1. Ecological Economics Lecture 10 Tiago Domingos Assistant Professor Environment and Energy Section Department of Mechanical Engineering Doctoral Program and Advanced Degree in Sustainable Energy Systems Doctoral Program in Mechanical Engineering Doctoral Program in Environmental Engineering

2. Classes and Deadlines CLASSES Input-output analysis9th June,18:00-20:00 Economic valuation9th June,20:00-22:00 Multi-criteria assessment7th July,19:00-21:00 ASSIGNMENTS Climate change + discounting5th July Input-output assignment5th July Green accounting assignment5th July Multi-criteria assessment7th July (during class)

3. Present Value of Money Present Value –Conversion of money flows to their present value NPV: Net Present Value i: interest rate VF t (t): value at instant t If VF is in current prices then i is the nominal interest rate If VF is in constant prices then i is the real interest rate

4. Nominal vs. real interest rates The Fisher relation For low rates, this is approximately equal to

5. Present Value of Utility Welfare –Discrete time –Continuous time

6. Discount Rate Justification and Components The same monetary flow at different instants does not have the same value (time preference) –CONSUMPTION: Uncertainty Being alive in the future (individual vs. society) Preferences in the future Value of the benefit or the cost –CONSUMPTION: Impatience –PRODUCTION: Capital productivity (opportunity cost of capital) Under certain conditions, the discount rate is equal to the real market interest rate consumption discount rate per capita consumption growth rate elasticity of the marginal utility of consumption utility discount rate Turner et al. (1994), pp. 102-106. pure time preference rate variation in survival probability

7. Discount Rate Calculation Methods Pure rate of time preference –“ A universal point of view must be impartial about time, and impartiality about time means that no time can count differently from any other. In overall good, judged from a universal point of view, good at one time cannot differ from good at another. Hence...the [pure time] discount rate...must be nought” Broom (1992, p. 92) cit. in Pearce e Ulph (1998, p. 273) Variation in survival probability –Increase in mortality risk with age or –Average population mortality rate Elasticity of the marginal utility of consumption –Individual saving behaviour –Social judgement on income transfers between people Per capita consumption growth rate –Long run average of growth rate in real per capita consumption

8. Discount Rate Elasticity of the Marginal Utility of Consumption U(C) C C U(C)>0 Utility of consumption U’(C)>0 Marginal utility of consumption U’’(C)<0 Variation in marginal utility of consumption Elasticity of the marginal utility of consumption

9. Discount Rate Ethical Interpretation of the Elasticity of Marginal Utility Consider two families, with consumption resp. equal to C 1 and C 2, with C 1 = 2C 2. The ratio of the marginal utilities of consumption is: For different values of μ, this ratio is equal to: μ 0,50,71,01,52,05,010,0 2 - μ 0,70,60,50,350,250,03negl.

10. Discount Rate Estimate for the United Kingdom Pearce, D., D. Ulph (1998). A social discount rate for the United Kingdom. In D. Pearce, Economics and Environment, Edward Elgar, Cheltenham, UK, pp. 268-285. Estimate Pure rate of time preference Variation in survival probability Elasticity of marginal utility Per capita consumption growth rate Consump. discount rate Lower bound 0,0 0,71,30,9 Best estimate 0,3-1,10,81,32,4 Upper bound 0,5-1,21,52,25,0

11. Discount Rate Criticisms The future is given a very low value Limits to growth –It may not make sense to assume that economic growth will continue indefinitely (i.e., at a constant rate, i.e., exponentially) Negative discount rates –Countries with economic de-growth –The future has more value than the present