The probability of collapse of a renewable resource under climatic uncertainties

1. The probability of collapse of a renewable resource under climatic uncertainties En analyse af forskellige typer regulering under multiple former for usikkerheder Urs Steiner Brandt Department of Environmental and Business Economics, University of Southern Denmark.

2. Intro Some renewable resources have a critical stock level, below which the resource cannot recover without serious economic loses to the related harvesting industry. • Continuously high catching pressures • Changes in factors influencing the ecosystem • Catastrophic events An action or event that at any time pushes the stock below this critical level, has an (almost) irreversible effect on this stock. Such actions could be:

3. Questions to investigate The aim of this paper is to answer the following questions: Given uncertainty about the true level of this critical level and uncertainty about how future climate change will affect the growth rate of the resource: • What will be the consequences for the expected industry profit • Probability of conservation of the stock Of the following three policy proposals • A safety first policy, which aims to secure that the probability of extinction will not exceed a pre-determined level. • A policy that neglects the possibility that climate change might negatively affect the growth rate of the resource • A fully optimal approach, which aims at maximizing expected profits from harvesting the resource.

4. Model outline Two period model: Stock size at time t+1 is determined by the following growth function: Uncertainty about how future climate change will affect future growth rate of the resource (two possibilities): Uncertainty about the size of the critical stock level: v  N(0,)

5. Growth rate and safety level Define a safety level as: Consider only uncertainty about collapse level. Then, with (1-2k1) % certainty the collapse size will at any time be in the blue area in the figure:

6. Safety level given climate uncertainties • Questions and observations: • What is the safety level in this case? • The optimal level might imply a certain probability of collapse • Ignoring climate change might imply a high level of collapse

7. The optimal “ex ante” harvesting level The decision tree for the optimal solution (reference solution) It is assumed that collapse implies zero profit in period two.

8. Forsigtighedsprincippet Forsigtighedsprincippet har mange potentielle definitioner. Men er centreret omkring tre områder: • Den omvendte bevisbyrde, det er den agent, der er ansvarlig for den potentielt skadelige aktivitet eller handling, der skal frembringe vidnesbyrd om, at aktiviteten ikke resulterer i signifikant skade. • Etableringen af en forpligtelse til at foretage forsigtigheds-foranstaltninger for at imødegå potentielle skader, som ikke kan udelukkes. • Forsigtighedsprincippet fokuserer på at usikkerheden skal komme miljøet til gode.

9. What is the safety level in this case? Consider the “expected safety level”: But in the bad state, the probability of collapse is obviously higher than k1. Another definition (inspired by maximin): It is defined such that the probability of collapse will never be below k1, no matter which state will occur.

10. Decision criteria based on precaution Precautionary approach 1 Precautionary approach 2 Both principles imply rational behaviour subject to the precautionary constraint

11. More on decision criteria based on precaution For the precautionary approach 1, the following decision tree:

12. The Business as usual option Hence, under the BAU, the decision maker ignores the possibility that climate chance reduces the growth rate of the second-period stock.

13. The myopic solution Under the myopic solution, the DM ignores the future totally.

14. Results Sorry, not yet available, but the idea is to make: No learning, partial and fully learning cases:

15. Preliminary analysis Consider a situation where initially the DM only considers It optimizes and finds Assume that Case with optimality In the optimal case, the occurrence of has the following effects: 1) Lower growth rate in the second period => higher catch in the first period 2) Lower catch in the first period => lower probability of a collapse of the resource. There is no longer a simple relationship between changes in the growth rate and changes in the first period catch level.

16. Preliminary analysis…more Case with ignorance In this case, ignoring the possibility of implies that the prob(collapse) > 0. Case with precaution In the optimal case, the occurrence of has the effect that the first period catch level will be reduced.