Chapter 11 CostBenefit Analysis

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Chapter 11 Cost-Benefit Analysis

• How can we evaluate a government program?
• One possible answer is measuring the change in
  social welfare function before and after the
  policy was implemented.
• Another and less daunting task is formulating
  practical procedures for valuing the costs and
  benefits of goods and services provided by the
  government.
• A. Present Value (PV)
• Investment into public education will generate
  returns in the future. We compare the costs today
  with benefits later using PV analysis.
• How much will you be willing to pay today for
  receiving 100 in two years?
• The PV of future amount of money is the maximum
  one would be willing to pay today to receive
  exactly that amount.
• If interest, or discount, rate is 5 a year, then
  100 two years later would be worth 100 /
  (1.05)2 90.70 today. Note that this
  calculation is made when inflation is assumed to
  be absent.
• Suppose now that there was inflation, say ? a
  year. Consider a project which yields the same
  real amount of return, R0, in present prices for
  the following years. Then, the nominal amount of
  return in two years is R0 (1 ? )2.
• Also, the lenders are no longer willing to accept
  1 r next year for every dollar loaned now,
  since the nominal amount of 1 r next year is
  equivalent to the following real amount

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• Then, the lenders adjust their discount factor to
  (1r ) (1 ?), such that 1 loaned today is
  equivalent to 1 r in real amounts.
• Assume that a project generates a stream of real
  returns R0, R1, R2, etc. in the following years,
  with R0 denoting the current returns. Then, the
  PV of this project can be given by

• This shows that PV remains the same when either
  real or nominal amounts are used. It is important
  to use consistent measures however. If real
  amounts are used, then the real discount factor,
  (1r), should be used.
• B. Private Sector Project Evaluation
• Suppose a firm is considering two separate
  projects, X and Y. The projects yield the returns
  of (B1X C1X ) and (B1Y C1Y ) in one year.
• Two questions are relevant Are the projects
  admissible, or yield positive returns? Which one
  is preferable?
• Since this example involves returns in same
  periods, all we need to do is to see if one of
  (B1X C1X ) and (B1Y C1Y ) is positive and
  which one is larger.
• More generally, the PV criteria are
• 1) A project is admissible only if its PV 0,
• 2) When the two projects are separate, the
  preferred project has the greater PV.

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• A relatively large discount rate discriminates
  against projects with returns in the distant
  future.
• Internal Rate of Return The discount rate that
  would make the present value zero. An alternative
  to using PV to evaluate projects.
• A company spends 1,000 today to get 1,100 a
  year later. What is this investments rate of
  return, ? ?

• More generally, for a project with a stream of
  benefits and costs for T periods, the internal
  rate of return can be found solving

• The admissibility criterion is ? r.
  Comparability criterion is choosing the project
  with the higher internal discount rate.
• There are some problems with decision based on
  internal rate of return instead of PV criteria.
• Consider two projects, X and Y. Project X
  requires an expenditure of 100 today and yields
  110 in one year. Project Y requires 1,000 now
  and yields 1,080 next year. Assume that r
  0.06. Both satisfies admissibility criterion, but
  X has a higher rate of internal return.
• The first project has a profit of 4 10 - 6,
  where 6 is the opportunity cost of investing
  100 into the project rather than putting it into
  the bank. For the second project, this is 20
  80 - 60. Then, Y is better than X,
  contradicting internal rate of return criterion.

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• Benefit Cost Ratio A project yields a stream of
  benefits and costs. The present values of
  benefits and costs are given by

• The benefit cost ration is defined as B/C.
  Admissibility requires that B/C 1 or
  equivalently B - C 0. Theres no problem caused
  by this admissibility condition.
• Comparing projects requires one to choose the
  project with a larger B/C. But the problem is
  for any project costs may also be counted as
  negative benefits. Such a practice may make any
  project admissible. (See book for an example.)
• C. Discount Rate for Government Projects
• - The discount rate should reflect the
  opportunity cost of funds. What should govt use
  as a discount rate?
• - Rates based on Returns in Private Sector In
  general, the funds for a public project are
  collected via a variety of taxes, each affecting
  consumption and/or investment of individuals.
• - Suppose government extracts 1000 for a
  project, entirely at the expense of private
  investment. Also, let the (before-tax) annual
  rate of return be 12. Then the opportunity cost
  of government project is 120.
• - Taxes on investment need not be taken into
  account bc investment creates funds for the
  entire society. Whether or not it is taxed, the
  opportunity cost is 120 in any case.

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• When 1000 is entirely at the expense of private
  consumption, things a bit different.
• For every dollar consumed now, an individual
  gives up one dollar of consumption later and the
  rate of return that would be obtained if the
  dollar was saved. Hence, for every dollar
  consumed, the opportunity cost is how much an
  individual would get if he/she saved it, net of
  taxes.
• For these reasons, a weighted average of the
  discount factor can be used to determine the PV
  of public projects.
• Social Discount Rate Social discount rate is the
  valuation that society places on consumption
  sacrificed. Lower than the market discount rate
  due to the following reasons.
• A) Paternalism The society may be too focused on
  narrow self-interest and may not adequately
  consider the benefits to future generations. The
  govt should use the discount rate individuals
  use if attuned their care for future generations.
• B) Market inefficiency Investment is usually
  under provided in private markets since theres a
  positive externality associated with it. By
  applying a lower discount rate, the govt can
  attempt to partially correct these problems.
• Government discounting in Practice Govt
  agencies use a variety of discount rates,
  depending on the agency and projects. Usually 7
  except for projects with long range costs and
  benefits.
• The govt discounting practices sometimes give
  rise to bizarre outcomes, especially in the
  context of federal budget planning. The effects
  of a new expenditure program or taxes are
  reported only for the subsequent five-year
  period, discounted at a rate of zero!!!!

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• So a project with a current cost of 1000 which
  brings 1000 five years later is seen as having
  no effect on current deficit, even though PV is
  negative.
• Also, the fiscal consequences after five years
  are ignored!!!!
• D. Valuing Public Benefits and Costs
• - In private sector, valuing benefits and costs
  are relatively simple. Social benefits and costs
  of a public project, however, may not be
  reflected properly in prices, especially if there
  are imperfections in the market. For this reason,
  the government uses adjusted or shadow prices to
  calculate the benefits and costs of a project.
• - When government extracts some product from a
  monopoly, for example, it is not clear if the
  government should use a cost value based on
  market price (value to consumers) or marginal
  cost (value to producers). If no more of the
  monopolized product will be produced after govt
  extracts the resource, then the extraction comes
  at the expense of private consumers. If the same
  amount of product is produced, then the
  extraction comes at the expense of producers.
• Public sector projects may be so large that the
  market prices may change even if the markets are
  perfectly competitive. Then, the changes in
  consumer and producer surplus may be used to
  estimate the effect of the project on the
  economy. (Make sure you can do such a
  calculation, see Fig 11.1)
• Sometimes, the good the government provides or
  uses in a project is not really traded in a
  market. Remember the fast-train project between
  Albany NYC. Assume that each commuter will save
  1 hour going from or back to Albany. What is the
  benefit? Answer The after-tax hourly wage.

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• Sometimes, the hourly wage might not be given
  explicitly, but may be revealed from a persons
  behavior.
• When it comes to life-death situations, valuation
  may be quite hard and controversial. Two methods
  for assigning finite values are lost earnings
  and probability of death.
• When lost earnings are considered, the value of
  life is the present value of outputs or net
  earnings over life.
• Alternatively, by choosing certain types of
  goods, occupations, etc. people accept a certain
  amount of increase or decrease in the probability
  of death. For example, by driving a car, one
  increases the chance of death by a small amount.
  People pay a certain amount of money to decrease
  the probability of death by fire by installing
  smoke alarms, etc. The value of life is
  calculated by estimating the amount people will
  pay to reduce probability of death from 1 to 0,
  of course using these revealed preferences.
  Different studies found different values between
  3 5 million.
• E. Games Cost Benefit Analysts Play
• Chain-Reaction Game Any proposal can be made
  attractive by including the secondary, indirect
  benefits into account. Of course, this way any
  project can be made admissible and preferable.
  The opposite is also true for the costs and the
  subsequent unattractiveness.
• Labor Game This point is really an extension of
  the chain-reaction game. The wages of people
  employed are viewed as benefits of the project,
  even though they should really be counted as
  costs. Counting such benefits is correct only if
  the workers were unemployed.

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• Double-Counting Game The benefits of an
  irrigation project are given as 1) the increase
  in value of land, 2) present value of farming the
  land in the future. But these two things should
  actually be equivalent under competition. A
  farmer cannot both sell the land, reaping the
  benefits listed in 1 and farm it, getting the
  benefits in 2!
• F. Distributional Considerations
• For a firm, a project is usually undertaken if it
  has positive returns. As long as the present
  value is positive, a project is undertaken. This
  notion is sometimes used in public projects as
  well (Hick-Kaldor criterion). In such a case, a
  project is undertaken if there is a potential for
  Pareto improvements.
• In other cases in a public project, who gets the
  benefits and bears the costs may be important.
  Suppose that an irrigation project hurts the
  fishermen but helps the farmers. This is an
  distributional issue which the government may be
  inclined to correct by making appropriate
  transfers between gainers and losers.
• The government may increase its focus on
  distributional issues by assuming that a group in
  the population is especially deserving. Then, one
  dollar/person worth of costs for this group can
  only be allowed with more than one dollar/person
  benefits to others. In this way, a project that
  benefits this group may be accepted even though
  PV is negative when costs and benefits are not
  weighted.
• A problem with focusing too much on
  distributional issues is the injunction of
  political concerns with the costs and benefits.