# artificial ramp

determine d

e1:jc+ma*d=j0+m1*d;

determine j1

e2:j1=jc+ma*d+m2*(1-d);

solve for j1 and d

s1:linsolve([e1,e2],[j1,d]);

ej1:s1[1];

find the steady state j0, labeled J0

e3:ev(ej1,j1=j0);

s2:linsolve(e3,j0);

J0:rhs(s2[1]);

introduce perturbations

e4:ev(ej1,j1=J0+dj1,j0=J0+dj0);

solve for dj1

e4:ratsimp(e4);

fr:solve(e4, dj1);

dj1:rhs(fr[1]);

ratio:dj1/dj0;

final result

ratio:ratsimp(ratio);