utility maximization on the EV frontier

ev2.gms

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PROBLEM STATMENT
EV analysis from Hazell-Norton

ctnd. from ev.gms

Extension: find the optimal farm decision based on EUH; having the EV-frontier and assuming a utility function

3 sub-cases:
- risk averse
- risk neutral
- risk loving


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* --- data input

scalar intercept, slope;
execute_load "fit.gdx", intercept, slope;

display slope, intercept;

scalar r "absolute risk aversion [Arrow Pratt]";

scalar LP_solution "total returns at the LP solution point [upper bound]" /77216/;

positive variable totM "total returns [at the margin]";
variable totV "total variance";
variable utility "utility points of farmer";


equation
        U_ "utility funciton of the farmer"
        EV_ "we are at the ev frontier"
        maxtotM_ "maximum returns [where the frontier ends]"
;

U_..    utility =e= totM/1000 + r * (totM/1000)  * (totM/1000)
                     + r * (totV/1000) ;
EV_..   totV/1000 =e= (slope*totM + intercept)/1000;
maxtotM_ ..  totM =l= LP_solution;

model decision /U_, EV_, maxtotM_/;

* --- set to the solution of the LP
totM.L = LP_solution * 0.9;
totV.LO = 0.1;

* risk averse
r = -2;
solve decision using nlp maximizing utility;

display totM.L, utility.L;


* risk lover
r = 2;
solve decision using nlp maximizing utility;

display totM.L, utility.L;