1. Ecological Economics Lecture 08 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. 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

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

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

5. 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

6. 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

7. 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

8. 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.

9. 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

10. 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

11. Multisector Optimal Growth m-dimensional consumption bundle, including everything that influences well-being. –Includes all non-market commodities, e.g, produced at home, environmental services, … n-dimensional capital vector: –Includes man-made capital, natural resources, human capital (education and knowledge) and foreign capital. Time is included as a capital, to depict technological progress in production. Attainable production possibilities The model s.t.

12. Criteria for Sustainability, Pezzey (2004) EDE An economy is sustainable at time t if and only if the representative agent’s current utility does not exceed the maximum level of utility which can be sustained forever from t onwards. One-sided sustainability test: un-sustainable development. Multisector results in real terms. –Real Net Income, –Genuine Saving, – Consumption Investment Variation in Real Net Income Variation in Welfare

13. Welfare Relationships Both Genuine Savings and Green NNI are related to future consumption. These relationships can be used to empirically check the theory. If genuine saving is negative (or green NNI deacreases) then current consumption will decrease in the future.

14. Small Open Economy Include –stocks of commercial forests, –welfare costs of air emissions, The capital stocks are : –Domestic man-made capital, –Net foreign capital held privately or by the government, –Stock of commercial natural resources Production r – interest rate

15. Small Open Economy Households’ utility function depends on material consumption rate and (negatively) on the flow of emissions The vector of emissions depends on production and abatement expenditure. Maximize welfare subject to the above relations and having as controls consumption,, all forms of extraction,, abatement expenditure and trade balance. Conventional (SNA) NNI: Green Net National Income: Genuine Saving (Adjusted Net Saving):

16. Small Open Economy – Table of symbols Consumption rate at time t Utility Rate of emissions of air pollutants Production function Abatement expenditure Extraction of natural resources for domestic use, exports and from imports. Imports - Exports Constant nominal interest rate Stock of resources Man-made capital, Resource price Constant real interest rate Cost of extraction of resource Marginal cost of abatement = Marginal damage cost Marginal cost of abatement Net foreign capital

17. Small Open Economy Starting from conventional SNA aggregates: –Deduct the damage from flow pollution emissions, –Deduct (add) the value of rents from resource depletion (or not),

18. Models point to measure emissions at the –Marginal cost of abatement (MCA), or –Marginal social cost (MSC) = Marginal benefit of abatement (MBA), a.k.a. Marginal Damage Costs (MDC) Measurement away from the optimum –c, over-polluting (assumed current state) => a is upper bound –d, under-polluting => b is lower bound Social costs vs Marginal abatement Constant MDC

19. GNNI and GS in Portugal – Air Emissions How to value a unit of emissions? –Marginal benefit of avoided emission, –Marginal cost of emission (MDC), or –Marginal abatement costs? Marginal cost of emission per emitted pollutant [€2000/ton]: [€2000/t] Best Low High SO 2 6872 34729972 NH 3 7399 369910999 NO x 2040 11403040 VOC 1150 4501550 PM2,5 44000 2200064000

20. GNNI and GS in Portugal – Air Emissions

21. GNNI and GS in Portugal – Forests National Forest Inventory 2005/06 Average Volumes: Conifers Eucalyptus 95/9805/06 [m 3 /ha] 88.5 55 82.5

22. GNNI and GS in Portugal – Forests The depreciation of commercial forests in Portugal is on average 10% of the contribution of forestry to national product (around 4%).

23. GS in Portugal Without the value of time – Decreasing tendency throughout the period and negative GS after 2002. With the value of time – Decreasing tendency until 2001, but GS are always positive.

24. In 1993, SO2 costs of emissions, which represent around 30% of total emission costs, decreased substantially. Increases welfare but does not counteract the loss of production. Sustainability Message

25. What’s Missing? The depletion of water resources. The depletion of biodiversity. Depletion of stocks of fish. Inclusion of the value of ecosystem services. Soil quality. Distributional issues (intragenerational concerns)....