Chapter 9: comparative statics of fishery economics



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Date: 7 July 2000


CHAPTER 9: COMPARATIVE STATICS OF FISHERY ECONOMICS
We begin by laying out the equations that are used in the fishery models covered in the textbook and in these additional materials. The analysis in the chapter text uses continuous time notation. This convention is largely followed in this Word file. However, when we use Excel for dynamic simulation (as in exploit5.xls) we necessarily adopt discrete time, as spreadsheets are set up to do calculation recursively in discrete time intervals. To help the reader, we give the reader the model specifications in both forms (although our derivations are done here only in continuous time).
THE FISHERY MODELS: GENERAL FUNCTION SPECIFICATION




Continuous Time Model

Discrete Time Model

Pure biological growth (1)

dS/dt = G(S)

St+1-St = G(St)

Fishery production function (2)

H = H(E, S)

Ht = H(Et, St)

Net growth of fish stock (3)

dS/dt = G(S) - H

St+1-St = G(St) - Ht

Fishery revenue (4)

B = PH, P constant

Bt = PHt, P constant

Fishery costs (5)

C = C(E)

Ct = C(Et)

Fishery profit (6)

NB = B - C

NBt = Bt - Ct










FISHING EFFORT DYNAMICS







Open access entry rule (7)

dE/dt = dNB

Et+1-Et =dNBt

Private property entry rule (8)

dE/dt = d(dNB/dE)*E

Et+1-Et =d(dNBt/dEt)*E










STEADY STATE CONDITIONS







Biological equilibrium (9)

G = H

Gt = Ht

Economic equilibrium (10)

E(t) = E*

Et+1 = Et = E*


FISHERY MODEL: WITH ASSUMED FUNCTIONAL FORMS




Continuous Time Model

Discrete Time Model

Pure biological growth (1)





Fishery production function (2)

H = eES

Ht = eEtSt

Net growth of fish stock (3)

- H



Fishery revenue (4)

B = PH, P constant

Bt = PHt, P constant

Fishery costs (5)

C =wE

Ct =wEt

Fishery profit (6)

NB = B - C = PeES -wE

NBt = Bt - Ct = PeEtSt -wEt










FISHING EFFORT DYNAMICS






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