PRODUCTIONProduction is related to supply of goods &services.Production is defined as “The creation of utility withcreation or addition of value”.
They are the productive resourcesrequired to produce a given product.these productive resources are…….1) Raw materials2) Services of workers3) Capital4) Organising of work.Generally the factors of production are LAND LABOUR CAPITAL
DEFNITIONS LAWS OF PRODUCTIONGeneralization governing relationship between input &output. PRODUCTION FUNCTIONRelationship between input and output of a firm THEORY OF POPULATIONWhich govern the supply of labour.
THE BASIC BIOLOGY OF THEMODELThe Gordon-schaefer(GS)model considers a single fish stock in isolation and is concerned with the way in which the stock grows over a time. it is based upon the logistic growth model.Let us suppose that we have an area of sea , we introduce a small fish population to it .The growth ,G , of the population P over a time period t’ will be a function of the initial size of the population ;That is,…. dp / dt=G=f(P).
Now the area of sea is relatively small. Suppose that to begin with , population growth will be roughly proportional to the initial population ; that is,…… G= Ap . The constant a’ is called the intrinsic growth rate. Since any given area of sea is ,by definition, limited in size ,there must be some maximum size of fish population that can be supported . this maximum is usually called the environmental carrying capacity(ECC).and is denoted by K. As the fish population size approaches the ECC so crowding of the sea area will increasingly become a problem.
The growth rate,G, of the population may then be expected to fall,according to the degree of crowding..at any particular moment,the growth rate will be propotional to the difference between the ECC and the population at the time.this gives us the growth equation. G=aP[(K-P)/K] =aP(1-P/K). In the absence of fishing ,the population size will be equal to the ECC. Differentiating the equation and setting it equal to zero,we must see that maximum growth of the fish stock occurs when the population size is half of the ECC;that is , G=a(1-2P/K)=0Hence P=K/2
THE BIOLOGICAL PRODUCTIVITYCURVE.Maximum growth g r o w t h k2 Population size x
THE EFFECT OF FISHING-The shortrun. Having consider the unexploited fish stock Now introduced fishing It is postulated that the yield Y.It depends on two factors……..1. The size of the fish population at the beginning.2. The amount of fishing effort f’. Y=y(P,f).
FISHING EFFORT Economists think of effort in terms of the boats, men, gear and so on that are required for the fishing activity this is usually termed as nominal effort. Other word is effective fishing effort. F.Defined as “the fraction of the average population taken by fishing “
The F is achieved by considering the propotion of the stock that survives fishing. Precisely ,it is the negative of the natural logarithm of the proportion of fish surviving in a year. F=qf. q=catchability coefficient. Clearly if q=1 then f and F are the same thing and the analysis of fishing will be the same whichever is used .
We shall use nominal effort and our simple short – run yield equation becomes Y=qfP. Here consider the way in which short-run yield will change in response to change in effort and population size.
POPULATION SIZE From eqn Y=qfP the given level of nominal effort,yield will vary linearly with population size .the greater is the population size,the greater will be the yield .
y sryf3 Yield sryf2 sryf3 x production size
DIMINISHING RETERN TOPOPULATION SIZEAmount of nominal effort is given .Population size is increases,the given amount of effort will be spread more thinly across the populationSo ability to catch of the fish to be less .Here yield may rise less than proportionatlyThere for,short-run yield to be a non-linear function of population size.Y=qfP.
SUSTAINABLE YIELD CURVE MSY G R O W T H ECC/2 EFFORT POPULATION
SUSTAINABLE YIELD CURVE It is simple quadratic function of effort . It is simple mirror image of the biological productivity curve . It is to notice the difference between the two the former is defined with respect to effort . the later is respect to population . The origin of sustainable yield curve correspond to ECC on the biological productivity curve .
SHORT RUN YIELD WITHDIMINISHING RETURNS TONOMINAL EFFORTMaximum possible short-run catch population size grownyield x Nominal effort
THE EFFECT OF FISHING –THELONG –RUN. Here we must combine our biological production function with our yield function. G=ap((1-P/K) Y=q fβp. At the beginning of the second period therefore the population size must be ECC-Y.
THE IMPACT OF FISHING ON THEPOPULATION SIZE YG Growth curveR SRYOWTH X POPULATIO P2 ECC N
BIOECONOMIC EQULIBRIUM OPEN-ACCESS. TOTAL REVENUE EXEEDS TOTAL COST
THE ECONOMICS OF FISHING COST TCf=Cf. C is the constant. Ac ,mc is straight forward Acf=MCf=c Y TCF=CF c o s t ACF=MCF effort X
FIGURE r Tc f1 c e o v s e Tc f2 t n u e TRf effort c r o e s v t e AC2=MC2 n MR u e effort AR