hhmax.gms : A Household Maximization Problem
Definition of the Index Sets ---------------------------------------
Reference:
- Hosoe, N, Gasawa, K, and Hashimoto, H, Handbook of Computible General Equilibrium Modeling. University of Tokyo Press, Tokyo, Japan, 2004.
Small Model of Type: NLP
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$ Title A Household's Utility Max. Model in Ch. 3 (HHMAX,SEQ=274)
* Definition of the Index Sets ---------------------------------------
Set i goods /BRD bread,
MLK milk/
h factors /CAP capital,
LAB labor/;
* Definition of Parameters -------------------------------------------
Parameter alpha(i) share parameter in utility function
/BRD 0.2
MLK 0.8/;
Parameter px(i) price of the i-th good
/BRD 1
MLK 2/;
Parameter pf(h) price of the h-th factor
/CAP 2
LAB 1/;
Parameter FF(h) factor endowment
/CAP 10
LAB 20/;
* Definition of Primal/Dual Variables --------------------------------
Positive Variable X(i) consumption of the i-th good
;
Variable UU utility
;
Equation eqX(i) household demand function
obj utility function
;
* Specification of Equations ------------------------------------------
eqX(i).. X(i) =e= alpha(i)*sum(h, pf(h)*FF(h))/px(i);
obj.. UU =e= prod(i, X(i)**alpha(i));
* Setting Lower Bounds on Variables to Avoid Division by Zero ---------
X.lo(i)=0.001;
* Defining the Model --------------------------------------------------
Model HHmax /all/;
* Solving the Model ---------------------------------------------------
Solve HHmax maximizing UU using NLP;
* ---------------------------------------------------------------------
* end of model --------------------------------------------------------
* ---------------------------------------------------------------------
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