Chapter 10: The Social Discount Rate,
Cost of Public Funds, and the Value of
Information
© Harry Campbell & Richard Brown
School of Economics
The University of QueenslandBENEFIT-COST ANALYSIS
BENEFIT-COST ANALYSIS
Financial and Economic
Financial and Economic
Appraisal using Spreadsheets
Appraisal using Spreadsheets

Three reasons why NPV>0 may not be the appropriate rule to
identify projects which are efficient from a social viewpoint:
•
the social discount rate may be lower than the market rate
of interest;
•
the marginal cost of public funds may exceed unity (ie. $1 of
public funds costs more than $1);
•
undertaking an irreversible investment involves a loss of
option value.

The Social Discount Rate
Why does the market discount future benefits and costs?
•

It is reasonable to employ a utility growth factor in discounting
public projects: if future generations are going to be wealthier than
us, we should take this into account in sacrificing present
consumption to make provision for the future.
It is not reasonable to employ a utility discount factor in
discounting public projects: we should not treat the utility of future
generations as any less important than that of the present
generation.

Developing our simple example: instead of using the real market
rate of interest of 4% as the discount rate for public projects, we
would adjust it downwards by the amount of the utility discount
factor (1%) to get a social discount rate equal to the utility growth
factor (3%).
Using a social discount rate would tend to make investment
projects more attractive, but the 1% difference in discount rate
would be crucial in only a few cases.

The Marginal Cost of Public Funds
Raising public funds to undertake investment projects involves
three types of costs:
•
collection costs: costs of running the tax office;
•
compliance costs: costs incurred by taxpayers;
•
deadweight loss: costs of misallocation of resources as
people
respond to prices distorted by taxes.


If the required quantity of public funds is raised at minimum cost,
the marginal cost of public funds from each source will be the same.

The deadweight loss resulting from selling bonds to the public.
Suppose $100 worth of government bonds is sold on the market,
and that $50 is diverted from private consumption spending, and
$50 from private investment spending.
The tax rate on the returns to private investment is around 1/3.
Since the after-corporation tax rate of return on private investment
must equal the government bond rate r, the before-tax rate of
return on private investment must be r* = 1.5r.
(Why? Because r*(1 - 1/3) = r )

Now we can work out the cost to the economy of displacing $50
worth of private consumption and $50 worth of private investment:
•
the loss of $50 worth of private consumption costs $50
•
the $50 worth of private investment would have yielded an
annual before-tax return of $50r*. The present value of this return
(at the market rate of interest) is $50(r*/r) = $50*1.5 = $75.
The cost to the economy of raising $100 of public funds by
borrowing from the public is $125. The deadweight loss is $25
and the marginal cost of public funds is $1.25 per dollar i.e. 1.25.

The deadweight loss resulting from collecting additional tax revenues.
There is a wide range of taxes in our economy:
•
personal and business income taxes
•

0
L
1
Quantity of Labour (Hours)

In Figure 10.1:
•
the after-tax wage falls from W
0
to W
1
as a result of the
increase in tax rate;
•
the quantity of labour supplied falls from L
0
to L
1
because
of the upward sloping supply curve.
The cost to households of the tax increase is the loss of producer
surplus: ABDE + BCD
The extra tax revenue to government is measured by: ABDE - FGCB
The cost per dollar of additional revenue is the ratio of the cost to
households to the extra tax revenue.

Summary:
•
Cost to the economy of additional public funds:
Area ABDE + BCD;

.
The value of the corresponding extra leisure time is measured by
area DCL
0
L
1
.
The difference between these two measures is a loss to the
economy, termed a deadweight loss.
The marginal cost of public funds is:
1 + additional deadweight loss
additional quantity of funds

Two complications:
1. When household labour supply falls, household earned income falls.
When earned income falls, the household’s eligibility for social security
payments rises. Some of the extra tax revenue raised will have to be
used to fund increased social security payments rather than the public
project the extra tax revenues are intended to fund.
2. Some public projects will, by their nature, cause a shift of the
labour supply curve, and this may tend to increase or decrease the
effects of the tax rate increase on the quantity of labour supplied and
the quantity of leisure demanded.

Estimates of the marginal cost of public funds:
In Australia and other OECD countries most estimates of the
marginal cost of public funds are in the 1.2 - 1.3 range. In other
words, there is an additional deadweight loss of around 25 cents
per dollar of extra tax revenue raised.
Implications of the marginal cost of public funds for social benefit-

is net benefit in year 0 (known with certainty)
R
H
is net benefit from year 1 onwards if the high
price prevails
R
L
is net benefit from year 1 onwards if the low
price prevails
q is the probability of the high price prevailing
(1-q) is the probability of the low price prevailing
r is the rate of interest