[Swift-commit] r3003 - in SwiftApps/SEE/trunk: . subproblems
noreply at svn.ci.uchicago.edu
noreply at svn.ci.uchicago.edu
Tue Jul 7 16:41:30 CDT 2009
Author: aespinosa
Date: 2009-07-07 16:41:29 -0500 (Tue, 07 Jul 2009)
New Revision: 3003
Added:
SwiftApps/SEE/trunk/subproblems/
SwiftApps/SEE/trunk/subproblems/producer_graph.mod
SwiftApps/SEE/trunk/subproblems/producer_tree.mod
Log:
Added subproblems directory from orig tarballs
Added: SwiftApps/SEE/trunk/subproblems/producer_graph.mod
===================================================================
--- SwiftApps/SEE/trunk/subproblems/producer_graph.mod (rev 0)
+++ SwiftApps/SEE/trunk/subproblems/producer_graph.mod 2009-07-07 21:41:29 UTC (rev 3003)
@@ -0,0 +1,194 @@
+##### Producer Variables #####
+#
+# Producers_Input: quantity of the input commodities used
+# Producers_Output: quantity of the output commodities produced
+#
+# Producers_Functions_Input: quantity of the inputs used by the production function
+# Producers_Functions_Output: quantity of the outputs produced by the production function
+#
+##### Notes #####
+#
+# (1) Input and Output are the primary optimization variables
+# (2) Functions_Input and Functions_Output are internal variables
+#
+##### Example #####
+#
+# Input[p1, usa, usa, agr];
+# Input[p1, usa, eur, agr];
+# Input[p1, usa, usa, lab];
+# Input[p1, usa, usa, cap];
+# Output[p1, usa, usa, agi];
+#
+# FInput[p1, usa, f1, usa, lab];
+# FInput[p1, usa, f1, usa, cap];
+# FOutput[p1, usa, f1, usa, kla];
+#
+# FInput[p1, usa, f2, usa, agr];
+# FInput[p1, usa, f2, eur, agr];
+# FInput[p1, usa, f2, usa, kla];
+# FOutput[p1, usa, f2, usa, agi];
+#
+# Input[p1, eur, usa, agr];
+# Input[p1, eur, eur, agr];
+# Input[p1, eur, eur, lab];
+# Input[p1, eur, eur, cap];
+# Output[p1, eur, eur, agi];
+#
+# FInput[p1, eur, f1, eur, lab];
+# FInput[p1, eur, f1, eur, cap];
+# FOutput[p1, eur, f1, eur, kla];
+#
+# FInput[p1, eur, f2, usa, agr];
+# FInput[p1, eur, f2, eur, agr];
+# FInput[p1, eur, f2, eur, kla];
+# FOutput[p1, eur, f2, eur, agi];
+#
+# Input[p1, row, usa, agr];
+# Input[p1, row, eur, agr];
+# Input[p1, row, row, agr];
+# Input[p1, row, row, lab];
+# Input[p1, row, row, cap];
+# Output[p1, row, eur, agi];
+#
+# FInput[p1, row, f1, row, lab];
+# FInput[p1, row, f1, row, cap];
+# FOutput[p1, row, f1, row, kla];
+#
+# FInput[p1, row, f2, usa, agr];
+# FInput[p1, row, f2, eur, agr];
+# FInput[p1, row, f2, row, agr];
+# FInput[p1, row, f2, row, kla];
+# FOutput[p1, row, f2, row, agi];
+#
+#####
+
+var Producers_Input {p in Producers, r in Producers_Regions[p], Producers_Inputs[p,r]} := 1.0;
+var Producers_Output {p in Producers, r in Producers_Regions[p], Producers_Outputs[p,r]} := 1.0;
+
+var Producers_Functions_Input {p in Producers, r in Producers_Regions[p], f in Producers_Functions_Regions[p,r], Producers_Functions_Inputs[p,r,f]} := 1.0;
+var Producers_Functions_Output {p in Producers, r in Producers_Regions[p], f in Producers_Functions_Regions[p,r], Producers_Functions_Outputs[p,r,f]} := 1.0;
+
+##### Producer Optimization Problem #####
+#
+# maximize Producers_Profits {p in Producers, r in Producers_Regions[p]}:
+# (sum {(ro,ko) in Producers_Outputs[p,r]} ((Producers_Revenues[p,r,ro,ko] -
+# Producers_RRPriceTax_Revenues[p,r,ro,ko]*Producers_RRPriceRate_Revenues[p,r,ro,ko] -
+# Producers_ROPriceTax_Revenues[p,r,ro,ko]*Producers_ROPriceRate_Revenues[p,r,ro,ko]
+# )*(if ko in Homogenous_Commodities the HPrice[ko] else Price[ro,ko]) -
+# Producers_RRQuantityTax_Revenues[p,r,ro,ko]*Producers_RRQuantityRate_Revenues[p,r,ro,ko] -
+# Producers_ROQuantityTax_Revenues[p,r,ro,ko]*Producers_ROQuantityRate_Revenues[p,r,ro,ko]
+# )*Producers_Output[p,r,ro,ko] -
+# sum {(ri,ki) in Producers_Inputs[p,r]} ((Producers_Expenditures[p,r,ri,ki] +
+# Producers_RRPriceTax_Expenditures[p,r,ri,ki]*Producers_RRPriceRate_Expenditures[p,r,ri,ki] +
+# Producers_RIPriceTax_Expenditures[p,r,ri,ki]*Producers_RIPriceRate_Expenditures[p,r,ri,ki]
+# )*(if ki in Homogenous_Commodities then HPrice[ki] else Price[ri,ki]) +
+# Producers_RRQuantityTax_Expenditures[p,r,ri,ki]*Producers_RRQuantityRate_Expenditures[p,r,ri,ki] +
+# Producers_RIQuantityTax_Expenditures[p,r,ri,ki]*Producers_RIQuantityRate_Expenditures[p,r,ri,ki]
+# )*Producers_Input[p,r,ri,ki]
+# )/Producers_Scale[p,r];
+#
+# Producers_Functions_Positive_Def {p in Producers, r in Producers_Regions[p], f in Producers_Functions_Regions[p,r], (ro,ko) in Producers_Functions_Positive[p,r,f]}:
+# Producers_Functions_Output[p,r,f,ro,ko] <= cesp(Producers_Functions_Scale[p,r,f,ro,ko]*Producers_Functions_Scale_Factor[p,r,f,ro,ko], Producers_Functions_Sigma[p,r,f,ro,ko], {(ri,ki) in Producers_Functions_Inputs[p,r,f]: Producers_Functions_Share[p,r,f,ro,ko,ri,ki] > 0} (Producers_Factors_Index[p,r,ri,ki], Producers_Functions_Share[p,r,f,ro,ko,ri,ki], Producers_Functions_Input[p,r,f,ri,ki]));
+#
+# Producers_Functions_Leontief_Def {p in Producers, r in Producers_Regions[p], f in Producers_Functions_Regions[p,r], (ro,ko) in Producers_Functions_Leontief[p,r,f], (ri,ki) in Producers_Functions_Inputs[p,r,f]: Producers_Functions_Share[p,r,f,ro,ko,ri,ki] > 0}:
+# Producers_Functions_Output[p,r,f,ro,ko] <= Producers_Functions_Scale[p,r,f,ro,ko]*Producers_Functions_Scale_Factor[p,r,f,ro,ko]*Producers_Functions_Input[p,r,f,ri,ki];
+#
+# Producers_Inputs_Balance_Def {p in Producers, r in Producers_Regions[p], (rf,kf) in Producers_Inputs[p,r]}:
+# Producers_Input[p,r,rf,kf] >= sum {f in Producers_Functions_Regions[p,r]: (rf,kf) in Producers_Functions_Inputs[p,r,f]} Producers_Functions_Input[p,r,f,rf,kf];
+#
+# Producers_Outputs_Balance_Def {p in Producers, r in Producers_Regions[p], (rf,kf) in Producers_Outputs[p,r]}:
+# Producers_Output[p,r,rf,kf] <= sum {f in Producers_Functions_Regions[p,r]: (rf,kf) in Producers_Functions_Outputs[p,r,f]} Producers_Functions_Output[p,r,f,rf,kf];
+#
+# Producers_Intermeds_Balance_Def {p in Producers, r in Producers_Regions[p], (rf,kf) in Producers_Intermeds[p,r]}:
+# sum {f in Producers_Functions_Regions[p,r]: (rf,kf) in Producers_Functions_Outputs[p,r,f]} Producers_Functions_Output[p,r,f,rf,kf] >= sum {f in Producers_Functions_Regions[p,r]: (rf,kf) in Producers_Functions_Inputs[p,r,f]} Producers_Functions_Input[p,r,f,rf,kf] ;
+#
+##### Notes #####
+#
+# (1) All variables are constrained to be nonnegative
+#
+##### First-Order Optimality Conditions #####
+#
+# Producers_Profit: report of producer profit given the optimal PInput and POutput
+#
+# m_pro_pos: multiplier on Positive production functions
+# m_pro_leo: multiplier on Leontief production functions
+# m_pro_in_bal: multiplier on input commodity balance constraints
+# m_pro_out_bal: multiplier on output commodity balance constraints
+# m_pro_inter_bal: multiplier on intermediate commodity balance constraints
+#
+#####
+
+var Producers_Profit {p in Producers, r in Producers_Regions[p]} := 1.0;
+
+var m_pro_pos {p in Producers, r in Producers_Regions[p], f in Producers_Functions_Regions[p,r], (ro,ko) in Producers_Functions_Positive[p,r,f]} := 1.0;
+var m_pro_leo {p in Producers, r in Producers_Regions[p], f in Producers_Functions_Regions[p,r], (ro,ko) in Producers_Functions_Leontief[p,r,f], (ri,ki) in Producers_Functions_Inputs[p,r,f]: Producers_Functions_Share[p,r,f,ro,ko,ri,ki] > 0} := 1.0;
+
+var m_pro_in_bal {p in Producers, r in Producers_Regions[p], (rf,kf) in Producers_Inputs[p,r]} := 1.0;
+var m_pro_out_bal {p in Producers, r in Producers_Regions[p], (rf,kf) in Producers_Outputs[p,r]} := 1.0;
+var m_pro_inter_bal {p in Producers, r in Producers_Regions[p], (rf,kf) in Producers_Intermeds[p,r]} := 1.0;
+
+subject to
+
+Producers_Profits_Def {p in Producers, r in Producers_Regions[p]}:
+ Producers_Profit[p,r] complements Producers_Profit[p,r] =
+ sum {(ro,ko) in Producers_Outputs[p,r]} ((Producers_Revenues[p,r,ro,ko] -
+ Producers_RRPriceTax_Revenues[p,r,ro,ko]*Producers_RRPriceRate_Revenues[p,r,ro,ko] -
+ Producers_ROPriceTax_Revenues[p,r,ro,ko]*Producers_ROPriceRate_Revenues[p,r,ro,ko]
+ )*(if ko in Homogenous_Commodities then HPrice[ko] else Price[ro,ko]) -
+ Producers_RRQuantityTax_Revenues[p,r,ro,ko]*Producers_RRQuantityRate_Revenues[p,r,ro,ko] -
+ Producers_ROQuantityTax_Revenues[p,r,ro,ko]*Producers_ROQuantityRate_Revenues[p,r,ro,ko]
+ )*Producers_Output[p,r,ro,ko] -
+ sum {(ri,ki) in Producers_Inputs[p,r]} ((Producers_Expenditures[p,r,ri,ki] +
+ Producers_RRPriceTax_Expenditures[p,r,ri,ki]*Producers_RRPriceRate_Expenditures[p,r,ri,ki] +
+ Producers_RIPriceTax_Expenditures[p,r,ri,ki]*Producers_RIPriceRate_Expenditures[p,r,ri,ki]
+ )*(if ki in Homogenous_Commodities then HPrice[ki] else Price[ri,ki]) +
+ Producers_RRQuantityTax_Expenditures[p,r,ri,ki]*Producers_RRQuantityRate_Expenditures[p,r,ri,ki] +
+ Producers_RIQuantityTax_Expenditures[p,r,ri,ki]*Producers_RIQuantityRate_Expenditures[p,r,ri,ki]
+ )*Producers_Input[p,r,ri,ki];
+
+Producers_Tax_Def {rr in Regions}:
+ Producers_Tax[rr] complements Producers_Tax[rr] =
+ sum {p in Producers, r in Producers_Regions[p], (ro,ko) in Producers_Outputs[p,r]: r == rr} (Producers_RRPriceTax_Revenues[p,r,ro,ko]*Producers_RRPriceRate_Revenues[p,r,ro,ko]*(if ko in Homogenous_Commodities then HPrice[ko] else Price[ro,ko]) + Producers_RRQuantityTax_Revenues[p,r,ro,ko]*Producers_RRQuantityRate_Revenues[p,r,ro,ko])*Producers_Output[p,r,ro,ko] +
+ sum {p in Producers, r in Producers_Regions[p], (ro,ko) in Producers_Outputs[p,r]: ro == rr} (Producers_ROPriceTax_Revenues[p,r,ro,ko]*Producers_ROPriceRate_Revenues[p,r,ro,ko]*(if ko in Homogenous_Commodities then HPrice[ko] else Price[ro,ko]) + Producers_ROQuantityTax_Revenues[p,r,ro,ko]*Producers_ROQuantityRate_Revenues[p,r,ro,ko])*Producers_Output[p,r,ro,ko] +
+ sum {p in Producers, r in Producers_Regions[p], (ri,ki) in Producers_Inputs[p,r]: r == rr} (Producers_RRPriceTax_Expenditures[p,r,ri,ki]*Producers_RRPriceRate_Expenditures[p,r,ri,ki]*(if ki in Homogenous_Commodities then HPrice[ki] else Price[ri,ki]) + Producers_RRQuantityTax_Expenditures[p,r,ri,ki]*Producers_RRQuantityRate_Expenditures[p,r,ri,ki])*Producers_Input[p,r,ri,ki] +
+ sum {p in Producers, r in Producers_Regions[p], (ri,ki) in Producers_Inputs[p,r]: ri == rr} (Producers_RIPriceTax_Expenditures[p,r,ri,ki]*Producers_RIPriceRate_Expenditures[p,r,ri,ki]*(if ki in Homogenous_Commodities then HPrice[ki] else Price[ri,ki]) + Producers_RIQuantityTax_Expenditures[p,r,ri,ki]*Producers_RIQuantityRate_Expenditures[p,r,ri,ki])*Producers_Input[p,r,ri,ki];
+
+Producers_Opt_Input {p in Producers, r in Producers_Regions[p], (ri,ki) in Producers_Inputs[p,r]}:
+ 0 <= Producers_Input[p,r,ri,ki] complements ((Producers_Expenditures[p,r,ri,ki] +
+ Producers_RRPriceTax_Expenditures[p,r,ri,ki]*Producers_RRPriceRate_Expenditures[p,r,ri,ki] +
+ Producers_RIPriceTax_Expenditures[p,r,ri,ki]*Producers_RIPriceRate_Expenditures[p,r,ri,ki]
+ )*(if ki in Homogenous_Commodities then HPrice[ki] else Price[ri,ki]) +
+ Producers_RRQuantityTax_Expenditures[p,r,ri,ki]*Producers_RRQuantityRate_Expenditures[p,r,ri,ki] +
+ Producers_RIQuantityTax_Expenditures[p,r,ri,ki]*Producers_RIQuantityRate_Expenditures[p,r,ri,ki]
+ )/Producers_Scale[p,r] - m_pro_in_bal[p,r,ri,ki] >= 0;
+
+Producers_Opt_Output {p in Producers, r in Producers_Regions[p], (ro,ko) in Producers_Outputs[p,r]}:
+ 0 <= Producers_Output[p,r,ro,ko] complements m_pro_out_bal[p,r,ro,ko] - ((Producers_Revenues[p,r,ro,ko] -
+ Producers_RRPriceTax_Revenues[p,r,ro,ko]*Producers_RRPriceRate_Revenues[p,r,ro,ko] -
+ Producers_ROPriceTax_Revenues[p,r,ro,ko]*Producers_ROPriceRate_Revenues[p,r,ro,ko]
+ )*(if ko in Homogenous_Commodities then HPrice[ko] else Price[ro,ko]) -
+ Producers_RRQuantityTax_Revenues[p,r,ro,ko]*Producers_RRQuantityRate_Revenues[p,r,ro,ko] -
+ Producers_ROQuantityTax_Revenues[p,r,ro,ko]*Producers_ROQuantityRate_Revenues[p,r,ro,ko]
+ )/Producers_Scale[p,r] >= 0;
+
+Producers_Opt_Functions_Input {p in Producers, r in Producers_Regions[p], f in Producers_Functions_Regions[p,r], (ri,ki) in Producers_Functions_Inputs[p,r,f]}:
+ 0 <= Producers_Functions_Input[p,r,f,ri,ki] complements (if (ri,ki) in Producers_Inputs[p,r] then m_pro_in_bal[p,r,ri,ki]) + (if (ri,ki) in Producers_Intermeds[p,r] then m_pro_inter_bal[p,r,ri,ki]) - sum {(ro,ko) in Producers_Functions_Positive[p,r,f]: Producers_Functions_Share[p,r,f,ro,ko,ri,ki] > 0} d_cesp(Producers_Factors_Index[p,r,ri,ki], Producers_Functions_Scale[p,r,f,ro,ko]*Producers_Functions_Scale_Factor[p,r,f,ro,ko], Producers_Functions_Sigma[p,r,f,ro,ko], {(r1,k1) in Producers_Functions_Inputs[p,r,f]: Producers_Functions_Share[p,r,f,ro,ko,r1,k1] > 0} (Producers_Factors_Index[p,r,r1,k1], Producers_Functions_Share[p,r,f,ro,ko,r1,k1], Producers_Functions_Input[p,r,f,r1,k1]))*m_pro_pos[p,r,f,ro,ko] - sum {(ro,ko) in Producers_Functions_Leontief[p,r,f]: Producers_Functions_Share[p,r,f,ro,ko,ri,ki] > 0} Producers_Functions_Scale[p,r,f,ro,ko]*Producers_Functions_Scale_Factor[p,r,f,ro,ko]*m_pro_leo[p,r,f,ro,ko,ri,ki] >= 0;
+
+Producers_Opt_Functions_Output {p in Producers, r in Producers_Regions[p], f in Producers_Functions_Regions[p,r], (ro,ko) in Producers_Functions_Outputs[p,r,f]}:
+ 0 <= Producers_Functions_Output[p,r,f,ro,ko] complements (if (ro,ko) in Producers_Functions_Positive[p,r,f] then m_pro_pos[p,r,f,ro,ko]) + (if (ro,ko) in Producers_Functions_Leontief[p,r,f] then sum {(ri,ki) in Producers_Functions_Inputs[p,r,f]: Producers_Functions_Share[p,r,f,ro,ko,ri,ki] > 0} m_pro_leo[p,r,f,ro,ko,ri,ki]) - (if (ro,ko) in Producers_Outputs[p,r] then m_pro_out_bal[p,r,ro,ko]) - (if (ro,ko) in Producers_Intermeds[p,r] then m_pro_inter_bal[p,r,ro,ko]) >= 0;
+
+Producers_Functions_Positive_Def {p in Producers, r in Producers_Regions[p], f in Producers_Functions_Regions[p,r], (ro,ko) in Producers_Functions_Positive[p,r,f]}:
+ 0 <= m_pro_pos[p,r,f,ro,ko] complements cesp(Producers_Functions_Scale[p,r,f,ro,ko]*Producers_Functions_Scale_Factor[p,r,f,ro,ko], Producers_Functions_Sigma[p,r,f,ro,ko], {(ri,ki) in Producers_Functions_Inputs[p,r,f]: Producers_Functions_Share[p,r,f,ro,ko,ri,ki] > 0} (Producers_Factors_Index[p,r,ri,ki], Producers_Functions_Share[p,r,f,ro,ko,ri,ki], Producers_Functions_Input[p,r,f,ri,ki])) - Producers_Functions_Output[p,r,f,ro,ko] >= 0;
+
+Producers_Functions_Leontief_Def {p in Producers, r in Producers_Regions[p], f in Producers_Functions_Regions[p,r], (ro,ko) in Producers_Functions_Leontief[p,r,f], (ri,ki) in Producers_Functions_Inputs[p,r,f]: Producers_Functions_Share[p,r,f,ro,ko,ri,ki] > 0}:
+ 0 <= m_pro_leo[p,r,f,ro,ko,ri,ki] complements Producers_Functions_Scale[p,r,f,ro,ko]*Producers_Functions_Scale_Factor[p,r,f,ro,ko]*Producers_Functions_Input[p,r,f,ri,ki] - Producers_Functions_Output[p,r,f,ro,ko] >= 0;
+
+Producers_Inputs_Balance_Def {p in Producers, r in Producers_Regions[p], (rf,kf) in Producers_Inputs[p,r]}:
+ 0 <= m_pro_in_bal[p,r,rf,kf] complements Producers_Input[p,r,rf,kf] - sum {f in Producers_Functions_Regions[p,r]: (rf,kf) in Producers_Functions_Inputs[p,r,f]} Producers_Functions_Input[p,r,f,rf,kf] >= 0;
+
+Producers_Outputs_Balance_Def {p in Producers, r in Producers_Regions[p], (rf,kf) in Producers_Outputs[p,r]}:
+ 0 <= m_pro_out_bal[p,r,rf,kf] complements sum {f in Producers_Functions_Regions[p,r]: (rf,kf) in Producers_Functions_Outputs[p,r,f]} Producers_Functions_Output[p,r,f,rf,kf] - Producers_Output[p,r,rf,kf] >= 0;
+
+Producers_Intermeds_Balance_Def {p in Producers, r in Producers_Regions[p], (rf,kf) in Producers_Intermeds[p,r]}:
+ 0 <= m_pro_inter_bal[p,r,rf,kf] complements sum {f in Producers_Functions_Regions[p,r]: (rf,kf) in Producers_Functions_Outputs[p,r,f]} Producers_Functions_Output[p,r,f,rf,kf] - sum {f in Producers_Functions_Regions[p,r]: (rf,kf) in Producers_Functions_Inputs[p,r,f]} Producers_Functions_Input[p,r,f,rf,kf] >= 0;
+
Property changes on: SwiftApps/SEE/trunk/subproblems/producer_graph.mod
___________________________________________________________________
Name: svn:executable
+ *
Added: SwiftApps/SEE/trunk/subproblems/producer_tree.mod
===================================================================
--- SwiftApps/SEE/trunk/subproblems/producer_tree.mod (rev 0)
+++ SwiftApps/SEE/trunk/subproblems/producer_tree.mod 2009-07-07 21:41:29 UTC (rev 3003)
@@ -0,0 +1,97 @@
+##### Producer Variables #####
+#
+# Producers_Input: quantity of the input and intermediate commodities used
+# Producers_Output: quantity of the output commodities produced
+#
+#####
+
+var Producers_Input {p in Producers, r in Producers_Regions[p], Producers_Inputs[p,r] union Producers_Intermeds[p,r]} := 1.0;
+var Producers_Output {p in Producers, r in Producers_Regions[p], Producers_Outputs[p,r]} := 1.0;
+
+check {p in Producers, r in Producers_Regions[p]}: card(Producers_Inputs[p,r] inter Producers_Intermeds[p,r]) = 0;
+check {p in Producers, r in Producers_Regions[p]}: card(Producers_Outputs[p,r] inter Producers_Intermeds[p,r]) = 0;
+
+param Producers_PTR {p in Producers, r in Producers_Regions[p], (ro,ko) in Producers_Outputs[p,r]} :=
+ Producers_RRPriceTax_Revenues[p,r,ro,ko]*Producers_RRPriceRate_Revenues[p,r,ro,ko] +
+ Producers_ROPriceTax_Revenues[p,r,ro,ko]*Producers_ROPriceRate_Revenues[p,r,ro,ko];
+param Producers_QTR {p in Producers, r in Producers_Regions[p], (ro,ko) in Producers_Outputs[p,r]} :=
+ Producers_RRQuantityTax_Revenues[p,r,ro,ko]*Producers_RRQuantityRate_Revenues[p,r,ro,ko] +
+ Producers_ROQuantityTax_Revenues[p,r,ro,ko]*Producers_ROQuantityRate_Revenues[p,r,ro,ko];
+
+param Producers_PTE {p in Producers, r in Producers_Regions[p], (ri,ki) in Producers_Inputs[p,r]} :=
+ Producers_RRPriceTax_Expenditures[p,r,ri,ki]*Producers_RRPriceRate_Expenditures[p,r,ri,ki] +
+ Producers_RIPriceTax_Expenditures[p,r,ri,ki]*Producers_RIPriceRate_Expenditures[p,r,ri,ki];
+param Producers_QTE {p in Producers, r in Producers_Regions[p], (ri,ki) in Producers_Inputs[p,r]} :=
+ Producers_RRQuantityTax_Expenditures[p,r,ri,ki]*Producers_RRQuantityRate_Expenditures[p,r,ri,ki] +
+ Producers_RIQuantityTax_Expenditures[p,r,ri,ki]*Producers_RIQuantityRate_Expenditures[p,r,ri,ki];
+
+Producers_Tax_Def {rr in Regions}:
+ Producers_Tax[rr] complements Producers_Tax[rr] =
+ sum {p in Producers, r in Producers_Regions[p], (ro,ko) in Producers_Outputs[p,r]: r == rr} (Producers_RRPriceTax_Revenues[p,r,ro,ko]*Producers_RRPriceRate_Revenues[p,r,ro,ko]*(if ko in Homogenous_Commodities then HPrice[ko] else Price[ro,ko]) + Producers_RRQuantityTax_Revenues[p,r,ro,ko]*Producers_RRQuantityRate_Revenues[p,r,ro,ko])*Producers_Output[p,r,ro,ko] +
+ sum {p in Producers, r in Producers_Regions[p], (ro,ko) in Producers_Outputs[p,r]: ro == rr} (Producers_ROPriceTax_Revenues[p,r,ro,ko]*Producers_ROPriceRate_Revenues[p,r,ro,ko]*(if ko in Homogenous_Commodities then HPrice[ko] else Price[ro,ko]) + Producers_ROQuantityTax_Revenues[p,r,ro,ko]*Producers_ROQuantityRate_Revenues[p,r,ro,ko])*Producers_Output[p,r,ro,ko] +
+ sum {p in Producers, r in Producers_Regions[p], (ri,ki) in Producers_Inputs[p,r]: r == rr} (Producers_RRPriceTax_Expenditures[p,r,ri,ki]*Producers_RRPriceRate_Expenditures[p,r,ri,ki]*(if ki in Homogenous_Commodities then HPrice[ki] else Price[ri,ki]) + Producers_RRQuantityTax_Expenditures[p,r,ri,ki]*Producers_RRQuantityRate_Expenditures[p,r,ri,ki])*Producers_Input[p,r,ri,ki] +
+ sum {p in Producers, r in Producers_Regions[p], (ri,ki) in Producers_Inputs[p,r]: ri == rr} (Producers_RIPriceTax_Expenditures[p,r,ri,ki]*Producers_RIPriceRate_Expenditures[p,r,ri,ki]*(if ki in Homogenous_Commodities then HPrice[ki] else Price[ri,ki]) + Producers_RIQuantityTax_Expenditures[p,r,ri,ki]*Producers_RIQuantityRate_Expenditures[p,r,ri,ki])*Producers_Input[p,r,ri,ki];
+
+##### Producer Optimization Problem #####
+#
+# maximize Producers_Profits {p in Producers, r in Producers_Regions[p]}:
+# (sum {(ro,ko) in Producers_Outputs[p,r]}
+# ((Producers_Revenues[p,r,ro,ko] - Producers_PTR[p,r,ro,ko])*(if ko in Homogenous_Commodities then HPrice[ko] else Price[ro,ko]) - Producers_QTR[p,r,ro,ko])*Producers_Output[p,r,ro,ko] -
+# sum {(ri,ki) in Producers_Inputs[p,r]}
+# ((Producers_Expenditures[p,r,ri,ki] + Producers_PTE[p,r,ri,ki])*(if ki in Homogenous_Commodities then HPrice[ki] else Price[ri,ki]) + Producers_QTE[p,r,ri,ki])*Producers_Input[p,r,ri,ki]
+# )/Producers_Scale[p,r];
+#
+# Producers_Functions_Positive_Def {p in Producers, r in Producers_Regions[p], f in Producers_Functions_Regions[p,r], (ro,ko) in Producers_Functions_Positive[p,r,f]}:
+# (if (ro,ko) in Producers_Outputs[p,r] then Producers_Output[p,r,ro,ko] else Producers_Input[p,r,ro,ko]) <= cesp(Producers_Functions_Scale[p,r,f,ro,ko]*Producers_Functions_Scale_Factor[p,r,f,ro,ko], Producers_Functions_Sigma[p,r,f,ro,ko], {(ri,ki) in Producers_Functions_Inputs[p,r,f]: Producers_Functions_Share[p,r,f,ro,ko,ri,ki] > 0} (Producers_Factors_Index[p,r,ri,ki], Producers_Functions_Share[p,r,f,ro,ko,ri,ki], Producers_Input[p,r,ri,ki]));
+#
+# Producers_Functions_Leontief_Def {p in Producers, r in Producers_Regions[p], f in Producers_Functions_Regions[p,r], (ro,ko) in Producers_Functions_Leontief[p,r,f], (ri,ki) in Producers_Functions_Inputs[p,r,f]: Producers_Functions_Share[p,r,f,ro,ko,ri,ki] > 0}:
+# (if (ro,ko) in Producers_Outputs[p,r] then Producers_Output[p,r,ro,ko] else Producers_Input[p,r,ro,ko]) <= Producers_Functions_Scale[p,r,f,ro,ko]*Producers_Functions_Scale_Factor[p,r,f,ro,ko]*Producers_Input[p,r,ri,ki];
+#
+##### Notes #####
+#
+# (1) All variables are constrained to be nonnegative
+#
+##### First-Order Optimality Conditions #####
+#
+# Producers_Profit: report of producer profit given the optimal PInput and POutput
+#
+# m_pro_pos: multiplier on Positive production functions
+# m_pro_leo: multiplier on Leontief production functions
+#
+#####
+
+var Producers_Profit {p in Producers, r in Producers_Regions[p]} := 1.0;
+
+var m_pro_pos {p in Producers, r in Producers_Regions[p], f in Producers_Functions_Regions[p,r], (ro,ko) in Producers_Functions_Positive[p,r,f]} := 1.0;
+var m_pro_leo {p in Producers, r in Producers_Regions[p], f in Producers_Functions_Regions[p,r], (ro,ko) in Producers_Functions_Leontief[p,r,f], (ri,ki) in Producers_Functions_Inputs[p,r,f]: Producers_Functions_Share[p,r,f,ro,ko,ri,ki] > 0} := 1.0;
+
+subject to
+
+Producers_Profits_Def {p in Producers, r in Producers_Regions[p]}:
+ Producers_Profit[p,r] complements Producers_Profit[p,r] =
+ sum {(ro,ko) in Producers_Outputs[p,r]}
+ ((Producers_Revenues[p,r,ro,ko] - Producers_PTR[p,r,ro,ko])*(if ko in Homogenous_Commodities then HPrice[ko] else Price[ro,ko]) - Producers_QTR[p,r,ro,ko])*Producers_Output[p,r,ro,ko] -
+ sum {(ri,ki) in Producers_Inputs[p,r]}
+ ((Producers_Expenditures[p,r,ri,ki] + Producers_PTE[p,r,ri,ki])*(if ki in Homogenous_Commodities then HPrice[ki] else Price[ri,ki]) + Producers_QTE[p,r,ri,ki])*Producers_Input[p,r,ri,ki];
+
+Producers_Opt_Input {p in Producers, r in Producers_Regions[p], (ri,ki) in Producers_Inputs[p,r] union Producers_Intermeds[p,r]}:
+ 0 <= Producers_Input[p,r,ri,ki] complements
+ (if (ri,ki) in Producers_Inputs[p,r] then ((Producers_Expenditures[p,r,ri,ki] + Producers_PTE[p,r,ri,ki])*(if ki in Homogenous_Commodities then HPrice[ki] else Price[ri,ki]) + Producers_QTE[p,r,ri,ki])/Producers_Scale[p,r]) +
+ (if (ri,ki) in Producers_Intermeds[p,r] then
+ (sum {f in Producers_Functions_Regions[p,r]: (ri,ki) in Producers_Functions_Positive[p,r,f]} m_pro_pos[p,r,f,ri,ki] +
+ sum {f in Producers_Functions_Regions[p,r]: (ri,ki) in Producers_Functions_Leontief[p,r,f]} (sum {(ri2,ki2) in Producers_Functions_Inputs[p,r,f]: Producers_Functions_Share[p,r,f,ri,ki,ri2,ki2] > 0} m_pro_leo[p,r,f,ri,ki,ri2,ki2]))) -
+ sum {f in Producers_Functions_Regions[p,r], (ro,ko) in Producers_Functions_Positive[p,r,f]: (ri,ki) in Producers_Functions_Inputs[p,r,f] and Producers_Functions_Share[p,r,f,ro,ko,ri,ki] > 0} d_cesp(Producers_Factors_Index[p,r,ri,ki], Producers_Functions_Scale[p,r,f,ro,ko]*Producers_Functions_Scale_Factor[p,r,f,ro,ko], Producers_Functions_Sigma[p,r,f,ro,ko], {(ri2,ki2) in Producers_Functions_Inputs[p,r,f]: Producers_Functions_Share[p,r,f,ro,ko,ri2,ki2] > 0} (Producers_Factors_Index[p,r,ri2,ki2], Producers_Functions_Share[p,r,f,ro,ko,ri2,ki2], Producers_Input[p,r,ri2,ki2]))*m_pro_pos[p,r,f,ro,ko] -
+ sum {f in Producers_Functions_Regions[p,r], (ro,ko) in Producers_Functions_Leontief[p,r,f]: (ri,ki) in Producers_Functions_Inputs[p,r,f] and Producers_Functions_Share[p,r,f,ro,ko,ri,ki] > 0} Producers_Functions_Scale[p,r,f,ro,ko]*Producers_Functions_Scale_Factor[p,r,f,ro,ko]*m_pro_leo[p,r,f,ro,ko,ri,ki] >= 0;
+
+Producers_Opt_Output {p in Producers, r in Producers_Regions[p], (ro,ko) in Producers_Outputs[p,r]}:
+ 0 <= Producers_Output[p,r,ro,ko] complements
+ sum {f in Producers_Functions_Regions[p,r]: (ro,ko) in Producers_Functions_Positive[p,r,f]} m_pro_pos[p,r,f,ro,ko] +
+ sum {f in Producers_Functions_Regions[p,r]: (ro,ko) in Producers_Functions_Leontief[p,r,f]} (sum {(ri,ki) in Producers_Functions_Inputs[p,r,f]: Producers_Functions_Share[p,r,f,ro,ko,ri,ki] > 0} m_pro_leo[p,r,f,ro,ko,ri,ki]) -
+ ((Producers_Revenues[p,r,ro,ko] - Producers_PTR[p,r,ro,ko])*(if ko in Homogenous_Commodities then HPrice[ko] else Price[ro,ko]) - Producers_QTR[p,r,ro,ko])/Producers_Scale[p,r] >= 0;
+
+Producers_Functions_Positive_Def {p in Producers, r in Producers_Regions[p], f in Producers_Functions_Regions[p,r], (ro,ko) in Producers_Functions_Positive[p,r,f]}:
+ 0 <= m_pro_pos[p,r,f,ro,ko] complements cesp(Producers_Functions_Scale[p,r,f,ro,ko]*Producers_Functions_Scale_Factor[p,r,f,ro,ko], Producers_Functions_Sigma[p,r,f,ro,ko], {(ri,ki) in Producers_Functions_Inputs[p,r,f]: Producers_Functions_Share[p,r,f,ro,ko,ri,ki] > 0} (Producers_Factors_Index[p,r,ri,ki], Producers_Functions_Share[p,r,f,ro,ko,ri,ki], Producers_Input[p,r,ri,ki])) - (if (ro,ko) in Producers_Intermeds[p,r] then Producers_Input[p,r,ro,ko] else Producers_Output[p,r,ro,ko]) >= 0;
+
+Producers_Functions_Leontief_Def {p in Producers, r in Producers_Regions[p], f in Producers_Functions_Regions[p,r], (ro,ko) in Producers_Functions_Leontief[p,r,f], (ri,ki) in Producers_Functions_Inputs[p,r,f]: Producers_Functions_Share[p,r,f,ro,ko,ri,ki] > 0}:
+ 0 <= m_pro_leo[p,r,f,ro,ko,ri,ki] complements Producers_Functions_Scale[p,r,f,ro,ko]*Producers_Functions_Scale_Factor[p,r,f,ro,ko]*Producers_Input[p,r,ri,ki] - (if (ro,ko) in Producers_Intermeds[p,r] then Producers_Input[p,r,ro,ko] else Producers_Output[p,r,ro,ko]) >= 0;
+
Property changes on: SwiftApps/SEE/trunk/subproblems/producer_tree.mod
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Name: svn:executable
+ *
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