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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.

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Intro

Some renewable resources have a critical stock level, below which the resource cannot recover without serious economic loses to the related harvesting industry.

Such actions could be:

An action or event that at any time pushes the stock below this critical level, has an (almost) irreversible effect on this stock.

• Continuously high catching pressures

• Changes in factors influencing the ecosystem

• Catastrophic events

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Questions to investigate

• 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.

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:

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Model outline

),(1 ttt SqgS

},{ BAUL

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:

1 BAUL

Two period model: Stock size at time t+1 is determined by the following growth function:

v N(0,)tt vSS

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Growth rate and safety level

Define a safety level as:

2 1 1 1 2 1Prob( ( ( ), ) )safeS q S S S k

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:

)( 11 Sq safe

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Safety level given climate uncertainties

Questions and observations:

1) What is the safety level in this case?

2) The optimal level might imply a certain probability of collapse

3) Ignoring climate change might imply a high level of collapse

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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.

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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.

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What is the safety level in this case?

safe BAU BAU1 1 2 1 1 2

L L2 1 1 2 1

Eq (k ) = arg{prob(θ=θ )×Prob(S (q (θ ),S )<S )

+prob(θ=θ )×Prob(S (q (θ ),S )<S }=k

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.

1 1 1 1( ) ( )safe safeq k Eq k

1111211 })),(((arg{)( kSSqSprobkq Lsafe

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Decision criteria based on precautionPrecautionary approach 1

112

21

)),((:..

max1

kqSprobts L

q

Precautionary approach 2

11 2

BAU2 1 1 2

L2 1 1 2 1

max

. . : prob( = ) Prob( ( ( ), ) )

prob( = ) Prob( ( ( ), ) }

q

BAU

L

s t S q S S

S q S S k

Both principles imply rational behaviour subject to the precautionary constraint

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More on decision criteria based on precaution

For the precautionary approach 1, the following decision tree:

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The Business as usual option

1)( ..

max 21q1

BAUpts

Hence, under the BAU, the decision maker ignores the possibility that climate chance reduces the growth rate of the second-period stock.

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The myopic solution

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q max

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

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Results

Action q1 Expected collapse

Profits

Precaution * * *

BAU * * *

Optimal * * *

Sorry, not yet available, but the idea is to make:

No learning, partial and fully learning cases:

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Preliminary analysis

Consider a situation where initially the DM only considers

It optimizes and finds

BAU

)(*1

BAUq

Assume that ),0()(),0( 1*11

LsafeBAUBAUsafe qqq

Case with optimalityIn the optimal case, the occurrence of has the following effects:

1) Lower growth rate in the second period => higher catch in the first period2) 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.

L

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Preliminary analysis…more

L

Case with precautionIn the optimal case, the occurrence of has the effect that the first period catch level will be reduced.

Case with ignoranceIn this case, ignoring the possibility of implies that the prob(collapse) > 0.

L

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