/* INPUT PROJ1 ------- Deterministic Growth model from
                       K.L.Judd: Projection Methods for Solving
                       Aggregate Growth Models, J.Econ.Th. 58, 1992  */

library projec2;

/* Parameters of model */
alpha   = 1/3;
beta    = .95;
gama    = -.5;

/* calibration on steady state */
aa  = 1/(alpha*beta);

/* constants of model */
nst     = 1;                /* number of state variables */
ncon    = 1;                /* number of control variables */
nfc     = 6;                /* degree of approximation */
nnn     = nst~nfc~ncon;     /* row vector of basic constants of model */
x       = {.333, 1.667};    /* interval of state variable */
a0      = zeros(1,1);

/* procedure for residual function */
proc _FRES(k,a);
    local R,h1,h2,h3,h4,h5,h6,h7,h8;
    h1  = AA*k^alpha;                  /* f(k(t)) */
    h2  = __APROX(k,a);                /* h(k(t)) */
    h3  = h1-h2;                       /* k(t+1) */
    h4  = __APROX(h3,a);               /* h(k(t+1)) */
    h7  = __GPOW(h4,gama);             /* u'(h(k(t+1))) */
    h8  = alpha*AA*h3^(alpha-1);       /* f'(k(t+1)) */
    h5  = beta*h7*h8;                  /* beta*u'(h(k(t+1)))*f'(k(t+1) */
    h6  = __GPOW(h2,gama);             /* u'(h(k(t))) */
    R   = h6-h5;
    retp(R);
endp;

/* initial value of parameters */
a0      = zeros(nst+1,ncon);/* initial values of parameters
                               linear approximation */
a0[1]   = .5;
a0[2]   = .2;

PROJSET;
_prsave = 1;
_prinit = 0;
_prsvfn = "a_6";
{a,ret} = PROJEC(&_FRES,nnn,x,a0);