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Common Pool Politics and Inecient Fishery Management Julia Homann and Martin Quaas July 8 2014 Julia Homann Christian-Albrechts-University International Institute of Fishery Economics and Trade July 7 - July 11 2014 - Brisbane Kiel 1/24 Outline 1 Motivation 2 Model Set-up 3 The Common Pool Politics 4 Conclusion Julia Homann Christian-Albrechts-University International Institute of Fishery Economics and Trade July 7 - July 11 2014 - Brisbane Kiel 2/24 Motivation • 30% of sh stocks worldwide overshed in 2009 (FAO 2012) • most important tool in sheries management: total allowable catch (TAC) • in some countries the TAC system is quite successful (e.g. New Zealand, Iceland) • in others it is not (e.g. EU, Chile) Julia Homann Christian-Albrechts-University International Institute of Fishery Economics and Trade July 7 - July 11 2014 - Brisbane Kiel 3/24 Motivation • our approach: dierent institutional set-up may lead to dierent levels of eciency of TAC management • successful - single person decision • not successful - council decision Julia Homann Christian-Albrechts-University International Institute of Fishery Economics and Trade July 7 - July 11 2014 - Brisbane Kiel 4/24 Motivation • our approach: dierent institutional set-up may lead to dierent levels of eciency of TAC management • successful - single person decision • not successful - council decision Does group decision-making result in ineciently high TACs? And if so, under which conditions? Julia Homann Christian-Albrechts-University International Institute of Fishery Economics and Trade July 7 - July 11 2014 - Brisbane Kiel 4/24 The Model Assumptions I • TACs are set by a group of decision-makers (in a council) • decisions are made with majority voting • decisions on TACs are based on a dynamic game in discrete time Julia Homann Christian-Albrechts-University International Institute of Fishery Economics and Trade July 7 - July 11 2014 - Brisbane Kiel 5/24 The Model Assumption II • two types of decision-makers: patient (p ) and impatient (i ) with discount factors ρ > ρ p i • objective: nd optimal escapement that maximises discounted prots considering the choice of escapement of the other group Julia Homann Christian-Albrechts-University International Institute of Fishery Economics and Trade July 7 - July 11 2014 - Brisbane Kiel 6/24 The Model Assumptions III • escapement = stock − harvest: s t = x − h where h = TAC t t (1) t • current prots: xt π(h ) = Z t (p − c (x ))dx ≡ π(x ) − π(s ) t t (2) st • stock dynamics: x +1 = z g (s ) t with t t (3) E (z ) = 1; [z , z ] ⊂ [0, ∞) t Julia Homann Christian-Albrechts-University International Institute of Fishery Economics and Trade July 7 - July 11 2014 - Brisbane Kiel 7/24 The Model Assumptions IV • majority m= • • m can change over time due to elections ( i p if majority of impatient decision-makers if majority of patient decision-makers (4) q is the probability of an impatient majority (1 − q ) is the probability of a patient majority Julia Homann Christian-Albrechts-University International Institute of Fishery Economics and Trade July 7 - July 11 2014 - Brisbane Kiel 8/24 Optimal Fisheries Management (Clark 1990) • assume: majority is not changing • maximisation problem: ∞ X δ max E ( sj t =1 t −1 (π(x ) − π(s ))) t t subject to x +1 = z g (s ) t t Julia Homann Christian-Albrechts-University International Institute of Fishery Economics and Trade July 7 - July 11 2014 - Brisbane Kiel t (5) 9/24 Optimal Fisheries Management (Clark 1990) • assume: majority is not changing • maximisation problem: ∞ X δ max E ( sj t =1 t −1 (π(x ) − π(s ))) t t subject to x +1 = z g (s ) t t t (5) • optimal feedback strategy: constant escapement s ? (x ) = min{x ; s ? } j j with j = {i ; p } and s? p > s? i > 0 (6) Julia Homann Christian-Albrechts-University International Institute of Fishery Economics and Trade July 7 - July 11 2014 - Brisbane Kiel 9/24 The Common Pool Politics • assume: change in majority is possible • implication: choice of escapement of the other group has to be considered in own optimal management decision Julia Homann Christian-Albrechts-University International Institute of Fishery Economics and Trade July 7 - July 11 2014 - Brisbane Kiel 10/24 The Common Pool Politics • Bellman equation v (x , m) to nd optimal escapement (with j = {i ; p}): v (x , m) = π(x ) − π(ŝ (x )) + ρ (q v (zg (ŝ (x )), i ) +(1 − q ) v (zg (ŝ (x )), p )) j j j j • ŝ j (7) = optimal feedback strategy of majority Julia Homann Christian-Albrechts-University International Institute of Fishery Economics and Trade July 7 - July 11 2014 - Brisbane Kiel 11/24 The Common Pool Politics • Bellman equation v (x , m) to nd optimal escapement (with j = {i ; p}): v (x , m) = π(x ) − π(ŝ (x )) + ρ (q v (zg (ŝ (x )), i ) +(1 − q ) v (zg (ŝ (x )), p )) j j j j • ŝ j (7) = optimal feedback strategy of majority • optimal feedback strategy: constant escapement ŝ (x ) = min{x ; ŝ } j j with j = {i ; p} and ŝ p > ŝ i > 0 Julia Homann Christian-Albrechts-University International Institute of Fishery Economics and Trade July 7 - July 11 2014 - Brisbane Kiel (8) 11/24 The Common Pool Politics Proposition 1. Patient decision-makers do not deviate from their optimal escapement strategy, i.e. their dominant strategy is ŝ (x ) = s ? (x ). p p Julia Homann Christian-Albrechts-University International Institute of Fishery Economics and Trade July 7 - July 11 2014 - Brisbane Kiel 12/24 The Common Pool Politics Proposition 2. Impatient decision-makers deviate from their optimal escapement policy if and only if s ∗ > zg (s ∗ ). p i Julia Homann Christian-Albrechts-University International Institute of Fishery Economics and Trade July 7 - July 11 2014 - Brisbane Kiel 13/24 The Common Pool Politics Proposition 2. Impatient decision-makers deviate from their optimal escapement policy if and only if s ∗ > zg (s ∗ ). p i This is given if ρ − ρ > ρ̄. p i Julia Homann Christian-Albrechts-University International Institute of Fishery Economics and Trade July 7 - July 11 2014 - Brisbane Kiel 13/24 The Common Pool Politics Proposition 2. Impatient decision-makers deviate from their optimal escapement policy if and only if s ∗ > zg (s ∗ ). p i This is given if ρ − ρ > ρ̄. p i The impatient decision-makers will then choose a strictly lower escapement level than their individually optimal one, i.e. ŝ (x ) < s ? (x ). i i Julia Homann Christian-Albrechts-University International Institute of Fishery Economics and Trade July 7 - July 11 2014 - Brisbane Kiel 13/24 The Common Pool Politics Julia Homann Christian-Albrechts-University International Institute of Fishery Economics and Trade July 7 - July 11 2014 - Brisbane Kiel 14/24 The Common Pool Politics Julia Homann Christian-Albrechts-University International Institute of Fishery Economics and Trade July 7 - July 11 2014 - Brisbane Kiel 15/24 Conclusion • annual TAC update procedure induces uncertainty regarding next period's majority and its choice of escapement Julia Homann Christian-Albrechts-University International Institute of Fishery Economics and Trade July 7 - July 11 2014 - Brisbane Kiel 16/24 Conclusion • annual TAC update procedure induces uncertainty regarding next period's majority and its choice of escapement • given that (a) the current majority is impatient (b) ρ − ρ > ρ̄ p i Julia Homann Christian-Albrechts-University International Institute of Fishery Economics and Trade July 7 - July 11 2014 - Brisbane Kiel 16/24 Conclusion • annual TAC update procedure induces uncertainty regarding next period's majority and its choice of escapement • given that (a) the current majority is impatient (b) ρ − ρ > ρ̄ p i uncertainty motivates the reduction of the impatients' escapement level Julia Homann Christian-Albrechts-University International Institute of Fishery Economics and Trade July 7 - July 11 2014 - Brisbane Kiel 16/24 Conclusion • annual TAC update procedure induces uncertainty regarding next period's majority and its choice of escapement • given that (a) the current majority is impatient (b) ρ − ρ > ρ̄ p i uncertainty motivates the reduction of the impatients' escapement level • problem could be solved by a binding agreement including a harvest-control-rule between both groups of decision-makers Julia Homann Christian-Albrechts-University International Institute of Fishery Economics and Trade July 7 - July 11 2014 - Brisbane Kiel 16/24 Alternative Management Agreement including transfer payments "∞ # "∞ X X E δ −1 (π(x ) − π(s ∗ (x ))) > E δ t t p t p t =1 t =1 t i −1 # (π(x ) − π(s ∗ (x ))) t i t (9) • optimal harvest-control-rule s ∗ (x ) = s∗ p • patient decision-makers will compensate the impatient decision-makers in form of direct transfer payment, log-rolling, etc. Julia Homann Christian-Albrechts-University International Institute of Fishery Economics and Trade July 7 - July 11 2014 - Brisbane Kiel 17/24 Thank you for your attention! Julia Homann Christian-Albrechts-University International Institute of Fishery Economics and Trade July 7 - July 11 2014 - Brisbane Kiel 18/24 Optimal Fisheries Management (Clark 1990) • current prots xt R (p − c (x ))dx ≡ π(x ) − π(s ) t t st • maximisation problem: max ∞ X si t • gives =1 δ t −1 (π(x ) − π(s )) subject to t t x +1 = z g (s ) t t t (10) s ? = min{x ; s ? } as solution of j j π 0 (s ) = ρ j • (4) implies that g 0 (s )π0 (g (s )) s ? is increasing in ρ j j (11) (Clark 1990) Julia Homann Christian-Albrechts-University International Institute of Fishery Economics and Trade July 7 - July 11 2014 - Brisbane Kiel 19/24 Bellman equations I • Bellman equations v (x , m) of the impatient decision-makers v (x , i ) = π(x ) − π(ŝ (x )) + ρ (q v (zg (ŝ (x )), i ) +(1 − q ) v (zg (ŝ (x )), p )) (12) v (x , p) = π(x ) − π(ŝ (x )) + ρ (q v (zg (ŝ (x )), i ) +(1 − q ) v (zg (ŝ (x )), p )) (13) i i i i p i p p • with ŝ (x ) as feedback strategy of the patient decision-makers p Julia Homann Christian-Albrechts-University International Institute of Fishery Economics and Trade July 7 - July 11 2014 - Brisbane Kiel 20/24 Bellman equations II • Bellman equations V (x , m) of the patient decision-makers V (x , i ) = π(x ) − π(ŝ (x )) + ρ (q V (zg (ŝ (x )), i ) +(1 − q ) V (zg (ŝ (x )), p )) (14) V (x , p) = π(x ) − π(ŝ (x )) + ρ (q V (zg (ŝ (x )), i ) +(1 − q ) V (zg (ŝ (x )), p )) (15) p i i i p p p p • with ŝ (x ) as feedback strategy of the impatient decision-makers i Julia Homann Christian-Albrechts-University International Institute of Fishery Economics and Trade July 7 - July 11 2014 - Brisbane Kiel 21/24 Alternative Management Agreement without transfer payments (Breton and Keoula 2014) • maximize the weighted sum of the present values for both groups (16) max E [αV (x ) + (1 − α)v (x )] ( ) s x • α reects the majority in the council • optimal harvest-control rule s (x ) = max {s ∗ ; x } with s∗ i ≤ s∗ ≤ s∗ p Julia Homann Christian-Albrechts-University International Institute of Fishery Economics and Trade July 7 - July 11 2014 - Brisbane Kiel 22/24 Optimal Fisheries Management Julia Homann Christian-Albrechts-University International Institute of Fishery Economics and Trade July 7 - July 11 2014 - Brisbane Kiel 23/24 Literature Breton, M., Keoula, M. Y., 2014. A great sh war model with asymmetric players. Ecological Economics 97 (0), 209 223. Clark, C. W., 1990. Mathematical Bioeconomics, 2nd Edition. Wiley, New York. Julia Homann Christian-Albrechts-University International Institute of Fishery Economics and Trade July 7 - July 11 2014 - Brisbane Kiel 24/24