pak.gms : Optimal Patterns of Growth and Aid
This model explores the use of external resources to accelerate
development by supplying additional resources to increase imports
and investment. Terminal conditions cannot reproduced from the text.
All units in billions of 1965 rupees.
Reference:
- Chenery, H B, and Macewan, A, Chapter 9: Optimal Patterns of Growth and Aid. In Chenery, H B, Ed, Structural Change and Development Policy. Oxford University Press, New York and Oxford, 1979.
Large Model of Type: LP
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$Title Optimal Patterns of Growth and Aid (PAK,SEQ=34)
$Stitle Basic Data
$Ontext
This model explores the use of external resources to accelerate
development by supplying additional resources to increase imports
and investment. Terminal conditions cannot reproduced from the text.
All units in billions of 1965 rupees.
Chenery, H B, and Macewan, A, Chapter 9: Optimal Patterns of Growth
and Aid. In Chenery, H B, Ed, Structural Change and Development
Policy. Oxford University Press, New York and Oxford, 1979.
$Offtext
Sets te extended planning period / 1962*1985 /
t(te) planning period / 1963*1985 /
j sectors / non-traded, traded /
Scalars fbb foreign aid 1962 / 1.183 /
sb saving 1962 / 3.381 /
tib total investment 1962 / 4.564 /
mb imports 1962 / 3.743 /
eb exports 1962 / 2.559 /
gnpb gnp 1962 / 37.380 /
cb consumption 1962 / 33.999 /
rho discount rate / .08 /
r post plan discount / .10 /
g post plan growth / .073 /
gama cost of foreign capital/ 2.0 /
d post plan weight / 1.0 /
alpha marginal savings rate / .24 /
mgnp marginal import rate on gnp / .10 /
mi marginal import rate on investment / .35 /
p population growth / .025 /
beta maximum growth of investment / .13 /
ee export growth / .049 /
q aid ration / .5 /
num years without aid / 4 /
Parameter k(j) capital output ratio / non-traded = 3.0, traded = 4.5 /
delt(t) discount factor
dis discounting for post horizon cons
vb(j) base year outputs
e(t) exports ;
e(t) = eb*(1+ee)**ord(t); display e;
delt(t)= (1+rho)**(-ord(t)); display delt;
dis = (1+r)**(-card(t))*(1-alpha)*(1+g)/(r-g); display dis;
vb("non-traded") = gnpb;
$Stitle model definition
Variables gnp(t) gross national product
v(t,j) net output
ti(te) total investment
i(te,j) investment
ks(te,j) capital stock
s(t) gross savings
f(t) net capital inflow
fb total discounted aid
m(t) traditional imports
c(te) consumption
w welfare
Positive Variables v, i, s;
Equations gnpd(t) gnp definition
invd(t) investment definition
invt(te) investment totals
tgap(t) trade gap
incd(t) national income definition
capb(t,j) capacity balance
kbal(te,j) capital stock balance
savl(t) maximum savings
impl(t) minimum imports
invu(te) upper bound on investment
invl(te) lower bound on investment
conl(te) lower bound on consumption
fup (t) upper bound on f(t)
taid total aid definition
wdef welfare definition ;
gnpd(t).. gnp(t) =e= sum(j, v(t,j));
invd(t).. ti(t) =e= s(t) + f(t);
invt(te).. ti(te) =e= sum(j, i(te,j));
tgap(t).. f(t) =e= m(t) - e(t) - v(t,"traded");
incd(t).. gnp(t) =e= c(t) + ti(t) - f(t);
capb(t,j).. v(t,j) =l= vb(j) + 1/k(j)* ks(t,j);
kbal(te+1,j).. ks(te+1,j) =e= ks(te,j) + i(te,j);
savl(t).. s(t) =l= sb + alpha*(gnp(t) - gnpb);
impl(t).. m(t) =g= mb + mgnp*(gnp(t) - gnpb) + mi*(ti(t) - tib);
invu(te+1).. ti(te+1) =l= (1+beta)*ti(te);
invl(te+1).. ti(te+1) =g= ti(te);
conl(te+1).. c(te+1) =g= (1+p)*c(te);
fup(t).. f(t) =l= q*gnp(t);
taid.. fb =e= sum(t, delt(t)*f(t));
wdef.. w =e= sum(t, delt(t)*c(t)) - gama*fb + d*dis*gnp("1985");
ks.fx("1962",j) = 0;
i.fx("1962","non-traded") = tib; i.fx("1962","traded") = 0;
c.fx("1962") = cb;
f.up(t) = inf$(card(t)-ord(t) ge num);
Model pak1 /all/;
Solve pak1 maximizing w using lp;
Parameter rep summary report (billions of rupees) ;
rep(t,"f") = f.l(t);
rep(t,"gnp") = gnp.l(t);
rep(t,"ti") = ti.l(t);
rep(t,"s") = s.l(t);
rep(t,"c") = c.l(t);
Display rep;
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