Topic 5: Discounting the Future

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Topic 5Discounting the Future

• David Letson
• University of Miami
• David Hume Facts alone cannot tell us what we
  should do.

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Main Points

• Opposite of compound interest
• Two economic reasons for discounting
• How can we choose a discount rate?
• Equity and sustainability

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What is Discounting?

• Lowers importance of future costs and benefits.
• Converts them to present values.
• How to evaluate choices with long term effects?
• Higher rates may imply faster depletion.

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Equation PV Bt / (1r)t

• where PV is present value,
• Bt is the benefit in year t, and
• r is the discount rate.

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Opposite of compound interest.

• 100 invested today at 6 is 34K in 100 years.
• 200 in 12 years is 100 today, if 6 is discount
  rate.
• Investing 100 at 6 yields
• 200 in 12 years,
• 400 in 24 years,
• 3300 in 60 years, and
• 34,000 in 100 years.
• Each is worth 100 today if we discount at 6.

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Why discount? Two reasons.

• opportunity cost of capital
• productivity of capital
• time preference in consumption
• impatience
• future generations may be better off.

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Tim Brennan Citizens and consumers

• Consumers have time preference.
• Citizens may feel obligation to future
  generations.
• Discounting as market test.
• What we do as citizens.

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How to choose a discount rate?

• Does unique rate exist?
• Critical for concerns with long time horizon.
• climate change
• biodiversity loss
• Geoffrey Heal Discount rate is not something we
  measure it is something we choose

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Not only long term concerns.

• Clark (1973) shows that
• If whalers discount rates gt whale growth rates
  and
• If whales size makes them easy to catch even as
  they are depleted
• Then individuals will hunt whales to extinction.

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Discounting Individuals vs society

• Savings as a public good.
• Finite life expectancy.
• Capital gains taxation.
• Govt as processor of citizen wants.
• Risk pooling opportunities.

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Is discounting sustainable?

• Profits from exhaustibles must be re-invested.
• With discounting, some profits consumed.
• Hartwicks cake-eating dilemma.

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Ethical concerns about equal standing

• Rawls All generations must be equally well (or
  poorly) off.
• Veil of ignorance implies a zero discount rate.
  
• Also implies subsistence.

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Distributive effects of public projects

• Kaldor-Hicks decision rule maximizes benefits.
• Potential compensation
• Future generations cant vote.

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Conclusions

• Efficiency convert cost benefit streams to a
  PV.
• Fairness sustainability.
• Robert Solow Maybe the idea of a unitary
  decision maker is not very helpful...