Fishery Dynamics

Fishery

Problem: 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 economics

Math in general very hard but special assumptions put analysis within reach:

1. Natural growth of biomass (stock) S: . Parabola, quadratic.[pic 1]
2. “Effort” by fishers E
3. Harvest (catch): H = SE. Straight line in a graph of H vs. S; steeper for higher E.
4. 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]