Essay About Intersection Of Parabola S And Higher E.Net Growth Of Stock

Fishery Dynamics
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FisheryProblem: lack of property rights.Traditional or communal rights may not work in an impersonal society; the market becomes more important.Important: Canonical example of the tragedy of the commons in contemporary economicsMath in general very hard but special assumptions put analysis within reach:Natural growth of biomass (stock) S: . Parabola, quadratic.[pic 1]“Effort” by fishers EHarvest (catch): H = SE. Straight line in a graph of H vs. S; steeper for higher E.Net growth of stock: [pic 2]Steady state:. Stock sustained at intersection of parabola S(1-S) & straight line SE.[pic 3]Maximum sustainable yield (msy): max SE = S(1 – S) at. .[pic 4][pic 5] If E > ½, slight decrease in E entails short-run decrease & a long-run increase in harvest

Let (world) price of fish be p and wage of fishers be w < p.Open access: anyone can enter. (No property right of exclusion. Excess entry.)Rent (“profit”) per period “dissipated” (is zero) by entry and resulting over-fishing:. Solve: . [pic 6][pic 7]This stock is sustained if w and p do not change. Stock is equal to (= ½) only if w/p = ½. Open-access stock can be greater or less than.[pic 8][pic 9]If w = p,  and the fishery is not exploited.[pic 10]Over-fishing: as price rises with a given wage, equilibrium stock falls toward zero.First step in analysis. Maximize net, sustained, economic yield or net rent per year.Sustained. Therefore, F(S) = H and S > 0. S(1 – S) = SE; S = 1 –E.. Parabola, quadratic.[pic 11]Roots (points where ρ is zero) are at E = {0, 1 – w/p}Maximum is at the average of the roots: .[pic 12]Stock is [pic 13]Always true that. A small reduction in effort at the msy level gives a savings of cost but not much change in harvest. Maximizing rent balances the two effects, at a point where the parabola S(1 – S) is decreasing.[pic 14]