Cost-Benefit Analysis: The Details How can economics help determine the optimal size of a project or extent of a regulation?

Cost-Benefit Analysis: The Details

How can economics help determine the optimal size of a project or extent of a regulation?

A few examples

What should be the CO concentration standard in tailpipe emissions?

How large should the Channel Islands marine reserve be?

Can we measure loss to recreationists of the Forest Adventure Pass?

Add another lane to Hwy 101? Close Mission Canyon to cyclists? What habitat to buy to protect endangered

species (e.g., Least Bell’s Vireo – bird)

CBA: main principle

Quantify all costs and benefits in a common measure (usually $) Note that we have ways of quantifying non-market,

even non-use values. Common metric need not be $ -- e.g., health- health

analysis, with health as metric E.g., consider a regulation that saves lives Benefits directly measured in terms of lives saved Costs indirect: costs increase deaths since lower

incomes lead to higher mortality ($13 million in extra costs results in 1 statistical death)

• E.g., Compare risks in lower and higher income countries Compare projects based on net effects on health.

When to do CBA?

Need to compare reg’s to achieve externally defined social goals – CEA

Need to set a level of a reg, balancing pluses and minues: CBA

Need to decide on a project with multiple goals that cannot be reduced to a single metric: multi-goal analysis

Example – issue is how big

Project size, Q. Benefits = B(Q)Costs = C(Q)

Maximize Net Benefits, B(Q)-C(Q) Ignore issue for time being of how to

quantify B(Q) and C(Q)

TB(Q)

TC(Q)

Q

$

Q

$Q*

TB(Q)-TC(Q)

One view ofthis problem:Maximize TB-TC

TB(Q)

TC(Q)

Q

$

QMB(Q)

MC(Q)

$

Q* is whereTB-TC is maximized.Also where MB=MC.

Q*

xC

Discrete sized projects

If deciding between projects A, B, CPick one with highest net benefits (TB-TC),

provided net benefits > 0. May have values that are difficult to

quantify.Quantify values you can, then compare

projects along as few dimensions as possible (“multi-criteria analysis”); examine tradeoffs between alternatives.

Big Questions

How to measure/conceptualize benefits?

How to measure/conceptualize costs? How to treat costs and benefits that

occur at different points in time? How to deal with distributional issues? How to deal with risk?

Question #1: Conceptualizing Benefits

Suppose a river is dead, what is the value of reducing pollution by one unit?

What is the value of increasing visual range by a unit in the West?

How do we value the extra units of electricity?

Basic measure of value is willingness-to-pay

Demand curve is marginal willingness to pay

Quantity of water

MWTP First units very valuable

Last units less valuable

Consumers Surplus (CS)

D(x)

x

$

q

p

CS(q)

How are benefits calculated?

Demand, D(x), measures MB.Consumers Surplus is the total benefit

to consumers minus their cost.

q

pqdxxDqCS0

)()(

Example – gross value of water from new dam (excluding costs)

Acre-feet of water

Price

Demand for water

New dam

. . .

. . . . . . .

. . . . .. .

. . . . . . .

Add’l Value

What about nonmarket goods?

Air quality

Price

Suppose there were a market:

Demand for air quality

BUT, NO MARKET: price similar to MWTP

Environmental goods

Demand for env goods just as real as demand for market goods – just harder to measure

Demand is a measure of intensity of preferences

Costs are simpler

Some units are cheap to produce “Marginal” units are most expensive Costs consist of

Fixed costsMarginal costs

Marginal costs plus fixed costs add up to total costs

Quantity

MC

First units cheapest

Last units pricey

Costs come in different flavors:Private, external and social

In principle, need to capture all costs and benefits.

Social costs may exceed private costs.

Difference is the “external cost” – the monetized cost of the externality.

$/gal

GallonsOf Gasoline

MPC

Q0

P0

Social vs. Private Costs

In principle, need to capture all costs and benefits.

Social costs may exceed private costs.

Difference is the “external cost” – the monetized cost of the externality.

$/gal

GallonsOf Gasoline

MPCMEC

Q0

P0

Social vs. Private Costs

In principle, need to capture all costs and benefits.

Social costs may exceed private costs.

Difference is the “external cost” – the monetized cost of the externality.

$/gal

GallonsOf Gasoline

MSC

MPCMEC

Q*

P*

Q0

P0

Producer Surplus (PS)

x

$

p

q

PS(q)

MC(x)

How are costs calculated?

Supply, S(x), is same thing as MC.Producer Surplus is the total revenue

to producers minus their cost.

q

dxxSpqqPS0

)()(

Put it together

Q

P

. . .

. . . . . . .

. . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . .

Total Surplus

Where is CS+PS maximized?

Demand, D(x)

Supply, S(x)

q1 q*

p

x

$CS

PS

Tension: Too little producedAt too high price. CS low, PS high

Suppose goods supplied in fixed amount

Land

Price Supply of land

Producer surplus (goes to land owners)

Consumer surplus

Demand for land

MarketPrice

If captured all costs & benefits

Then we want to maximize CS + PS which would occur where Supply = Demand.

Challenge is to capture all costs and benefits to accurately measure MC & MB.

NoteSurplus Max equals CS+PS maximum

First Theorem of Welfare Economics

In a competitive marketSurplus is maximized at a market equilibrium

ImplicationsCan rely on market if we are sure of

competitive market

Example: Add a dam

Q Water

P:rice

Supply of water increases; price falls.What happens to PS? CS?

XXXXXXXXXXXX $$$$$##################

PS: Before: # and X After: X and $

CS: ??

Implicit Assumptions: Distribution

Distributional consequences ignored Put in dam: some win, some lose Benefits cancel losses OK if compensation occurs

Compensation Principle Dam is good idea if winners can compensate

losers If there is enough surplus, dam is a good idea BUT, compensation need not occur

Implicit Assumptions: Income

Restaurant meals

Price

Y=$30,000 per year

Y=$50,000 per year

Demand and thus surplus depend on income distribution

Therefore: Change in income distribution will change results of CBATO USE CBA, MUST BELIEVE INCOME DISTRIBUTION IS OK

Implicit Assumptions: Completeness

What happens with difficult to monetize benefits?E.g., clear view of Santa Cruz Islands

Difficult to monetize benefits often omitted

Results in bias against environmental benefits

Implicit Assumptions: Other

Moral and political dimensions omittedShould we do a cost-benefit analysis

on executing someone who has committed a crime?

Are there other issues when lives are at stake?

Are intergenerational issues adequately treated by CBA?

Ten Steps to doing and using a CBA

1. Decide whose benefits and costs count 2. Select the portfolio of alternative projects 3. Catalog potential physical impacts and determine how they are

measured 4. Predict quantitative physical impacts over life of project 5. Monetize (or other metric) all impacts 6. Discount for time to find present values 7. Sum: add up all benefits and costs 8. Perform sensitivity analysis 9. Choose alternative with largest social benefits 10. Make policy recommendation, using CBA only as part of guidance 11. Identify limitations specific to your analysis