Econ 330: Public Finance
Dr. Reyadh Faras
Dr. Reyadh Faras 1
How should the government decide whether or not to
pursue a particular project?
The theory of welfare economics provides a
framework for deciding: Evaluate the social welfare
function before and after the project, and see whether
social welfare increases.
If it does, then do the project.
Welfare economics provides the basis for cost-benefit
“A set of practical procedures for guiding public
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Cost-benefit analysis allows policymakers to do what
markets do automatically (allocate resources to a
project as long as the marginal social benefit exceeds
the marginal social cost).
Project evaluation usually requires comparing costs
and benefits from different time periods.
A. Projecting present dollars into the future
If $R are invested for T years at an interest rate of r,
at the end of T years, it will be worth $R x (1+r)T.
This formula shows the future value of money
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B. Projecting future dollars into the present (present
Present value of a future amount is the maximum
amount you would be willing to pay today for the right
to receive the money in the future.
When the interest rate is r, the present value of a
promise to pay $R in T years is: $R / (1+r) T.
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Thus, even with no inflation, money in the future worth
less than today and must be discounted by an amount
that depends on the interest rate and when the money
r is referred to as the discount rate and (1+r) T as the
discount factor for money T periods into the future.
The present value (PV) of a stream of payments is
found as follows:
PV = R0 + R1 / (1+r) + R2 / (1+r)2 + ….. + RT / (1+r )T
Ignoring discounting makes projects that yield
returns in the future appear more valuable than they
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Private Sector Project Evaluation
Suppose a firm has a choice between two projects X and Y.
Real costs and benefits (C&B) are realized immediately.
Q: Are the projects admissible?
A: A project is admissible if its net return is positive
Q: Which project is preferable?
A: The one with the higher net return.
In reality, projects involve a stream of real costs and
benefits (occur over time).
The present value of the stream of income is:
PV = B0-C0 + B1-C1 / (1+r) + B2-C2 / (1+r)2 + ….. + BT-CT / (1+r )T
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If the discount rate chosen is too high, it tends to
discriminate against projects with returns that occur in
the relatively distant future and vice versa.
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A. Internal Rate of Return
The internal rate of return (ρ) is the discount rate that
would make the PV of the project just equal to zero.
It is defined as the (ρ) that solves the equation:
B0-C0 + B1-C1 /(1+ ρ) + B2-C2 /(1+ ρ)2 + .. + BT-CT /(1+ ρ )T = 0
An obvious admissibility criterion is to accept a
project if (ρ) exceeds the firm’s opportunity cost of
If two projects are admissible, choose the one with the
higher value of (ρ).
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Problem: when projects differ in size, (ρ) can give
In contrast, the PV gives correct answers even when
projects differ in size.
B. Benefit-Cost Ratio
The benefit –cost ratio is defined as B / C.
Admissibility requires that a project’s cost-benefit
ratio exceeds one.
This rule always gives correct guidance, that’s
because B/C>1 implies that B-C>1, which is just the
PV criterion for admissibility.
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As a basis for comparing admissible projects, however,
this ratio is useless.
The internal rate of return and the benefit-cost ratio
can lead to incorrect inferences.
The present value criterion is more reliable guide.
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Discount Rate for Government Projects
Sensible decision making by the government also
requires calculating the PV.
There are problems in selecting a public sector
A. Rates Based on Returns in the Private Sector
If the government extracts $X from a private sector
investment (that yields r% return) for a project, society
loses $(X x r%) that would have been generated by the
private sector project.
The opportunity cost of the government project is the
(r%) rate of return in the private sector, which is the
appropriate discount rate.
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B. Social Discount Rate
Social rate of discount measures the valuation society
places on consumption that is sacrificed in the present.
Social discount rate is lower than the market rate of
return for several reasons:
1. Concern for Future Generations
The public sector decision makers care not only about
the welfare of current generation but future generations
as well, while the private sector cares only about its own
Hence, the private sector devotes few resources to
saving, which implies applying high discount rate to
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People (even with self-interest) may not be farsighted
enough to weigh adequately benefits in the future; they
discount them at too high rates.
3. Market Inefficiency
Private investments generate positive externalities that
benefit other firms, this leads to under-provision of
investment by private markets.
By applying a discount rate lower than the market’s,
the government can correct this inefficiency.
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C. Government Discounting in Practice
The US federal government uses a variety of discount
rates, depending on the agency and the type of project.
Federal agencies are required to use a real rate of
return of 7%, assuming that this will measure the
before-tax rate of return on private sector projects.
However, for many projects involving costs and
benefits that come in over long periods of time, a real
rate of return of 2% is used; as an approximation to the
consumption rate of time preference, that is, the after
tax rate of return.
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Valuing Public Benefits and Costs
Evaluating private projects is done by comparing
costs and benefits incurred to the firm and it is
straightforward; benefits are revenues received and
costs are payments for inputs; both are measured at
The evaluation problem is more complicated for the
government because market prices may not reflect
social benefits and costs.
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Ways for measuring the benefits and costs of public
A. Market Prices
In well functioning competitive economy, prices reflect
the marginal cost of production and its marginal value
Problem: in reality, markets have imperfections, (e.g.
monopoly and externalities) which makes prices do not
necessarily reflect marginal costs and benefits.
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B. Adjusted Market Prices
Prices in imperfect markets do not reflect their
marginal social cost.
The shadow price is the underlying social marginal
cost and it diverges from market price due to market
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The monopolist price is higher than the marginal cost
(MC), should the government measure input costs at
(monopolist) market price or at marginal cost?
Answer: it depends on the impact of government
purchase on the market:
a. If production increases by the exact amount used by
the project, the social opportunity cost is the value of
resources used for the extra production (MC).
b. If production does not increase, the government
purchase come at the expense of private consumers,
who value the good at its demand price.
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Q: When the government purchases an input subject to
sales tax, should the producer's or the purchaser's price
be used in calculating the cost?
A: same as the case of monopoly (if production
increases use producer's price, if not use consumer's
If a worker for a public project is hired away from a
private job, then his opportunity cost is the wage rate
earned in the private sector.
If the worker was involuntarily unemployed, the wage
does not represent the opportunity cost.
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C. Consumer Surplus
In contrast to the small private firms, public sector
projects are relatively large and they may change
Example, if a public project reduces marginal costs,
Q: how should the increase in output valued; at its
original price or the new (lower) price?
A: project benefit can be measured using the
“the difference between the amount the consumer is
willing to pay and the amount it actually paid.”
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Games Cost-Benefit Analysts Play
There are additional common errors committed in cost
A. The Chain-Reaction Game
Advocates of public projects can make them more
attractive by counting secondary profits arising from it
as part of the benefits, while ignoring losses induced by
Consistency requires counting secondary benefits and
A problem with chain-reaction game is that it counts
as benefits changes that are merely transfers.
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B. The Labor Game
Advocates of public projects count wages paid to
workers as benefits, while in fact they are costs of
Even in an area with high unemployment, it is
unlikely that all project workers would have been
unemployed, or they would have remained so for a long
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C. The Double Counting
If a public project increases the land's value, the
government counts as benefits the increase in land's
value and the PV of the stream of net income obtained
from its use.
Problem: land owner can either sell it or use it, not
Under competition, the sale price just equals the PV
of the net income obtained from land use.
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