Hi,

I am practicing building IO model by using GAMS.

Could you please help me fill me the equation to let model calculate x1,x2,x3,m,w,depr and profit per sector.

As I know, I have to use the equation x=Ax+d.

But how to code above eqn in to program is a problem. I try to do it many times but still cannot do it.

Could you please advise?

Thank you in advance.

$Title Basic input-output model

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Author Ekko van Ierland

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SET

ALLSET “Set with all elements in order”

/AGRI “Agricultural sector”

INDU “Industrial sector”

SERV “Services sector”

CONS “Consumer - final demand”

INV “Investments by origin - final demand”

GOVT “Government - final demand”

EXPORT “Exports - final demand”

TOTOUT “Total production outputs”

IMPO “Imports”

DEPR “Depreciation - primary inputs”

WAGES “Total labour expenditures - primary inputs”

PROFIT “Total profits and capital payments - primary inputs”

TOTIN “Total inputs in production or total demand by sector”

/

J(ALLSET) “Production sectors”

/AGRI, INDU, SERV/

D(ALLSET) “Final demand sectors”

/CONS, INV, GOVT, EXPORT/

Prim(ALLSET) “Primary inputs”

/DEPR, WAGES, PROFIT/

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*The following says that you can use both names I and J to refer to set J.

ALIAS (I,J);

TABLE IODATA(ALLSET,ALLSET) Input-output table in billions of US dollars

AGRI INDU SERV CONS INV GOVT EXPORT TOTOUT

AGRI 10 30 40 100 0 40 180 400

INDU 20 60 50 300 200 30 340 1000

SERV 40 60 10 200 0 20 170 500

IMPO 60 120 20 400 100 100 0 800

DEPR 10 20 10 40

WAGES 200 600 300 1100

PROFIT 60 110 70 240

TOTIN 400 1000 500 1000 300 190 690

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out(i) = sum(j, IODATA(i,j)) + IODATA(i,“D”) ;

va0(j) = IO(“cap”,j) + IO(“lab”,j) ;

ene0(j) = sum(en, IO(en,j)) ;

vae0(j) = va0(j) + ene0(j) ;

ax(i,j) = IODATA(i,j)/out(j) ;

avae(j) = vae0(j)/out(j) ;

ax(i,j) = IODATA(i,j)/out(j) ;

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PARAMETERS

FD(I,D) Final demand (billion US dollars) by demand sector D for goods made by sector I

INCOME(D) Total income of final demand sector D (billion US dollars)

A(I,J) Input-output coefficients from sector I to sector J

PI_coef(Prim,J) Primary inputs coefficients of input Prim in sector J

Imp_coef(ALLSET) Import coefficients of production or final demand sector

RESULT(ALLSET,ALLSET) Resulting IO-table;

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FD(I,D) = IODATA(I,D);

INCOME(D) = IODATA(“TOTIN”,D);

A(I,J) = IODATA(I,J)/IODATA(J,“TOTOUT”);

PI_coef(Prim,J) = IODATA(Prim,J)/IODATA(J,“TOTOUT”);

Imp_coef(J) = IODATA(“IMPO”,J)/IODATA(J,“TOTOUT”);

Imp_coef(D) = IODATA(“IMPO”,D)/INCOME(D);

display FD, INCOME, A, PI_coef, Imp_coef;

VARIABLES

X(I,j) Production quantity of good I (billion US dollars)

IMPORT Import quantities (billion US dollars)

PI(Prim) Primary inputs (billion US dollars)

OBJ Objective (dummy);

EQUATIONS

QX(I,j) equation of goods I

Qimport import equation

QPI(prim) primary input equation

QOBJ objective value euqation

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QX(I,j)… X(I,j)=e= (A(i,j)*X(i,j))+d(j);

QOBJ… obj=e= sum((i,j),(X(i,j)));

- build the basic input-output equations using the given parameters and variables

MODEL IO /ALL/

SOLVE IO USING DNLP MAXIMIZING OBJ;