ex post means coming after. Ex post CBAs, therefore, come after a project has been completed.

Strength: They are based on less speculative information (since all costs and benefits have already occurred.)

Weakness: They have less power to influence resource allocation for the current project. But they can affect resource allocation for similar future projects. (If a past project was not cost-beneficial, Congress won't likely fund another like it.)

 

VII. Accounting Stance and Standing

A decision must be made at the beginning as to the geographic scope of the study: whose costs and benefits to count? The scope could be local, state, regional, national or global. With any scope smaller than global, you can encounter some accounting problems. Mainly, a lot of global transfers (i.e., the cost to group A = the benefit received by group B) show up as local benefits. Examples:

1. local CBA shows employment gains but not attendant employment losses occurring outside the region

2. local government CBA shows increased tax revenues as a benefit but not attendant consumption/savings decreases by citizens.

 

Beware of these sub-global studies; they can be abusive.

 

For government CBA, the proper perspective is almost always global (Executive Order 12291: measure the costs and benefits regardless to whom they may accrue.).

So, for a global analysis, think of the social project as a single production process where:

inputs = costs, outputs = benefits; and damages = either negative benefits or positive costs.

   

VIII. Economic vs. Financial Analyses

Government economic CBA analyses are the principal focus of this course. Financial CBA is another type of analysis important in the business world. The private sector has an obvious interest in financial analysis and planning to insure that they make the proper business decisions. We can, however, differentiate economic and financial CBA.

Following is a summary of the difference between economic and a financial CBA analysis (adapted with changes from Brooks, Ffolliott, Gregerson and DeBano, Hydrology and the Management of Watersheds, Ch. 14).

 

Comparison of financial and economic CBA analyses:

 

Summary: a financial analysis deals strictly with market-traded goods and services and accountable money flows. Economic analysis examines social benefits and costs, valued at society's willingness-to-pay.