Fisheries Enforcement: Basic Theory Paper presented at COBECOS Kick-off meeting Salerno February, 22-3, 2007 Ragnar Arnason

Introduction Fisheries management needs enforcement –Without it there is no fisheries management Enforcement is expensive Enforcement is complicated  Optimal fisheries policy needs to take enforcement into account Enforcement theory is fundamentally the theory of crime (Becker 1968)

Model Social benefits of fishing: B(q,x)- ·q Shadow value of biomass Enforcement sector: Enforcement effort:e Cost of enforcement:C(e) Penalty:f Announced target:q* Private benefits of fishing:B(q,x) Exogenous

Model (cont.) Probability of penalty function (if violate) :  (e) (e)(e) e 1

Model (cont.) q  (q;e,f,q*) q* (e)f(e)f Private costs of violations:  (q;e,f,q*)=  (e)  f  (q-q*), if q  q*  (q;e,f,q*) = 0, if q<q*

Model (cont.) Private benefits under enforcement Social benefits with costly enforcement: B(q,x)-  (e)  f  (q-q*), q  q* B(q,x), otherwise B(q,x)- q-C(e)

Private behaviour Maximization problem: Max B(q,x)-  (e)  f  (q-q*)  Enforcement response function: q=Q(e,f,x)q=Q(e,f,x) Necessary condition: B q (q,x)-  (e)  f=0

q e q* [lower f] [higher f] Free access q Enforcement response function

Optimal enforcement Social optimality problem B(q,x)- q-C(e). subject to: q=Q(e,f,x), e  0, f fixed. Necessary conditions, if q=Q(e,f,x)>q* Q(e*,f,x)=q*, otherwise

Social optimality: Illustration e $ e*e* e°

The discontinuity problem Analytically merely cumbersome Practically troublesome –Stop getting responses to enforcement alterations To avoid the problem –Set q* low enough (lower than the real target) –Aim for the appropriate level of noncompliance A well chosen q* is not supposed to be reached (  Non-compliance is a good sign!)

Some observations 1.Costless enforcement  traditional case (B q = ) 2.Costly enforcement  i.The real target harvest has to be modified (....upwards, B q < ) ii. Optimal enforcement becomes crucial iii.The control variable is enforcement  not “harvest”! iv.The announced target harvest is for show only v.Non-compliance is the desired outcome 3.Ignoring enforcement costs can be very costly i.Wrong target “harvest” ii.Inefficient enforcement

An example Private fishing benefits: Cost of enforcement: Probability of penalty: Shadow value of biomass: (assumed known) (can calculate on the basis of biomeconomic model)

Example (cont.) Enforcement response function: e, enforcement q, harvest f=2p f=pf=p f=0.5p

Example (cont.) Socially optimal harvest: f, penalty q, harvest q* (no enforcement cost)

To apply theory: Empirical requirements 1.The private benefit function of fishing, B(q,x) 2.The shadow value of biomass, 3.The enforcement cost function, C(e) 4.The penalty function,  (e) 5.The penalty structure, f Note: Items 1 & 2 come out of a bio-economic model of the fishery. Items 3, 4 and 5 are special enforcement data

To apply theory (cont) In real empirical cases, the functions will normally be more complicated –Include more variables (if only for statistical purposes) –Vary across fisheries and management systems However, they must contain the basic elements of the theory

Extensions 1.Different enforcement targets (controls) –How does that affect theory –A vector of controls 2.Disaggregation (fishing units, gear, areas) 3.Alternative fishing opportunities 4.Optimal mix of enforcement tools –Vector of tools –Cost of each –Efficiency of each –Optimal mix (calculation of gains) 5.The structure (not only severity) of penalties

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