Stock & Flow Equations
(01) Accumulated Discounted Fishery Profit= INTEG (
discounted fishery profit inflow,
0)
Units: $
(02) Accumulated Fishery Profit= INTEG (
total fishery profit inflow,
0)
Units: $
(03) adjusted price=
MIN(Current Mkt Price * "supply(Q) effect on price", max price)
Units: $/fish
Max price keeps the adjustment within a restricted zone of
reasonable prices. Due to competition and substitute products,
prices can only adjust so high. Outside market forces and
competition will drive down the market price, especially with
competition from Aquaculture.
(04) base case switch=
1
Units: Dmnl
base case = 1, and we start the simulation with several vessels
and then allow the investment to start at year 10. other cases =
0, when the switch is set to off, we allow investment from the
start.
(05) "biomass add, new fish"=
"growth, regeneration rate, NL"
Units: fish/Year
(06) catch per ship=
normal catch per ship * "effect of fish density on catch per ship, NL"
Units: fish / ship / Year
(07) Current Mkt Price= INTEG (
price changes,
initial mkt price)
Units: $/fish
(08) discount rate=
0.1
Units: Dmnl
10% cost of capital, or discount rate.
(09) discounted fishery profit inflow=
total profit/(1+ discount rate)^(Time/"std. time")
Units: $/Year
(10) "effect of catch per ship on desire to grow, NL" = WITH LOOKUP (
catch per ship,
([(0,-0.6)-(25,1)],(0,-0.48),(2.5,-0.45),(5,-0.37),(7.5,-0.27),(10,0),(12.5
,0.64),(15,0.9),(17.5,0.995),(20,0.995),(22.5
,1),(25,1) ))
Units: Dmnl
-
(11) "effect of fish density on catch per ship, NL" = WITH LOOKUP (
fish density,
([(0,0)-(1,1)],(0,0),(0.1,0.4),(0.2,0.68),(0.3,0.8),(0.4,0.88),(0.5,0.96
),(0.6,1),(0.7,1),(0.8,1),(0.9,1),(1,1) ))
Units: Dmnl
-
“… and shown below in graphic mode”
(12) FINAL TIME = 40
Units: Year
The final time for the simulation.
(13) fish density=
Fish Stock / max fishery size
Units: Dmnl
(14) fish harvest=
MIN(total catch, Fish Stock/TIME STEP)
Units: fish/Year
The fish harvest is equal to the computed catch. However, as the
stock dwindles the biomass is reduced in a smoothed fashion.
Similar to or based on, "all outflows require first order
control," [
17] (pp. 545-546). Generically, outflow =
min (desired outflow, maximum outflow), where, maximum outflow =
stock / minimum residence time.
(15) Fish Stock= INTEG (
"biomass add, new fish"-fish harvest,
initial fish stock)
Units: fish
(16) "gap (fleet size)"=
"goal: desired fleet size" - Ships at Sea
Units: ships
(17) "goal: desired fleet size"=
Ships at Sea * (1 + inclination to expand fleet)
Units: ships
(18) growth rate=
0.1
Units: fraction
base rate = 10% rate of growth’ ... can be used for sensitivity
analysis.
(19) "growth, regeneration rate, NL" = WITH LOOKUP (
fish density,
([(0,0)-(1,600)],(0,0),(0.1,50),(0.2,100),(0.3,200),(0.4,320),(0.5,500),
(0.6,550),(0.7,480),(0.8,300),(0.9,180),(1,0) ))
Units: fish/Year
-
“… and shown below in graphic mode.” Note: this also corresponds with the expected relationship between surplus production and biomass for the simple Schaefer biomass dynamic model [
27] (p. 300).
(20) inclination to expand fleet=
normal desire to grow * "effect of catch per ship on desire to grow, NL"
Units: Dmnl
(21) initial fish stock=
3750
Units: fish
(22) initial mkt price=
200
Units: $/fish
(23) initial ships at sea=
10
Units: ships
(24) INITIAL TIME = 0
Units: Year
The initial time for the simulation.
(25) max fishery size=
4000
Units: fish
(26) max price=
400
Units: $/fish
(27) normal catch per ship=
25
Units: fish/ship/Year
(28) normal desire to grow=
IF THEN ELSE(base case switch, 0+STEP(growth rate, 11), growth rate)
Units: fraction
growth rate = 0.10 or 10% in the base case.
(29) price changes=
(adjusted price - Current Mkt Price)/time to adjust prices
Units: $/fish/Year
(30) purchase or retire ships=
"gap (fleet size)" / time to adjust fleet size
Units: ships / Year
(31) SAVEPER =
TIME STEP
Units: Year [0,?]
The frequency with which output is stored.
(32) Ships at Sea= INTEG (
purchase or retire ships,
initial ships at sea)
Units: ships
(33) smoothed catch info=
SMOOTHI(total catch, time to avg catch, total catch)
Units: fish/Year
(34) "std. expense/ship"=
2500
Units: $/Year/ship
(35) "std. time"=
1
Units: Year
(36) "supply(Q) effect on price" = WITH LOOKUP (
total catch/smoothed catch info,
([(0.8,0.8)-(5,2)],(0.0366748,1.1),(0.268949,1.05),(0.525672,1.02),(1,1
),(1.50367,0.968421),(2.01711,0.947368),(2.02934,0.940351),(2.31051,0.933333
),(3,0.9),(4,0.89),(5,0.89) ))
Units: Dmnl
The supply effect on price is moderate. The market for fish is
constrained by outside forces, substitutability, and other
regional markets.\!Dmnl
(37) TIME STEP = 1
Units: Year [0,?]
The time step for the simulation.
(38) time to adjust fleet size=
1
Units: Year
(39) time to adjust prices=
1
Units: Year
(40) time to avg catch=
2
Units: years
(41) total catch=
catch per ship * Ships at Sea
Units: fish / Year
(42) total fishery profit inflow=
total profit
Units: $/Year
(43) total profit=
total revenue - ("std. expense/ship" * Ships at Sea)
Units: $/Year
(44) total revenue=
total catch * Current Mkt Price
Units: $/Year