Social welfare economics foundations for CBA

G. Mason

2010

Under consumption of public good

• What examples exist of public goods you care that others under consume?

• What examples of public goods make no difference that others under-consume?

QA QBQC

QQ*

Social Demand

Direct and inverse demand

• Direct demand views quantity as the “dependent” variable and price as the “independent” variable or the driver.– QA = A0 - A1PA

• Inverse demand, views price as a marginal utility and measure of the willingness to pay for a specific quantity.– PA = A0 + A1QA

Social welfare rules

• Few actions by government make everyone better off; usually there are several winners and several losers.

• Who are the winners and losers in the following scenarios– Street repairs– Subsidies to the arts and culture– Mandatory vaccination of girls (under 12) for

HPV (see facts sheets)

Pareto Rules 1

• Program X improves the welfare of society if it makes at least one person better off without making anyone else worse off.

• Adler and Posner (reading cited in outline) identify several factors that prevent this rule for working.– Un observability of states of welfare– Un comparability of welfare among individuals

• Declining marginal utility of money suggests that those who are well off, would be worsened, if many others who are poor are made better off.

Pareto 2

• Assume a social preference function (aggregate demand for a public good) given by:

U(X1,X2, …XN).• Also assume H households in a community, and a single

road. Cyclists would like a bike path; council must decide.

• If the bike path is built, the average household will experience utility increase of ΔU.

• Council has an easy decision if:– ΔUh > 0 for all households and ΔUh > 0 for at least one

household, or if– ΔUh < 0 for at all one household and (ΔUh <0 for one household)

Pareto 3

• Most situations involve a mix of households that experience increases, neutral or negative utilities from a bike path (Who loses from a bike path?)

• Naïve solution is add utilities– Utot = ΔU1 + ΔU2 +…. ΔUh

• Utility is an ordinal measure, not cardinal• That means we cannot compare utilities

directly

Willingness to PayCompensating Variation

• Beneficiaries of bike path– What is the maximum amount you are willing to pay to

have the bike path constructed?

• Opponents of bike path– What is the minimum amount you are willing to accept

of the bike path were constructed.

• This is a proxy for the change in utility from the perspective of adopting the new.

• For household h, if compensating variation is CVh >0, then ΔUh > 0; if CVh <0, then ΔUh < 0; and if CVh =0, then ΔUh = 0.

Willingness to PayEquivalent Variation

• Beneficiaries of bike path– What is the minimum amount you would accept to

forgo the bike path?

• Opponents of the bike path– What is the maximum amount you would be willing to

pay to stop the bike path?

• This is the proxy for utility from the perspective of preserving the old.

• For household h, if equivalent variation is EVh >0, then ΔUh > 0; if EVh <0, then ΔUh < 0; and if EVh =0, then ΔUh = 0.

Beneficiaries Opponents

Compensating Variation

Move to New

Payment to get project

Payment to accept project

Equivalent Variation

Maintain the Old

Payment received to forgo project

Payment to prevent bike path

Several methods exist to measure willingness to pay, including revealed preference (demand studies) and direct surveys. These will be reviewed in more detail, later in the course

First compensation rule• It may be tempting to conduct a survey and then add

CVh across all households. If CVh > 0 this is the first compensation test in public policy

• Issues– To ensure Pareto optimality, those whose welfare declines with

the change must actually be compensated. (This raises mechanical issues of getting winners to pay losers). It also causes strategic biases if survey respondents raise “price” to get more money (ie., overstate their need for compensation)

– Marginal utility of income means that one can compare CV and EV only for those at the same income.

Key assumption of CBA – Government uses tax and transfer policies to ensure an optimal distribution of income, such that the marginal utility of income is equivalent for all.

Second compensation rule

• If EVh > 0 this is the second compensation test in public policy (subject to equal marginal utilities of income).

• This is the preservation scenario. If EV>0, then the minimum amount needed by cyclists to forgo the path, exceeds the maximum amount opponents would be willing to pay to preserve the status quo. This means the project proceeds

• If EV<0, then the opponents can buy off the beneficiaries and the project does not proceed.

Combining the rules1.CV> 0, EV > 0 (proceed)

– Both compensation rules are satisfied. Winners can compensate losers if the project were build, and losers could not compensate winners if the project were not built. If path does not exist, build it; the path exists retain it.

2.EV<0, CV<0 (do nor proceed)– Those who gain fro the status quo can compensate those who want the project; if the

project exists, those that want to cancel it, can compensate those that want to maintain it. If the path does not exist, do not build it; if it exists, destroy it.

3.CV>0, EV<0 – If there no path, winners can compensate losers. If there is a path, losers can compensate

winners. If there is no path, build it; if a path exists, get rid of it!4.EV>0, CV<0

– EV>0 implies that if there is a path, then destroying it would cause a welfare loss; if CV<0, then if there is no path, constructing it would cause a welfare loss.

The third and fourth situations are the essence of what is called the Scitovsky paradox or Scitovsky reversal If EV and CV are negative reject the project; If EV and CV are positive, adopt the project. Combinations 3 and 4 offer no guidance, and the status quo should be maintained, pending more data.

Consumer surplus

a

b

d

c

e

D

P1

P2

X1 X2

At P1, consumers are willing to buy X1. At smaller quantities, they are prepared to pay more, but not have to. “a” is the consumer surplus at P1

When prices drop, consumer surplus rises to a+b+c

Consumer surplus and CV,EV

• Normal goods – EV>ΔCS>CV

• Inferior goods – EV<ΔCS<CV

• EV= ΔCS=CV when income elasticity is zero.

• In general, measures of consumer surplus perform reasonably well in measuring changes in social welfare

Changes due to price of substitutes and complements

• Assume that X, Y and Z are three commodities

• Y is substitute for X and Z is a complement of X.

• A price decrease in X, reduces demand for Y, and increases the demand for Z

Dy1Py

y1 y2

Dy2f g

Price of X increases, reduces the demand for Y

Dz2Pz

z1 z2

Dz1h i

Price of X increases, increase the demand for z

Overall income has not changed: Therefore

b+d+f+g+h = d+e+f+h+j

Rearranging

b = e – g + j

And therefore b+c = (c + e) – g +j

Refer to previous figure as well for b, c d, and e

Recall that b+c was the increase in consumer surplus from a price reduction in x

Change in undistorted markets

a

b

d

c

e Dx

P1

P2

X1 X2

Px

MC

Undistorted means that P = MC

Price of X drops, but demand for the substitute Y falls and increases for the complement

ΔB=c+e-g+j

ΔW = ΔB - ΔC

Dy1

Py

y2 y1

Dy2

f g

Py

MC

Dz2

Pz

z1 z2

Dz1

h j

MC

Pz

ΔW = [c+e-g+j] – [e-g+j], or market by market

ΔW = [c+e-e] +[-g+g] + [j-j],

x y z

Distorted markets

k

m Dj

P2

P1

J1J2

Pj

MCj

The economy has three goods – J, K, L. L is a composite good representing all other goods except J and K

The price of J rises from P1 to P2. The demand drops for J, but rises for K and L.

The price of K is distorted because it is less than its marginal cost.J, K, and L are assumed to be

substitutes – when the price of J drops the demand for K and l increases.

DK2

Pk

K1 K2

DK1

n

Pk

MCk

q

MCk

In market J, consumers lose k + m

In markets K and L, they receive n + r.

ΔB = n + r – (k + m)

The resource cost declines for J = m, increases for K (q + n) and L (r)

ΔW = ΔB - ΔW = q + n + r - m

DL2

PL

L1 L2

DL1

PL

MCL

r