Solution Report

Size: px

Start display at page:

Download "Solution Report"

さいぞうつなかわ
7 years ago
Views:

1 CGE 3 GAMS * Date: 2018/07/24, Version GAMSIDE GAMS GAMSIDE GAMSIDE GAMS GAMS GAMS GAMS GAMS GAMS display $ alias solve * : Website: 1

2 Solution Report MCP Marginal GAMS ˆ 3 CGE GAMS (General Algebraic Modelling System) GAMS CGE GAMS ˆ GAMS ˆ GAMS User's Guide ž GAMS GAMS corporation ž HTML : ˆ Bruce McCarl ž GAMS ž McCarl ž gdxxrw.exe ž PDF : pdf ž HTML : 2

2. GAMSIDE 2 GAMSIDE GAMS Windows GAMS GAMS

3 2. GAMSIDE 2 GAMSIDE GAMS Windows GAMS GAMS GAMSIDE 1 GAMSIDE GAMS Windows GAMS 2.1 GAMS GAMS Windows 32bit 64bit 64bit Windows 64bit 2.2 GAMSIDE GAMSIDE GAMSIDE GAMSIDE GAMSIDE 1 GAMSIDE UNIX Mac GAMS Windows GAMS GAMSIDE Emacs Emacs GAMS mode for Emacs GAMSIDE 3

4 2. GAMSIDE C:YUserYstYDocumentsYgamsdirYprojdirYgamsproj.gpr GAMS C:YUserYstYDocumentsYgamsdirYprojdir GAMSIDE GAMS Project New Project g:ydropboxygams_practice practice New Project g:ydropboxygams_practice practice 4

5 2. GAMSIDE.gpr GAMSIDE GAMSIDE ide_howto.gms GAMSIDE File Open File Options MS 11pt MS 5

6 2. GAMSIDE File Options Colors Comment Italic Set associated text Bold 6

7 2. GAMSIDE 2.3 GAMSIDE GAMSIDE 1) GAMS 2) GAMSIDE GAMSIDE Bruce McCarl ˆ ˆ ide_howto.gms GAMS F9 Process Window GAMS 7

8 2. GAMSIDE *** Error 140 in G:DropboxYGAMS_practiceYide_howto.gms Unkown symbol Error Unknown symbol GAMS diplay i, j; j j unknown symbol j diplay i, j alias j F9 unknown symbol GAMS paramter paramter unknown symbol parameter paramter paramter 8

9 2. GAMSIDE GAMSIDE GAMS unrecognizable item ; gms gms gamma gamma(i) = 1 ; GAMS ; ; ; 1 Error at line 24 Compilation error Execution error division by zero 24 0 gms gms 24 GAMSIDE 18:

10 2. GAMSIDE 24 gamma(i) = gamma(i) / sigma; sigma sigma 0 division by zero sigma 0 10 Status: Normal completion GAMS ide_howto.gms ide_howto.lst LST 10

11 Display sigma LST sigma LST GAMSIDE GAMS ˆ ˆ GMS ˆ 3 GAMS 3.1 GAMS GAMS ˆ GAMS gms ž ˆ 11

12 ž GAMS ž sample.gms sample.lst lst LST GAMS ˆ declaration ˆ ž price Price PRICE GAMS ž GAMS ˆ ; ž GAMS ž ˆ ž * * ž $ontext $offtext GAMS ˆ ž j = {1,, n} f = {labor, capital, land} j f GAMS set ˆ ž GAMS parameter ž 2 CES ž ˆ 2 12

13 ž GAMS variable ž ˆ ž GAMS equation ˆ ž ž GAMS variable 4 x ˆ level value ž x x ž x.l x display x.l; x 10 x.l = 10; ˆ lower value upper value ž lower bound upper bound ž x.lo x.up x 0 x.lo = 0 ž GAM -inf GAMS +inf ˆ Marginal marginal value ž marginal ž 13

14 GAMS LP NLP MCP MIP 1: GAMS linear programming non-linear programming Mixed complementarity problem GAMS GAMS solver Solver GAMS 15 1 GAMS MCP MCP mixed complementarity problem MCP MCP MCP non-linear programming [ ] σ σ 1 max u = γ i (d i ) σ 1 σ {d 1,,d n} s.t. i i p i d i = m u d i i p i i m γ i σ 1 CGE GAMS CGE 3 L = [ i γ i (d i ) σ 1 σ ] σ [ σ 1 λ i p i d i m 3 CGE CGE ] 14

15 1 L = σ 1 γ j (d j ) σ 1 σ γ i (d i ) 1 σ λpi = 0 {d i } i=1,,n (1) d i j [ ] L λ = p i d i m = 0 {λ} (2) i {d i } n (1) 1 (2) n + 1 GAMS 3.3 GAMS utility_max.gms GAMS GAM- SIDE GAMS 3.4 $title $ontext Time-stamp: < :48:30 st> First-written: <2013/10/11> $offtext $title LST $ontext $offtext * * set i Index of goods / agr Agricultural goods man Manufacturing goods ser Services /; 15

16 set i set set set i Index of goods / agr Agricultural goods man Manufacturing goods ser Services /; / i agr man ser Index of goods i Agricultural goods set i / agr, man, ser /; set GAMS User Manual display display i; i display display GAMSIDE i agr man ser 16

17 3.4.3 $ $title $ set Dollar Control Option $ dollar control option GAMS compilation time execution time GAMS $ alias * i j alias(i,j); display j; alias i j alias static set static set dynamic set $ontext 17

18 $offtext parameter p(i) m ; Goods price Income p(i) m 2 parameter parameter parameter p(i) m Goods price Income ; p(i) m Goods price Income p(i) m p i i agr man ser p("agr") p("man") p("ser") 3 p p("agr")=1 p(i) parameter p(i), m; p("agr") = 1; p("man") = 2; p("ser") = 3; m = 100; display p, m; p m display p i i p Parameter p(i) Goods price / agr 1 man 2 ser 3 / m Income / 100 / 18

19 ; / $ontext $offtext parameter gamma(i) Weight parameter sigma Elasticity of substitution ; * gamma gamma(i) = 1; gamma(i) = gamma(i)/sum(j, gamma(j)); display gamma; sigma = 0.5; display sigma; gamma sigma gamma(i) = 1; gamma(i) = gamma(i)/sum(j, gamma(j)); gamma(i) 1/3 2 GAMS = $ontext variables $offtext variables d(i) Demand lambda Lagrange multiplier ; variables variable ˆ variables parameter ˆ variables d(i) lambda 19

20 3.4.7 * * $ontext equations e_ + $offtext equations e_d(i) 1st order condition for d(i) e_lambda 1st order condition for lambda ; equation equations equations variables ˆ (1) e_d(i) ˆ lambda (2) e_lambda * * e_d(i).. (sum(j, gamma(j)*(d(j))**((sigma-1)/sigma)))**(1/(sigma-1)) * gamma(i) * (d(i))**(-1/sigma) - lambda * p(i) =e= 0; e_lambda.. - (sum(i, p(i)*d(i)) - m) =e= 0;.. ; 2 ; = =e= =g= =l= 4 (1) (2) GAMS = 20

21 3.4.9 * * $ontext. e_d.d e_d d $offtext model utility_max Utility maximization / e_d.d, e_lambda.lambda /; model model / /; MCP. / e_d.d, e_lambda.lambda / e_d e_lambda 2 2 e_d d e_lambda lambda 4 1) 2) MCP NLP MCP 4 21

22 * * d.lo(i) = 0; lambda.lo = 0; * * d.l(i) = 10; lambda.l = 10; lo d lambda d lambda solve * * option mcp = path; solve utility_max using mcp; solve MCP NLP LP solve MCP solve utility_max using mcp; solve using mcp; option mcp = path; Solver MCP PATH 22

23 Solver Solver Solver Parameter results ; results(i,"price") = p(i); results("/","income") = m; results(i,"demand") = d.l(i); results("/","lambda") = lambda.l; results(i,"exp") = p(i)*d.l(i); results("sum","exp") = sum(i, results(i,"exp")); results("/","utility") = (sum(i, gamma(i)*(d.l(i))**((sigma-1)/sigma)))**(sigma/(sigma-1)); display results; results d(i) lambda results.l d.l(i) lambda.l MCP Solution Report REPORT SUMMARY 5 CGE 23

3.5.1 Solution Report Solution Report SOLVE SUMMARY ˆ MODEL ˆ TYPE MCP ˆ SOLVER solver MCP solver PATH SOVER STATUS MODEL STATUS STATUS 1 S O L V E S U M M A R Y MODEL

24 3.5.1 Solution Report Solution Report SOLVE SUMMARY ˆ MODEL ˆ TYPE MCP ˆ SOLVER solver MCP solver PATH SOVER STATUS MODEL STATUS STATUS 1 S O L V E S U M M A R Y MODEL utility_max TYPE MCP SOLVER PATH FROM LINE 115 **** SOLVER STATUS 1 Normal Completion **** MODEL STATUS 1 Optimal SOVER STATUS MODEL STATUS 1 S O L V E S U M M A R Y 24

25 MODEL utility_max TYPE MCP SOLVER PATH FROM LINE 115 **** SOLVER STATUS 2 Iteration Interrupt **** MODEL STATUS 6 Intermediate Infeasible utility_max.gms SolVAR VAR d Demand LOWER LEVEL UPPER MARGINAL agr INF E-7 man INF E-7 ser INF E-8 LOWER LEVEL UPPER MARGINAL VAR lambda INF. lambda Lagrange multiplier 3.1 GAMS lower value upper value level value marginal marginal value 4 LST LOWER LEVEL UPPER MARGINAL d("agr") 0 0 +INF marginal E-7=2.4569/ MCP Marginal Marginal MCP marginal d(i) e_d(i) e_d(i) e_d(i).. (sum(j, gamma(j)*(d(j))**((sigma-1)/sigma)))**(1/(sigma-1)) 25

26 4. GAMS * gamma(i) * (d(i))**(-1/sigma) - lambda * p(i) =e= 0; d(i) marginal 10 (sum(j, gamma(j)*(d(j))**((sigma-1)/sigma)))**(1/(sigma-1)) * gamma(i) * (d(i))**(-1/sigma) - lambda * p(i) = 10 d("agr") marginal e_d("agr") e_d("agr") e_d("agr") d("agr") marginal marginal 4 GAMS 5 1 min {h 1,,h n} e = i p i h i s.t. [ i γ i (h i ) σ 1 σ ] σ σ 1 = u GAMS γ i σ 3.3 u ˆ : ˆ : 26

f(x) x S (optimal solution) f(x ) (optimal value) f(x) (1) 3 GLPK glpsol -m -d -m glpsol -h -m -d -o -y --simplex ( ) --interior --min --max --check -

f(x) x S (optimal solution) f(x ) (optimal value) f(x) (1) 3 GLPK glpsol -m -d -m glpsol -h -m -d -o -y --simplex ( ) --interior --min --max --check - GLPK by GLPK http://mukun mmg.at.infoseek.co.jp/mmg/glpk/ 17 7 5 : update 1 GLPK GNU Linear Programming Kit GNU LP/MIP ILOG AMPL(A Mathematical Programming Language) 1. 2. 3. 2 (optimization problem) X