New bioeconomics of fisheries and forestry Olli Tahvonen University of Helsinki EAERE Venice Summer School 2011 Section 1, Fisheries Section 1, Fisheries 1
1. Introduction The question of managing The question of managing biological resources Actual resource management Actual resource management is dominated by ecologists and MSY -type objectives both in Resource forestry and fisheries y Applied Applied economics ecology New bioeconomics: Economic objectives The aim is to integrate sound with "oversimplified" Detailed economics and realistic economics and realistic ecology ecological models models taken directly from with MSY -type ecology objectives Applied cf. economics of nonrenewable mathematics h i resources 2
1. Introduction, cont. Two generic models in resource economics: Biomass harvesting model (fisheries) Optimal rotation model (forestry) Schaefer 1954, Gordon 1957, Plourde 1972, Clark 1976,... Faustmann 1849, Ohlin 1928, Samuelson 1976,... rt max U( h,x )e dt rt px(t )e w { h } 0 0 max max e rt s.t. x F( x ) h, { t } 1 x( ) x 0 0 Some extensions/alternatives: Some extensions/alternatives : Age-structured models Environmental values Spatial models p Market level age structured models Market level age-structured models Multispecies models,... Stand level size-structured models,... Optimal rotation with optimal thinning, initial density initial density,... 3
New bioeconomics of fisheries and forestry Content Content 0 Introduction 1 Fisheries 1 1 Age-structured population models in fisheries 1.1 Age-structured population models in fisheries 1.2 Generic age-structured optimization problem 1.3 Empirical example of an age-structured fishery model 1 4 On numerical optimization 1.4 On numerical optimization 2 Forestry 2.1 Market level age-structured model for timber/old growth/agriculture g g g 2.2 Stand level size-structured models 2.3 Generic size structured optimization problem 2.4 Empirical example of a size-structured model p p 3 Summary and discussion 4
Memory refresh: optimal solution for the Schaefer-Gordon-Clark biomass harvesting model bi h ti d l rt max max U( h ) U( h ) C( h x ) e C( h,x ) e dt dt { h } 0 Numerical example : 0 s.t. x F( x ) h, 25 x( ( ) ) x . 0 0 0 20 Some generic features: 15 d, h 1. The optimal steady state h*,x* is defined by Yield c ( h*,x*) x F'( x*) , "marginal rate of return 10 U '( h*) C ( h*,x*) equals interest" h F( x*) h* . 0 5 2. Optimal yield is an increasing function of biomass 2 O ti l i ld i i i f ti f bi 3. The optimal solution approaches the steady state 0 monotonically 0 20 40 60 80 100 120 4. If C =0 and F'(0)< it is optimal to deplete the Biomass, x x Optimal yield population (Clark 1973) Optimal yield Growth 5. MSY solution is determined by biological factors only F(x)=0.5x(1-x/100) U=u(h)-c(h,x) U(h)=h 1-0.95 , C(h,x)=15h,x -1.5 , r=0.02 5
Some problems related to the biomass models 1. The classical Gordon-Schaefer-Clark biomass model describes a biological population 1 Th l i l G d S h f Cl k bi d l d ib bi l i l l ti but simplifies the population as a homogenous biomass with no age or size structure 2. The classical Gordon-Schaefer-Clark model cannot specify to which age classes har esting sho ld be targeted harvesting should be targeted 3. Harvesting activity may change the population age structure, regeneration level but these effects are not possible to be included in the biomass framework 4. These and other age-truncation effects are intensively studied by ecologists 4 These and other age truncation effects are intensively studied by ecologists "Picture three human populations containing identical number of individuals. One of these is an old people's residential area, the second is a population of young children, and the third is a population of mixed age and sex. No amount of attempted correlation with factors outside the population would reveal that the first was doomed to extinction (unless maintained by immigration), the ld l th t th fi t d d t ti ti ( l i t i d b i i ti ) th second would grow fast but after a delay, and the third would continue to grow steadily." From Begon et al. (2011, p. 401) "Ecology". (perhaps the globally most widely used ecology textbook) Obviously something similar holds true in the cases of fish trees etc Obviously something similar holds true in the cases of fish, trees etc 6
Discussion on adding age structure to economic models: Wilen (1985, 2000): the biomass approach may at its best serve as a pedagogical tool Clark (1976 1990): Unfortunately the dynamics of many important biological resources Clark (1976, 1990): Unfortunately, the dynamics of many important biological resources cannot be realistically described by means of simple biomass models Hilborn and Walters 1992:. The biomass model is seen as a poor cousin of the age-structured analysis and is used only if age-structured data is unavailable Clark (1990, 2006), Hilborn and Walters (1992) and Wilen (1985): age-structured models are analytically incomprehensible However, this statement has turned out to be overly pessimistic 7
Remarks: Age-structured models are becoming important in general economics as well Age structured models are becoming important in general economics as well Instead of aggregate production functions with "capital stock" it is possible to specify capital as "vintages" (e.g. Boucekkine et al JET 1997,...) Adding internal structure to capital stock or labor will change many fundamental dd g e a s uc u e o cap a s oc o abo c a ge a y u da e a properties in models on economic growth and business cycles, for example. 8
Some history of age- and size-structured population models in biology P.H. Leslie (1945). Matrix models for age-structured populations L Lefkovich (1965) Matrix models for size structured populations L. Lefkovich (1965) Matrix models for size structured populations M.B. Usher (1966) Matrix models for tree populations =>Presently population studies in ecology rest heavily on age- or size structured models structured models and in fishery economics (or fishery ecology...difficult to make the distinction) Baranov (1918): The problem raised Beverton and Holt (1957): Famous "Dynamic pool model" Walters (1969): Pulse fishing solutions ( ) g Clark (1976, 1990): "The problem is incomprehensible" Hannesson (1975): Pulse fishing solutions Horwood (1987): Smooth harvesting solutions => almost all studies have used only numerical methods 9
A life cycle graph for an age-classified population with density dependence in recruitment in recruitment 4 x s st s 1 x x x x x x x x 1 1 t 2 t 1 1 2 2 2 3 t 4 t 3 4 x x x x 1 t 2 t 3 t 4 t x x x 1 1 t 2 t 2 t 3 t 3 t 2 2 3 3 h h h h 3 t 4 t 2 t 1 t Four age classes, s , , , 1 2 3 4 x number of individuals in age class s in the beginnig of period t (state variables) 0 st 1 share of individuals that survive in age class s share of individuals that survive in age class s 1 s the share s ,...,n die due to natural reasons ( natural morta lity ) 1 1 s number of offspring per individual in age class s 0 s therecruitment function :the number of offspring that survive to age class h i f i h b f ff i h i l 1 1 h the harvesting mortality (control variables) 10 st
Examples of commonly used recruitment functions Examples of commonly used recruitment functions Beverton Holt recruitment function : ( x ) ax / ( bx ) 1 0 0 0 bx bx Ri h Richer recuitment function : i f i ( ( x ) ) ax e 0 0 0 0 10 ( x ) . x / ( . x ) 0 9 1 0 1 0 0 0 8 cruits mber of rec 6 4 Num . x ( x ) ( x ) . x e x e 0 05 0 9 0 9 0 0 0 0 2 0 0 20 40 60 80 N mber of eggs Number of eggs N Number of "eggs" b f " " 11
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