BENEFIT-COST ANALYSIS
financial and economic
appraisal using spreadsheets
Consumer and Producer Surplus in
Benefit-Cost Analysis
(Campbell & Brown Chapter 7)
Harry Campbell & Richard Brown
School of Economics
UQ, St. Lucia 2003
Figure 7.1: Consumer Surplus
$
E
A
P0
C
P1
B
D
O
Q0
Q1
Trips per year
The market prices of project inputs or outputs will NOT
change if:
- the inputs or outputs are TRADED ie. price is
determined in world markets)
- the project is SMALL relative to the size of the
economy in which is undertaken
Examples of project outputs or inputs whose prices
might 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 predicted
to fall from P0 to P1 as a result of the increase in
quantity supplied from Q0 to Q1 (as in Figure 7.1).
How do we value the additional output (Q1 - Q0) in
a social benefit-cost analysis?
Project Analysis: use P1
Private Analysis: use P1
Efficiency Analysis: use (P0+P1)/2
Referent Group Analysis: calculate the aggregate
net benefits in the usual way
How do we account for the fall in price of the original
quantity of output, Q0? Clearly consumers benefit by
the amount (P0 - P1)Q0. When will that represent a
net benefit of the project?
When the fall in price from P0 to P1 represents a fall
in cost, as in the bridge example, the value (P0 - P1)Q0
is a net benefit which is included in the efficiency net
benefits.
When the fall in price does not represent a fall in cost, one
group is better off (consumers) and another group is worse
off (firms) by the same amount. The amount (P0 - P1)Q0 is
simply a transfer from consumers to firms and it nets out in
the efficiency benefit-cost analysis.
Suppose that the fall in product price is not matched by
a 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 the
referent group (as in the ICP case study):
efficiency net benefits fall but private net benefits fall
even more, hence RG net benefits rise. Consumers
benefit at the expense of the firm.
2. Suppose that the private firm is a member of the
referent group. Then efficiency net benefits are the same
as RG net benefits, and hence RG net benefits fall. The
reason for the fall is the lower value placed on the extra
output produced by the project.
The social benefit-cost analysis implements the KaldorHicks (K-H) criterion by assessing whether a project
is a potential Pareto improvement.
A potential Pareto improvement exists if the gainers from
a project could compensate the losers and still be
better off.
Gains and losses are measured as COMPENSATING
VARIATIONS.
Compensating variations are measured as areas of
consumer surplus under demand curves, or as
areas of producer surplus above supply curves.
Applying the Kaldor-Hicks criterion: suppose I said that
I was going to change the lecture time from 4 pm to 8 am.
That would suit some people (the gainers) and not suit
others (the losers).
To apply the K-H criterion, I ask each gainer to work out
how much money I could take away from them and still
leave them as well off as before the change. And I ask
each loser to work out how much money I would need
to pay to them to leave them as well off as before the
change. These sums are the compensating variations (CVs).
I ask each person to write their CV amount on a piece of
paper (positive for gainers, negative for losers). I then pass
the hat around: each person puts their piece of paper in the
hat and if the net value of the aggregate CV is positive, the
change is a potential Pareto improvement.
Figure 7.2(a): Consumer Surplus with Inelastic Demand
$
Price
D
P0
A
P1
F
Q
Quantity/year
Figure 7.2(b): Consumer Surplus with Elastic Demand
$
Price
P0
A
C
P1
F
D
Q0
Q1
Quantity/year
Figure 7.10: Effect of an Increase in Demand for Labour
$
S
V
W1
W0
U
D1
Z
D0
O
L0
L1
Labour Hours per year
Figure 7.3: Benefits of a Bridge
$
E
A
P0
C
P1
B
D
O
Q0
Q1
Trips per year
Figure 7.4: Effect of a Bridge Toll
$
E
A
P0
P2
H
F
C
P1
B
G
D
O
Q0
Q2
Q1
Trips per year
Figure 7.5: Subsidizing Bus Fares
$
A
C
P0
P1
S
B
E
D
O
Q0
Q1
Trips per year
Figure 7.6: Effects of Worker Training
$
S0
E
S1
A
w0
B
F
w1
C
H
G
D
O
L2
L0
L1
Labour Hours per Year
Effects of a worker training program:
On employers: skilled wage rate falls from
w0 to w1; benefit is measured by area
w0ABw1
On the original skilled labour force: skilled
wage rate falls from w0 to w1; cost is
measured by area
-w0AFw1
On trainees: they get jobs at wage w1
while their opportunity cost is measured
by 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
$
A
S0
S1
B
P0
C
P1
E
D
O
Q0
Q1
Water (megalitres per year)
Value of extra output of food = BCQ1Q0 (Fig. 7.7)
Value of extra output = Value of extra income
Extra income:
1. Water Authority: P1CQ10 - P0BQ00
2. Landowner: P0BCP1
Total extra income:
P1CQ10 - P0BQ00 + P0BCP1 = BCQ1Q0
Conclusion: there are two ways to measure the net
benefits of an irrigation project: the output approach
and the incomes approach.
Figure 7.8: Change in the Rental Value of Land
$
S
R1
F
R0
G
D1
D0
O
Q
Land Input (hectares per year)
Figure 7.9: Irrigation Water Sold at Less than Market Value
$
M
N
P
L
K
VMPW
O
Q0
Q1
Water (megalitres per year)
Suppose that extra labour is used on the irrigated
land. Under the incomes approach this would be
reflected in extra value of output.
Suppose that the extra labour was hired away from
a neighbouring valley. Then there would be an
equivalent fall in value of output in that valley. This
opportunity cost of labour would have to be
subtracted 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 both
are members of the referent group (see Fig. 7.10)
Figure 7.10: Effect of an Increase in Demand for Labour
$
S
V
W1
W0
U
D1
Z
D0
O
L0
L1
Labour Hours per year
Figure 7.11: Effects of Building a Bridge on the Benefits from a Ferry
(a)
(b)
D
SF
C
A
PF0
PF1
E
PB
B
DF0
DB1
DF1
QB
Bridge trips/yr
Ferry trips/yr
Figure A7.1: Compensating and Equivalent Variation
$
DU0
DU1
E
A
P0
G
F
P1
C
D0
O
Q0
Q1
Quantity/year
Compensating variation is the sum of money to be
taken from (paid to) a gainer (loser) so as to maintain
their original level of utility.
Hence we measure compensating variation under
utility constant demand curves.
For a fall in price from P0 to P1 (Fig. A7.1) the
CVF = P0AFP1(to be taken from the person)
For a rise in price from P1 to P0 (Fig. A7.1) the
CVR = P0GCP1 (to be paid to the person)
Why is CVR > CVF? Because utility and expenditure
are higher on DU1 than on DU0 and hence more
compensation is required to maintain them.