quocge.gms : A CGE Model with Quotas
Definition of sets for suffix ---------------------------------------
Reference:
- 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
<![CDATA[
$ Title A CGE Model with Quotas in Ch. 10.5 (QUOCGE,SEQ=280)
* Definition of sets for suffix ---------------------------------------
Set 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);
* ---------------------------------------------------------------------
* Loading data --------------------------------------------------------
Table SAM(u,v) social accounting matrix
BRD MLK CAP LAB IDT
BRD 21 8
MLK 17 9
CAP 20 30
LAB 15 25
IDT 5 4
TRF 1 2
HOH 50 40
GOV 9
INV
EXT 13 11
+ TRF HOH GOV INV EXT
BRD 20 19 16 8
MLK 30 14 15 4
CAP
LAB
IDT
TRF
HOH
GOV 3 23
INV 17 2 12
EXT
;
* Loading the initial values ------------------------------------------
Parameter 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 ---------------------------------------------------------
Parameter 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);
Parameter 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;
* ---------------------------------------------------------------------
* Defining model system -----------------------------------------------
Variable 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
;
Equation 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;
* ---------------------------------------------------------------------
* Defining and solving the model --------------------------------------
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 --------------------------------------------------
Parameter
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 ---------------------
Parameter 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;
* ---------------------------------------------------------------------
* end of model --------------------------------------------------------
* ---------------------------------------------------------------------
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