*Exhaustible Resource Extraction Problem


SET  T         TIME PERIODS                /1*50/
     TO(T)     OPTIMIZATION PERIOD         /2*50/

SCALAR  C  COST PARAMETER                  /1/;
SCALAR	A  DEMAND PARAMETER                /6/;
SCALAR  B  CONSTANT PARAMETER              /1/;
SCALAR  I  INTEREST RATE                   /1.1/;
      

*TFIRST(T) = YES$(ORD(T) EQ 1); TLAST(T) = YES$(ORD(T) EQ CARD(T));

VARIABLES  R(T)     RESOURCE STOCK IN EACH PERIOD
	   Q(T)     EXTRACTION IN EACH PERIOD
	   REV(T)   RETURNS IN EACH PERIOD
	   PROFIT   VALUE OF RETURNS

POSITIVE VARIABLES REV,PVR

EQUATIONS  EQM(T)   RESERVE EQUATION
	   YREV(T)  YEARLY RETURNS
	   OBJECTIVE OBJECTIVE FUNCTION;

EQM(T-1)..   R(T) =E= R(T-1) - Q(T);
YREV(TO)..    REV(TO) =E= ((A-B*Q(TO)/2)*Q(TO)) - ((C*Q(TO)*Q(TO))/2);
OBJECTIVE..  PROFIT =E= SUM(TO,REV(TO)*I**(1-ORD(TO)));

*SETTING INITIAL CONDITIONS

R.FX("1") = 100;
R.LO(T) = 0.0;
Q.LO(T) = 0.0;
MODEL RESOURCE / ALL /;
SOLVE RESOURCE MAXIMIZING PROFIT USING NLP;
DISPLAY R.L, Q.L;