Demand GAMS code

GAMS/demand.gms

+ 
+ SET com        / monogastrics, ruminants, wheat, maize, rice, oilcrops, pulses, starchyRoots /;
+ ALIAS (com, com2);
+ ALIAS (com, com3);
+      
+ SCALAR income / 100 /;
+      
+ TABLE subElasticities(com, com2)
+                     ruminants  wheat   maize    rice  oilcrops  pulses  starchyRoots
+     monogastrics          0.7   0.15     0.1     0.1      0.1      0.1          0.1
+     ruminants                    0.1     0.1     0.1      0.1      0.1          0.1
+     wheat                                0.6     0.6      0.4      0.4          0.4
+     maize                                        0.6      0.4      0.4          0.4
+     rice                                                  0.4      0.4          0.4
+     oilcrops                                                       0.5          0.5
+     pulses                                                                      0.5 ;
+     
+ subElasticities(com, com2)$subElasticities(com2, com) = subElasticities(com2, com);     
+ 
+ PARAMETER calories(com)
+   / monogastrics          3,
+     ruminants             5,
+     wheat                 1,
+     maize                 1,
+     rice                  1,
+     oilcrops              2,
+     pulses                1,
+     starchyRoots          1  / ;
+ calories(com) = 1;
+ 
+ PARAMETER idealDiet(com)
+   / monogastrics          1,
+     ruminants             1,
+     wheat                 1,
+     maize                 1,
+     rice                  1,
+     oilcrops              1,
+     pulses                1,
+     starchyRoots          1  / ;
+      
+ PARAMETER price(com)
+   / monogastrics          4,
+     ruminants             5,
+     wheat                 2,
+     maize                 2,
+     rice                  2,
+     oilcrops              2,
+     pulses                1,
+     starchyRoots          1  / ;
+       
+ PARAMETER comUtility(com);
+ comUtility(com) = 1;
+      
+      
+ Variables 
+     consumption(com)
+     diffIncrease(com)
+     diffDecrease(com)
+     subIncrease(com, com2)        proportion of each off-setting or substitution consumption matrix
+     subDecrease(com, com2)        proportion of each off-setting or substitution consumption matrix
+     totalCost
+     foodUtility
+     netUtility;
+     
+ Positive Variable consumption, subIncrease, subDecrease, diffIncrease, diffDecrease;
+     
+ Equations
+     budget_constraint
+     diff_constrainta(com)           
+     diff_constraintb(com)          
+     diff_constraintc(com)           
+     diff_constraintd(com)           can not decrease more than whole ideal consumption as would imply negative consumption
+     
+     subs_constraint1a(com)          
+     subs_constraint1b(com)           
+     subs_constraint2a(com)          
+     subs_constraint2b(com)           
+     subs_constraint3a(com2)          the different to ideal adds to the total used for substituting for alternative commodities
+     subs_constraint3b(com2)          the different to ideal adds to the total used for substituting for alternative commodities
+ 
+     food_utility_change_calc
+     total_cost_calc
+     net_utility_calc;
+
+ budget_constraint .. totalCost =l= income;
+ 
+ diff_constrainta(com) .. diffIncrease(com) =g= (consumption(com) - idealDiet(com));
+ diff_constraintb(com) .. diffDecrease(com) =g= -(consumption(com) - idealDiet(com));
+ diff_constraintc(com) .. diffIncrease(com) - diffDecrease(com) =e= consumption(com) - idealDiet(com);
+ diff_constraintd(com) .. diffDecrease(com) =l= idealDiet(com);
+ 
+ subs_constraint1a(com) ..   subIncrease(com, com) =e= 0;
+ subs_constraint1b(com) ..   subDecrease(com, com) =e= 0;
+ 
+ subs_constraint2a(com) ..   sum(com2, subDecrease(com, com2) * calories(com2)) =e= diffIncrease(com) * calories(com);
+ subs_constraint2b(com) ..   sum(com2, subIncrease(com, com2) * calories(com2)) =e= diffDecrease(com) * calories(com);
+ 
+ subs_constraint3a(com2) ..  sum(com, subDecrease(com, com2) * calories(com)) =e= diffDecrease(com2) * calories(com2);
+ subs_constraint3b(com2) ..  sum(com, subIncrease(com, com2) * calories(com)) =e= diffIncrease(com2) * calories(com2);
+  
+ food_utility_change_calc .. foodUtility =e= sum(com, 
+        comUtility(com) * ( (diffIncrease(com) + diffDecrease(com))**2 - 
+                              sum(com2, (subIncrease(com, com2) + subDecrease(com, com2))**2 * subElasticities(com, com2))
+                          ) );
+ 
+ total_cost_calc ..  totalCost =e= sum(com, consumption(com) * price(com));
+ 
+ net_utility_calc ..  netUtility =e=   ((totalCost/income)) * 25 + foodUtility;
+
+ MODEL DEMAND /ALL/ ;
+ 
+ consumption.l(com) = idealDiet(com);
+ 
+ SOLVE DEMAND USING NLP MINIMIZING netUtility;
+
+ display foodUtility.l, totalCost.l, subElasticities, idealDiet, subDecrease.l, subIncrease.l, consumption.l, diffIncrease.l, diffDecrease.l;
+ 
+ PARAMETER diff(com);
+ diff(com) = consumption.l(com) - idealDiet(com);
+ display diff;
+  
+ PARAMETER check(com);
+ check(com) = 0;
+*display check;
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