Chapter 11: Cost-Benefit Analysis Econ 330: Public Finance Dr. Reyadh Faras - PowerPoint PPT Presentation


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Chapter 11: Cost-Benefit Analysis Econ 330: Public Finance Dr. Reyadh Faras


* * * * * * * * * * * * * * Cost-Benefit Analysis How should the government decide whether or not to pursue a particular project? The ... – PowerPoint PPT presentation

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Title: Chapter 11: Cost-Benefit Analysis Econ 330: Public Finance Dr. Reyadh Faras

Chapter 11 Cost-Benefit Analysis Econ 330
Public Finance Dr. Reyadh Faras
  • Cost-Benefit Analysis
  • 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 analysis
  • A set of practical procedures for guiding public
    expenditure decisions.

  • 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).   
  • Present Value
  • 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 (1r)T.
  • This formula shows the future value of money
    invested now.

  • B. Projecting future dollars into the present
    (present value)
  • 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.
  • Example
  • When the interest rate is r, the present value of
    a promise to pay R in T years is R / (1r) T.

  • 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 is receivable.
  • r is referred to as the discount rate and (1r)
    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 / (1r) R2 / (1r)2 .. RT /
    (1r )T
  • Ignoring discounting makes projects that yield
    returns in the future appear more valuable than
    they really are.

  • Private Sector Project Evaluation
  • Suppose a firm has a choice between two projects
    X and Y.
  • Real costs and benefits (CB) are realized
  • Q Are the projects admissible?
  • A A project is admissible if its net return is
    positive (BgtC).
  • 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 / (1r) B2-C2 / (1r)2 ..
    BT-CT / (1r )T

Example 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.  
  • A.   Internal Rate of Return
  • The internal rate of return (?) is the discount
    rate that would make the PV of the project just
    equal to zero.
  • It is defined as the (?) that solves the
  • B0-C0 B1-C1 /(1 ?) B2-C2 /(1 ?)2 ..
    BT-CT /(1 ? )T 0
  • An obvious admissibility criterion is to accept
    a project if (?) exceeds the firms opportunity
    cost of funds, r.
  • If two projects are admissible, choose the one
    with the higher value of (?).

  • Problem when projects differ in size, (?) can
    give poor guidance.
  • 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 projects
    cost-benefit ratio exceeds one.
  • This rule always gives correct guidance, thats
    because B/Cgt1 implies that B-Cgt1, which is just
    the PV criterion for admissibility.

  • As a basis for comparing admissible projects,
    however, this ratio is useless.
  • Conclusion
  • The internal rate of return and the benefit-cost
    ratio can lead to incorrect inferences.
  • The present value criterion is more reliable

  • Discount Rate for Government Projects
  • Sensible decision making by the government also
    requires calculating the PV.
  • There are problems in selecting a public sector
    discount rate.
  • 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.

  • 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 welfare.
  • Hence, the private sector devotes few resources
    to saving, which implies applying high discount
    rate to future returns.

  • 2. Paternalism
  • 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
  • By applying a discount rate lower than the
    markets, the government can correct this

  • 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
  • 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.

  • 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 market prices.
  • The evaluation problem is more complicated for
    the government because market prices may not
    reflect social benefits and costs.

  • Ways for measuring the benefits and costs of
    public sector projects
  • A.   Market Prices
  • In well functioning competitive economy, prices
    reflect the marginal cost of production and its
    marginal value to consumers.
  • Problem in reality, markets have imperfections,
    (e.g. monopoly  and externalities) which makes
    prices do not necessarily reflect marginal costs
    and benefits.

  • 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 imperfection.     

  • 1. Monopoly
  • The monopolist price is higher than the marginal
    cost (MC), should the government measure input
    costs at (monopolist) market price or at marginal
  • 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.

  • 2. Taxes
  • 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
  • A same as the case of monopoly  (if production
    increases use producer's price, if not use
    consumer's price).
  • 3. Unemployment
  • 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.

  • C.   Consumer Surplus
  • In contrast to the small private firms, public
    sector projects are relatively large and they may
    change market prices.
  • 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
    consumer's surplus
  • the difference between the amount the consumer
    is willing to pay and the amount it actually

  • Games Cost-Benefit Analysts Play
  • There are additional common errors committed in
    cost benefit analysis.
  • 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 the project.
  • Consistency requires counting secondary benefits
    and losses.
  • A problem with chain-reaction game is that it
    counts as benefits changes that are merely 

  • B. The Labor Game
  • Advocates of public projects count wages paid to
    workers as benefits, while in fact they are costs
    of projects.
  • 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 time.

  • 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 both.
  • Under competition, the sale price just equals
    the PV of the net income obtained from land use.