quocge.gms : A CGE Model with Quotas


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  • 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

Category : GAMS Model library

Main file : quocge.gms

$title A CGE Model with Quotas in Ch. 10.5 (QUOCGE,SEQ=280)

No description.

Hosoe, N, Gasawa, K, and Hashimoto, H
Handbook of Computible General Equilibrium Modeling
University of Tokyo Press, Tokyo, Japan, 2004

Keywords: nonlinear programming, general equilibrium model, social accounting
          matrix, import quotas

   u    'SAM entry' / BRD, MLK, CAP, LAB, IDT, TRF, HOH, GOV, INV, EXT /
   i(u) 'goods'     / BRD, MLK                                         /
   h(u) 'factor'    /           CAP, LAB                               /;

Alias (u,v), (i,j), (h,k);

Table SAM(u,v) 'social accounting matrix'
         BRD   MLK   CAP   LAB   IDT   TRF   HOH   GOV   INV   EXT
   BRD    21     8                            20    19    16     8
   MLK    17     9                            30    14    15     4
   CAP    20    30
   LAB    15    25
   IDT     5     4
   TRF     1     2
   HOH                50    40
   GOV                             9     3    23
   INV                                        17     2          12
   EXT    13    11                                                ;

* Loading the initial values
   Y0(j)     'composite factor'
   F0(h,j)   'the h-th factor input by the j-th firm'
   X0(i,j)   'intermediate input'
   Z0(j)     'output of the j-th good'
   Xp0(i)    'household consumption of the i-th good'
   Xg0(i)    'government consumption'
   Xv0(i)    'investment demand'
   E0(i)     'exports'
   M0(i)     'imports'
   Q0(i)     "Armington's composite good"
   D0(i)     'domestic good'
   Sp0       'private saving'
   Sg0       'government saving'
   Td0       'direct tax'
   Tz0(j)    'production tax'
   Tm0(j)    'import tariff'
   FF(h)     'factor endowment of the h-th factor'
   Sf        'foreign saving in US dollars'
   pWe(i)    'export price in US dollars'
   pWm(i)    'import price in US dollars'
   tauz(i)   'production tax rate'
   taum(i)   'import tariff rate'
   Mquota(i) 'import quotas';

Td0       =  SAM("GOV","HOH");
Tz0(j)    =  SAM("IDT",j);
Tm0(j)    =  SAM("TRF",J);
F0(h,j)   =  SAM(h,j);
Y0(j)     =  sum(h, F0(h,j));
X0(i,j)   =  SAM(i,j);
Z0(j)     =  Y0(j) +sum(i,X0(i,j));
M0(i)     =  SAM("EXT",i);
tauz(j)   =  Tz0(j)/Z0(j);
taum(j)   =  Tm0(j)/M0(j);
Mquota(i) =  M0(i)*100;
Xp0(i)    =  SAM(i,"HOH");
FF(h)     =  SAM("HOH",h);
Xg0(i)    =  SAM(i,"GOV");
Xv0(i)    =  SAM(i,"INV");
E0(i)     =  SAM(i,"EXT");
Q0(i)     =  Xp0(i)+Xg0(i)+Xv0(i)+sum(j, X0(i,j));
D0(i)     = (1+tauz(i))*Z0(i)-E0(i);
Sp0       =  SAM("INV","HOH");
Sg0       =  SAM("INV","GOV");
Sf        =  SAM("INV","EXT");
pWe(i)    =  1;
pWm(i)    =  1;

display Y0, F0, X0,   Z0, Xp0, Xg0, Xv0, E0, M0, Q0, D0, Sp0, Sg0, Td0, Tz0, Tm0
        FF, Sf, tauz, taum;

* Calibration
   sigma(i) 'elasticity of substitution'
   psi(i)   'elasticity of transformation'
   eta(i)   'substitution elasticity parameter'
   phi(i)   'transformation elasticity parameter';

sigma(i) =  2;
psi(i)   =  2;
eta(i)   = (sigma(i)-1)/sigma(i);
phi(i)   = (psi(i)+1)/psi(i);

   alpha(i)  'share parameter in utility func.'
   beta(h,j) 'share parameter in production func.'
   b(j)      'scale parameter in production func.'
   ax(i,j)   'intermediate input requirement coeff.'
   ay(j)     'composite fact. input req. coeff.'
   mu(i)     'government consumption share'
   lambda(i) 'investment demand share'
   deltam(i) 'share parameter in Armington func.'
   deltad(i) 'share parameter in Armington func.'
   gamma(i)  'scale parameter in Armington func.'
   xid(i)    'share parameter in transformation func.'
   xie(i)    'share parameter in transformation func.'
   theta(i)  'scale parameter in transformation func.'
   ssp       'average propensity for private saving'
   ssg       'average propensity for government saving'
   taud      'direct tax rate';

alpha(i)  =  Xp0(i)/sum(j, Xp0(j));
beta(h,j) =  F0(h,j)/sum(k, F0(k,j));
b(j)      =  Y0(j)/prod(h, F0(h,j)**beta(h,j));
ax(i,j)   =  X0(i,j)/Z0(j);
ay(j)     =  Y0(j)/Z0(j);
mu(i)     =  Xg0(i)/sum(j, Xg0(j));
lambda(i) =  Xv0(i)/(Sp0+Sg0+Sf);
deltam(i) = (1+taum(i))*M0(i)**(1-eta(i))/((1+taum(i))*M0(i)**(1-eta(i)) + D0(i)**(1-eta(i)));
deltad(i) =  D0(i)**(1-eta(i))/((1+taum(i))*M0(i)**(1-eta(i)) +D0(i)**(1-eta(i)));
gamma(i)  =  Q0(i)/(deltam(i)*M0(i)**eta(i)+deltad(i)*D0(i)**eta(i))**(1/eta(i));
xie(i)    =  E0(i)**(1-phi(i))/(E0(i)**(1-phi(i))+D0(i)**(1-phi(i)));
xid(i)    =  D0(i)**(1-phi(i))/(E0(i)**(1-phi(i))+D0(i)**(1-phi(i)));
theta(i)  =  Z0(i)/(xie(i)*E0(i)**phi(i)+xid(i)*D0(i)**phi(i))**(1/phi(i));
ssp       =  Sp0/sum(h, FF(h));
ssg       =  Sg0/(Td0+sum(j, Tz0(j))+sum(j, Tm0(j)));
taud      =  Td0/sum(h, FF(h));

display alpha, beta,  b,   ax,  ay, mu, lambda, deltam, deltad, gamma, xie
        xid,   theta, ssp, ssg, taud;

   Y(j)    'composite factor'
   F(h,j)  'the h-th factor input by the j-th firm'
   X(i,j)  'intermediate input'
   Z(j)    'output of the j-th good'
   Xp(i)   'household consumption of the i-th good'
   Xg(i)   'government consumption'
   Xv(i)   'investment demand'
   E(i)    'exports'
   M(i)    'imports'
   Q(i)    "Armington's composite good"
   D(i)    'domestic good'
   pf(h)   'the h-th factor price'
   py(j)   'composite factor price'
   pz(j)   'supply price of the i-th good'
   pq(i)   "Armington's composite good price"
   pe(i)   'export price in local currency'
   pm(i)   'import price in local currency'
   pd(i)   'the i-th domestic good price'
   epsilon 'exchange rate'
   Sp      'private saving'
   Sg      'government saving'
   Td      'direct tax'
   Tz(j)   'production tax'
   Tm(i)   'import tariff'
   RT(i)   'rent accruing from import quotas'
   UU      'utility [fictitious]';

Positive Variable
   chi(i)  'marginal quasi-rent';

   eqpy(j)   'composite factor aggregation func.'
   eqX(i,j)  'intermediate demand function'
   eqY(j)    'composite factor demand function'
   eqF(h,j)  'factor demand function'
   eqpzs(j)  'unit cost function'
   eqTd      'direct tax revenue function'
   eqTz(j)   'production tax revenue function'
   eqTm(i)   'import tariff revenue function'
   eqXg(i)   'government demand function'
   eqXv(i)   'investment demand function'
   eqSp      'private saving function'
   eqSg      'government saving function'
   eqXp(i)   'household demand function'
   eqRT(i)   'quasi-rent function'
   eqpe(i)   'world export price equation'
   eqpm(i)   'world import price equation'
   eqepsilon 'balance of payments'
   eqpqs(i)  'Armington function'
   eqM(i)    'import demand function'
   eqD(i)    'domestic good demand function'
   eqchi1(i) 'import quota complementarity condition'
   eqchi2(i) 'import quota complementarity condition'
   eqpzd(i)  'transformation function'
   eqDs(i)   'domestic good supply function'
   eqE(i)    'export supply function'
   eqpqd(i)  'market clearing cond. for comp. good'
   eqpf(h)   'factor market clearing condition'
   obj       'utility function [fictitious]';

* domestic production
eqpy(j)..   Y(j)   =e= b(j)*prod(h, F(h,j)**beta(h,j));

eqX(i,j)..  X(i,j) =e= ax(i,j)*Z(j);

eqY(j)..    Y(j)   =e= ay(j)*Z(j);

eqF(h,j)..  F(h,j) =e= beta(h,j)*py(j)*Y(j)/pf(h);

eqpzs(j)..  pz(j)  =e= ay(j)*py(j) + sum(i, ax(i,j)*pq(i));

* government behavior
eqTd..      Td     =e= taud*(sum(h, pf(h)*FF(h)) + sum(j, RT(j)));

eqTz(j)..   Tz(j)  =e= tauz(j)*pz(j)*Z(j);

eqTm(i)..   Tm(i)  =e= taum(i)*pm(i)*M(i);

eqXg(i)..   Xg(i)  =e= mu(i)*(Td + sum(j, Tz(j)) + sum(j, Tm(j)) - Sg)/pq(i);

* investment behavior
eqXv(i)..   Xv(i)  =e= lambda(i)*(Sp + Sg + epsilon*Sf)/pq(i);

* savings
eqSp..      Sp     =e= ssp*(sum(h, pf(h)*FF(h)) + sum(j, RT(j)));

eqSg..      Sg     =e= ssg*(Td + sum(j, Tz(j)) + sum(j, Tm(j)));

* household consumption
eqXp(i)..   Xp(i)  =e= alpha(i)*(sum(h, pf(h)*FF(h)) + sum(j, RT(j)) - Sp - Td)/pq(i);

eqRT(i)..   RT(i)  =e= chi(i)*pm(i)*M(i);

* international trade
eqpe(i)..   pe(i)  =e= epsilon*pWe(i);

eqpm(i)..   pm(i)  =e= epsilon*pWm(i);

eqepsilon.. sum(i, pWe(i)*E(i)) + Sf =e= sum(i, pWm(i)*M(i));

* Armington function
eqpqs(i)..  Q(i)   =e=  gamma(i)*(deltam(i)*M(i)**eta(i) + deltad(i)*D(i)**eta(i))**(1/eta(i));

eqM(i)..    M(i)   =e= (gamma(i)**eta(i)*deltam(i)*pq(i)/((1 + chi(i)+taum(i))*pm(i)))**(1/(1 - eta(i)))*Q(i);

eqD(i)..    D(i)   =e= (gamma(i)**eta(i)*deltad(i)*pq(i)/pd(i))**(1/(1 - eta(i)))*Q(i);

eqchi1(i).. chi(i)*(Mquota(i) - M(i)) =e= 0;

eqchi2(i).. Mquota(i) -M(i) =g= 0;

* transformation function
eqpzd(i)..  Z(i)   =e= theta(i)*(xie(i)*E(i)**phi(i) + xid(i)*D(i)**phi(i))**(1/phi(i));

eqE(i)..    E(i)   =e= (theta(i)**phi(i)*xie(i)*(1 + tauz(i))*pz(i)/pe(i))**(1/(1 - phi(i)))*Z(i);

eqDs(i)..   D(i)   =e= (theta(i)**phi(i)*xid(i)*(1 + tauz(i))*pz(i)/pd(i))**(1/(1 - phi(i)))*Z(i);

* market clearing condition
eqpqd(i)..  Q(i)   =e= Xp(i) + Xg(i) + Xv(i) + sum(j, X(i,j));

eqpf(h)..   FF(h)  =e= sum(j, F(h,j));

* fictitious objective function
obj..       UU     =e= prod(i, Xp(i)**alpha(i));

* Initializing variables
Y.l(j)    = Y0(j);
F.l(h,j)  = F0(h,j);
X.l(i,j)  = X0(i,j);
Z.l(j)    = Z0(j);
Xp.l(i)   = Xp0(i);
Xg.l(i)   = Xg0(i);
Xv.l(i)   = Xv0(i);
E.l(i)    = E0(i);
M.l(i)    = M0(i);
Q.l(i)    = Q0(i);
D.l(i)    = D0(i);
pf.l(h)   = 1;
py.l(j)   = 1;
pz.l(j)   = 1;
pq.l(i)   = 1;
pe.l(i)   = 1;
pm.l(i)   = 1;
pd.l(i)   = 1;
epsilon.l = 1;
Sp.l      = Sp0;
Sg.l      = Sg0;
Td.l      = Td0;
Tz.l(j)   = Tz0(j);
Tm.l(i)   = Tm0(i);
RT.l(i)   = 0;
chi.l(i)  = 0;

* Setting lower bounds to avoid division by zero
Y.lo(j)    = 0.00001;
F.lo(h,j)  = 0.00001;
X.lo(i,j)  = 0.00001;
Z.lo(j)    = 0.00001;
Xp.lo(i)   = 0.00001;
Xg.lo(i)   = 0.00001;
Xv.lo(i)   = 0.00001;
E.lo(i)    = 0.00001;
M.lo(i)    = 0.00001;
Q.lo(i)    = 0.00001;
D.lo(i)    = 0.00001;
pf.lo(h)   = 0.00001;
py.lo(j)   = 0.00001;
pz.lo(j)   = 0.00001;
pq.lo(i)   = 0.00001;
pe.lo(i)   = 0.00001;
pm.lo(i)   = 0.00001;
pd.lo(i)   = 0.00001;
epsilon.lo = 0.00001;
Sp.lo      = 0.00001;
Sg.lo      = 0.00001;
Td.lo      = 0.00001;
Tz.lo(j)   = 0.0000;
Tm.lo(i)   = 0.0000;

* numeraire
pf.fx("LAB") = 1;

Model quocge / all /;

solve quocge maximizing UU using nlp;

* Simulation Runs: Imposition of Quotas on Bread Imports
Mquota("BRD") = M0("BRD")*0.9;

option bRatio = 1;

solve quocge maximizing UU using nlp;

* Display of changes
   dY(j),  dF(h,j), dX(i,j), dZ(j),    dXp(i),     dXg(i), dXv(i)
   dE(i),  dM(i),   dQ(i),   dD(i),    dpf(h),     dpy(j), dpz(i), dpq(i)
   dpe(i), dpm(i),  dpd(i),  depsilon, dTd,dTz(i), dTm(i), dSp,    dSg;

dY(j)    = (Y.l(j)  /Y0(j)  -1)*100;
dF(h,j)  = (F.l(h,j)/F0(h,j)-1)*100;
dX(i,j)  = (X.l(i,j)/X0(i,j)-1)*100;
dZ(j)    = (Z.l(j)  /Z0(j)  -1)*100;
dXp(i)   = (Xp.l(i) /Xp0(i) -1)*100;
dXg(i)   = (Xg.l(i) /Xg0(i) -1)*100;
dXv(i)   = (Xv.l(i) /Xv0(i) -1)*100;
dE(i)    = (E.l(i)  /E0(i)  -1)*100;
dM(i)    = (M.l(i)  /M0(i)  -1)*100;
dQ(i)    = (Q.l(i)  /Q0(i)  -1)*100;
dD(i)    = (D.l(i)  /D0(i)  -1)*100;
dpf(h)   = (pf.l(h) /1 -1)*100;
dpy(j)   = (py.l(j) /1 -1)*100;
dpz(j)   = (pz.l(j) /1 -1)*100;
dpq(i)   = (pq.l(i) /1 -1)*100;
dpe(i)   = (pe.l(i) /1 -1)*100;
dpm(i)   = (pm.l(i) /1 -1)*100;
dpd(i)   = (pd.l(i) /1 -1)*100;
depsilon = (epsilon.l/1 -1)*100;
dTd      = (Td.l    /Td0    -1)*100;
dTz(j)   = (Tz.l(j) /Tz0(j) -1)*100;
dTm(i)   = (Tm.l(i) /Tm0(i) -1)*100;
dSp      = (Sp.l    /Sp0    -1)*100;
dSg      = (Sg.l    /Sg0    -1)*100;

display dY,  dF, dX,  dZ,  dXp,      dXg, dXv, dE,  dM,  dQ, dD, dpf, dpy, dpz
        dpq, dpe,dpm, dpd, depsilon, dTd, dTz, dTm, dSp, dSg;

* Welfare measure: Hicksian equivalent variations
   UU0 'utility level in the base run eq.'
   ep0 'expenditure func. in the base run eq.'
   ep1 'expenditure func. in the C-f eq.'
   EV  'Hicksian equivalent variations';

UU0 = prod(i, Xp0(i)**alpha(i));
ep0 = UU0 /prod(i, (alpha(i)/1)**alpha(i));
ep1 = UU.l/prod(i, (alpha(i)/1)**alpha(i));
EV  = ep1 - ep0;

display EV;