/* habit .prg. Simulates constantinides style habit */

output file = habit.out reset;
library pgraph;

bet = 0.98;
thet = 0.95;
Dc = 1.01;     /* steady state values */
eta = 2;
Dc1 = 1.01;    /* size of one day higher consumption growth */

Rf = 1/(bet*dc^(-eta));

" bet" bet;
"thet" thet;
"  dc" dc;
" eta" eta;
"";
"  Rf"  rf;

/* check that basic foc is satisfied */

test =                    (dc-thet)^(-eta)
       + bet*thet*dc^(-eta)*(dc-thet)^(-eta)
       - bet*rf*(dc-thet)^(-eta)*dc^(-eta)
       - bet^2*rf*thet*(dc-thet)^(-eta)*dc^(-2*eta);

if abs(test) >= 1E-12 ;
    "error in foc. " test " should be zero";
endif;

/* find sequence of interest rates to clear market */

Rfv = (dc-thet)^(-eta) - bet*thet*dc^(-eta)*(dc-thet)^(-eta);
Rfv = Rfv/(bet*(dc-thet)^(-eta)*dc^(-eta) -
           bet^(2)*thet*(dc-thet)^(-eta)*dc^(-eta)*dc^(-eta) );

/* now do dates around intervention */
/* at intervention

Rfn = (dc-thet)^(-eta) - bet*thet*dc^(-eta)*(dc-thet)^(-eta);
Rfn = Rfv/(bet*(dc-thet)^(-eta)*dc^(-eta) -
           bet^(2)*thet*(dc-thet)^(-eta)*dc^(-eta)*dc^(-eta) );




output off;