Consumer and Producer Surplus in Benefit-Cost Analysis

(Campbell & Brown Chapter 7)

Harry Campbell & Richard BrownSchool of Economics

UQ, St. Lucia 2003

BENEFIT-COST ANALYSISBENEFIT-COST ANALYSISfinancial and economicfinancial and economic

appraisal using spreadsheetsappraisal using spreadsheets

Figure 7.1: Consumer Surplus

Trips per year Q1 Q0

P1

P0

O

B

D

C

A

E

$

The market prices of project inputs or outputs will NOTchange if:

- the inputs or outputs are TRADED ie. price is determined in world markets)

- the project is SMALL relative to the size of theeconomy in which is undertaken

Examples of project outputs or inputs whose pricesmight change:

- output: a bridge - price of trips across a river- input: wage of skilled labour in a local market

eg. ICP case study (Ch.7, p.26)

Suppose the market price of project output is predictedto fall from P0 to P1 as a result of the increase inquantity supplied from Q0 to Q1 (as in Figure 7.1).How do we value the additional output (Q1 - Q0) ina social benefit-cost analysis?

Project Analysis: use P1

Private Analysis: use P1

Efficiency Analysis: use (P0+P1)/2

Referent Group Analysis: calculate the aggregatenet benefits in the usual way

How do we account for the fall in price of the originalquantity of output, Q0? Clearly consumers benefit bythe amount (P0 - P1)Q0. When will that represent anet benefit of the project?

When the fall in price from P0 to P1 represents a fallin cost, as in the bridge example, the value (P0 - P1)Q0

is a net benefit which is included in the efficiency netbenefits.

When the fall in price does not represent a fall in cost, onegroup is better off (consumers) and another group is worseoff (firms) by the same amount. The amount (P0 - P1)Q0 issimply a transfer from consumers to firms and it nets out inthe efficiency benefit-cost analysis.

Suppose that the fall in product price is not matched bya fall in production cost.What is the effect on aggregate referent group benefits of allowing for the change in output price, compared to the case in which there is no change in price?

1. Suppose that the private firm is not a member of thereferent group (as in the ICP case study):efficiency net benefits fall but private net benefits falleven more, hence RG net benefits rise. Consumersbenefit at the expense of the firm.

2. Suppose that the private firm is a member of thereferent group. Then efficiency net benefits are the sameas RG net benefits, and hence RG net benefits fall. Thereason for the fall is the lower value placed on the extraoutput produced by the project.

The social benefit-cost analysis implements the Kaldor-Hicks (K-H) criterion by assessing whether a projectis a potential Pareto improvement.

A potential Pareto improvement exists if the gainers froma project could compensate the losers and still bebetter off.

Gains and losses are measured as COMPENSATINGVARIATIONS.

Compensating variations are measured as areas ofconsumer surplus under demand curves, or asareas of producer surplus above supply curves.

Applying the Kaldor-Hicks criterion: suppose I said thatI was going to change the lecture time from 4 pm to 8 am.That would suit some people (the gainers) and not suitothers (the losers).To apply the K-H criterion, I ask each gainer to work outhow much money I could take away from them and stillleave them as well off as before the change. And I askeach loser to work out how much money I would needto pay to them to leave them as well off as before thechange. These sums are the compensating variations (CVs).

I ask each person to write their CV amount on a piece ofpaper (positive for gainers, negative for losers). I then pass the hat around: each person puts their piece of paper in thehat and if the net value of the aggregate CV is positive, thechange is a potential Pareto improvement.

Figure 7.2(a): Consumer Surplus with Inelastic Demand

Price

P0

P1

Quantity/year Q

F

A

D

$

Figure 7.2(b): Consumer Surplus with Elastic Demand

F

Q1

Price

P0

P1

Quantity/year Q0

C

A

D

$

Figure 7.10: Effect of an Increase in Demand for Labour

L1 L0

D1

D0

V

Labour Hours per year

Z

W1

W0

O

U

S

$

Figure 7.3: Benefits of a Bridge

Trips per year Q1 Q0

P1

P0

O

B

D

C

A

E

$

Figure 7.4: Effect of a Bridge Toll Q2

H P2 F

G

Trips per year Q1 Q0

P1

P0

O

B

D

C

A

E

$

Figure 7.5: Subsidizing Bus Fares

S

Trips per year Q1 Q0

P1

P0

O

B

D

C A

E

$

Figure 7.6: Effects of Worker Training

$

w1

L2 L0

E

F

G

S1

S0

Labour Hours per Year L1

w0

O

B

D

C

A

H

Effects of a worker training program:

On employers: skilled wage rate falls fromw0 to w1; benefit is measured by area w0ABw1

On the original skilled labour force: skilledwage rate falls from w0 to w1; cost ismeasured by area -w0AFw1

On trainees: they get jobs at wage w1

while their opportunity cost is measuredby supply curve S1; benefit is area FBG

To work out total benefit: add ________to get total FABG

Figure 7.7: Benefits of an Irrigation Project

S1

S0

C

Water (megalitres per year) Q1 Q0

P1

P0

O

E

D

B

A

$

Value of extra output of food = BCQ1Q0 (Fig. 7.7)

Value of extra output = Value of extra income

Extra income:1. Water Authority: P1CQ10 - P0BQ002. Landowner: P0BCP1

Total extra income:P1CQ10 - P0BQ00 + P0BCP1 = BCQ1Q0

Conclusion: there are two ways to measure the netbenefits of an irrigation project: the output approachand the incomes approach.

Figure 7.8: Change in the Rental Value of Land

D1

D0

F

Land Input (hectares per year) Q

R1

R0

O

G

S

$

Figure 7.9: Irrigation Water Sold at Less than Market Value

VMPW

Q0

N

Water (megalitres per year) Q1

P K

O

L

M

$

Suppose that extra labour is used on the irrigatedland. Under the incomes approach this would bereflected in extra value of output.

Suppose that the extra labour was hired away froma neighbouring valley. Then there would be anequivalent fall in value of output in that valley. Thisopportunity cost of labour would have to besubtracted from the value of extra output.

If wages rise as a result of competition for labour,labour is better off and employers are worse off -the effect of the wage increase nets out if bothare members of the referent group (see Fig. 7.10)

Figure 7.10: Effect of an Increase in Demand for Labour

L1 L0

D1

D0

V

Labour Hours per year

Z

W1

W0

O

U

S

$

Figure 7.11: Effects of Building a Bridge on the Benefits from a Ferry

PF1

PF0

SF

DF0

DF1

A

B

C

Ferry trips/yr Bridge trips/yr

DB1

QB

PB

E

D

(b) (a)

Figure A7.1: Compensating and Equivalent Variation

DU1

DU0

Q1 Q0

C

D0

A

Quantity/year

E

P1

P0

O

F

G

$

Compensating variation is the sum of money to betaken from (paid to) a gainer (loser) so as to maintaintheir original level of utility.

Hence we measure compensating variation underutility constant demand curves.

For a fall in price from P0 to P1 (Fig. A7.1) theCVF = P0AFP1(to be taken from the person)

For a rise in price from P1 to P0 (Fig. A7.1) theCVR = P0GCP1 (to be paid to the person)

Why is CVR > CVF? Because utility and expenditureare higher on DU1 than on DU0 and hence morecompensation is required to maintain them.