chakra.gms : Optimal Growth Model
Simple one sector nonlinear optimal growth model
References:
- Kendrick, D, and Taylor, L, Numerical methods and Nonlinear Optimizing models for Economic Planning. In Chenery, H B, Ed, Studies of Development Planning. Harvard University Press, 1971.
- Chakravarty, S, Optimum Savings with a Finite Planning Horizon. International Economic Review 3 (1962), 338-355.
Small Model of Type: NLP
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$Title Optimal Growth Model (CHAKRA,SEQ=43)
$Ontext
Simple one sector nonlinear optimal growth model
Kendrick, D, and Taylor, L, Numerical methods and Nonlinear Optimizing
models for Economic Planning. In Chenery, H B, Ed, Studies of
Development Planning. Harvard University Press, 1971.
Chakravarty, S, Optimum Savings with a Finite Planning Horizon.
International Economic Review 3 (1962), 338-355.
$Offtext
Sets t extended horizon / 0*20 /
tb(t) base period
tt(t) terminal period ;
tb(t) = yes$(ord(t)eq 1); tt(t) = yes$(ord(t) eq card(t));
Display tb,tt;
Scalars delt rate of depreciation / .05 /
beta exponent on capital / .75 /
a efficiency parameter
r labor force growth rate / .025 /
eta elasticity / .9 /
z technical progress / .01 /
rho welfare discount / .03 /
y0 initial income / 4.275 /
k0 initial capital / 15.0 /
Parameters dis(t) discount factor
alpha(t) production function parameter ;
a = y0/k0**beta;
dis(t) = (1+rho)**(1-ord(t))/(1-eta);
alpha(t) = a*(1+r*(1-beta)+z)**(ord(t)-1);
Display a, dis, alpha ;
Variables c(t) consumption
y(t) income
k(t) capital stock
j performance index
Equations kb(t) capital stock balance
yd(t) income definition
jd performance index definition ;
jd.. j =e= sum(t, dis(t-1)*c(t-1)**(1-eta));
yd(t).. y(t) =e= alpha(t)*k(t)**beta;
kb(t+1).. k(t+1) =e= y(t) - c(t) + (1-delt)*k(t);
y.l(t) = y0*(1.06)**(ord(t)-1); k.l(t) = (y.l(t)/alpha(t))**(1/beta);
c.l(t) = y.l(t) + (1-delt)*k.l(t) - k.l(t+1); display c.l, k.l, y.l;
k.lo(t) = 1; y.lo(t) = 1; c.lo(t) =1; y.fx(tb) = y.l(tb); y.fx(tt) = y.l(tt);
Model growth / all /;
Solve growth maximizing j using nlp;
Parameter report solution summary ;
report(t,"k") = k.l(t); report(t,"y") = y.l(t); report(t,"c") = c.l(t);
report(t,"s-rate") = (y.l(t)-c.l(t))/y.l(t);
Display report;
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