1. Option Values and Accounting Prices Karl-Göran Mäler Beijer Institute of Ecological Economics

2. Option values and accounting prices Arrow and Fisher Two periods An irreversible change is contemplated in the first period. Information on the net benefits from the change is not known with certainty More information will be forthcoming in the second period

3. Option values Option value is defined as the expected value of the forthcoming information in the second period, when no irreversible change is made in the first period

4. Accounting price (Dasgupta and Mäler) A change in a capital asset is contemplated now The present value of future benefits from a marginal change of the asset now is estimated This present value is the accounting price of the asset.

5. Accounting price

6. Sustainable development … development that meets the needs of the present without compromising the ability of the future to meet their own needs. (Our Common Future, 1987)

7. Forrunners Allen Kneese and Bob Ayres And IUCN

8. Sustainable development Social welfare should not deteriorate But change in social welfare in period t is Thus the criterion for sustainable development is that this expression in non- negative

9. The shallow lake Runoff of phosphorous from a farm using fertilizers reach a lake Algae start to grow Eventually, the lake becomes so murky that sunlight will not reach the bottom and green plants will die Bottom becomes unstable and will release more phosphorous – positive feedback

10. Non convex dynamics Dynamics of ecosystems are usually non-convex This means that the right hand side of the differential equation is non convex in the state variable

11. The dynamics of eutrophication

12. The lake in equilibrium Phosphorous input Equilibrium points Stable parts Flip point Algae Unstable part

13. Consequences Multiple steady states Flips from one state to another Valuation difficult Use of taxes to achieve environmental improvements may be impossible

14. The accounting price of the stock of phosphorous Extremely difficult problem Very important problem: It has policy implications and implications for valuation

15. Salinity In south eastern Australia, there is a serious problem with salinity in the ground water

16. Ground water 2 m 6 m Saline ground water RESILIENCE Root zone

17. Accounting price for resilience

18. The accounting price F(X 0, s) cumulative probability distribution for flipping in time interval (t 0, s), given the initial stock of resilience X o U 1 (s) benefits at time s if a flip has not taken place U 2 (s) benefits after a flip

19. Accounting price vs option value Compare this last expression with Fisher’s expression for option values Superficially, these are very similar, indicating that there may be a deeper connection between these two concepts