;;;;
;;;; Qualitative Model after
;;;; ML Cropper, DR Lee and SS Pannu (1979):
;;;; "The Optimal Extinction of a Renewable Natural Resource,
;;;; Journal of Environmental Economics and Management 6, p. 341-349."
;;;;
;;;; Actually, it is a simplified version of the original model, namely
;;;; a version as proposed by the reviewer of our article.
;;;;
;;;; Eisenack et al.,  V. 6.7.2004
;;;;
;;;; Start simulation with 
;;;;   ./cq -I cropper.run
;;;;
;;;; Result: state transition graph with XXX  states
;;;; (after all standard filtering procedures).
;;;; 
;;;; View with: stg <CR> x <CR>  h <CR><CR>
;;;; 

;;; Begin definition of model

(quantity-spaces
 (X (0 Xm Xmax)   "resource stock")
 (Y (0 MSY Ymax)  "harvest")
 (F (0 MSY)       "rate of growth")
 (P (0 Pmax)      "price")
 (C (0 Cmax)      "harvesting costs")
 (dX (minf 0 inf) "dX")
 (dY (minf 0 inf) "dY")
) 

(constraints
 ((d//dt X dX))
 ((d//dt Y dY))
 ((add dX Y F) (0 0 0) (0 MSY MSY))
 ((add dY C P) (0 0 0))

 ((U- X F) (Xm MSY) (0 0) (Xmax 0))
 ((M- Y P))
 ((M- X C))

 ;; Exclusion of marginal cases 
 ((cornot X dX) (Xm 0)) 
 ((cornot X dY) (Xm 0)) 
 ((cornot Y dX) (MSY 0)) 
 ((cornot Y dY) (MSY 0)) 
)

;;; technical directives

(unreachable-values (X Xmax) (Y Ymax))

(weak-cycles)

(with-envisionment)

;;; initial state of simulation

(make-initial-state 
; (X ((Xm Xmax) nil))
 (Y ((0 MSY) nil))
 (F ((0 MSY) nil))
 (P ((0 Pmax) nil))
 (C ((0 Cmax) nil))
)