function y = findvh(vh,la,yf,A,B,THETA,BETTA,g)
%y = findvh(vh,la,yf,A,B,THETA,BETTA,g) evaluates the first-order conditions of the Ramsey problem w.r.t. v and c in the model described in 
%Schmitt-Grohe, Stephanie and Martin Uribe, 
%``Foreign Demand for Domestic Currency and The Optimal Rate of Inflation'' %Journal of Money, Credit and Banking, forthcoming. 
%
%(c) Stephanie Schmitt-Grohe and Martin Uribe
% Date: January 5,  2011


vbar = sqrt(B/A); %satiation velocity

Vmax = sqrt((1+B)/A);

v = vbar + (Vmax-vbar) * abs(vh(1)) / (1+abs(vh(1))); 

h = abs(vh(2)) / (1+abs(vh(2)));

vf = v;
S=A*v+B/v-2*sqrt(A*B);
Sv = A-B/v^2;

%Solving the feasibility constraint in the steady-state yields
c = (h - g + yf / vf * (1-(1-v^2*Sv) / BETTA)) / (1+S);


%The following expressions were produced with primal_form.m


%Derivative of the Lagrangean w.r.t v

Lvs = THETA*(-yf/v^2-2*yf/v*(1-v^2*(A-B/v^2))/(1+A*v+B/v-2*(A*B)^(1/2)+v*(A-B/v^2))*A/BETTA-(A-B/v^2)*c)/(1+yf/v-yf/v*(1-v^2*(A-B/v^2))/BETTA-(1+A*v+B/v-2*(A*B)^(1/2))*c-g)+BETTA*THETA*(yf/v^2*(1-v^2*(A-B/v^2))/BETTA-yf/v*(-2*v*(A-B/v^2)-2*B/v)/BETTA+2*yf/v*(1-v^2*(A-B/v^2))/(1+A*v+B/v-2*(A*B)^(1/2)+v*(A-B/v^2))*A/BETTA)/(1+yf/v-yf/v*(1-v^2*(A-B/v^2))/BETTA-(1+A*v+B/v-2*(A*B)^(1/2))*c-g)+la*(THETA/(1+yf/v-yf/v*(1-v^2*(A-B/v^2))/BETTA-(1+A*v+B/v-2*(A*B)^(1/2))*c-g)^2*(-yf/v+yf/v*(1-v^2*(A-B/v^2))/BETTA+(1+A*v+B/v-2*(A*B)^(1/2))*c+g)*(-yf/v^2-2*yf/v*(1-v^2*(A-B/v^2))/(1+A*v+B/v-2*(A*B)^(1/2)+v*(A-B/v^2))*A/BETTA-(A-B/v^2)*c)-THETA/(1+yf/v-yf/v*(1-v^2*(A-B/v^2))/BETTA-(1+A*v+B/v-2*(A*B)^(1/2))*c-g)*(yf/v^2+2*yf/v*(1-v^2*(A-B/v^2))/(1+A*v+B/v-2*(A*B)^(1/2)+v*(A-B/v^2))*A/BETTA+(A-B/v^2)*c))+la*BETTA*(THETA/(1+yf/v-yf/v*(1-v^2*(A-B/v^2))/BETTA-(1+A*v+B/v-2*(A*B)^(1/2))*c-g)^2*(-yf/v+yf/v*(1-v^2*(A-B/v^2))/BETTA+(1+A*v+B/v-2*(A*B)^(1/2))*c+g)*(yf/v^2*(1-v^2*(A-B/v^2))/BETTA-yf/v*(-2*v*(A-B/v^2)-2*B/v)/BETTA+2*yf/v*(1-v^2*(A-B/v^2))/(1+A*v+B/v-2*(A*B)^(1/2)+v*(A-B/v^2))*A/BETTA)-THETA/(1+yf/v-yf/v*(1-v^2*(A-B/v^2))/BETTA-(1+A*v+B/v-2*(A*B)^(1/2))*c-g)*(-yf/v^2*(1-v^2*(A-B/v^2))/BETTA+yf/v*(-2*v*(A-B/v^2)-2*B/v)/BETTA-2*yf/v*(1-v^2*(A-B/v^2))/(1+A*v+B/v-2*(A*B)^(1/2)+v*(A-B/v^2))*A/BETTA));

y(1) =Lvs*(v-(B/A)^(1/2)) + Lvs*(Lvs>0);


%derivative of the Lagrangean w.r.t. c

Lcs = 1/c+THETA*(-yf/v*(1-v^2*(A-B/v^2))/c/BETTA-1-A*v-B/v+2*(A*B)^(1/2))/(1+yf/v-yf/v*(1-v^2*(A-B/v^2))/BETTA-(1+A*v+B/v-2*(A*B)^(1/2))*c-g)+THETA*yf/v*(1-v^2*(A-B/v^2))/c/(1+yf/v-yf/v*(1-v^2*(A-B/v^2))/BETTA-(1+A*v+B/v-2*(A*B)^(1/2))*c-g)+la*(THETA/(1+yf/v-yf/v*(1-v^2*(A-B/v^2))/BETTA-(1+A*v+B/v-2*(A*B)^(1/2))*c-g)^2*(-yf/v+yf/v*(1-v^2*(A-B/v^2))/BETTA+(1+A*v+B/v-2*(A*B)^(1/2))*c+g)*(-yf/v*(1-v^2*(A-B/v^2))/c/BETTA-1-A*v-B/v+2*(A*B)^(1/2))-THETA/(1+yf/v-yf/v*(1-v^2*(A-B/v^2))/BETTA-(1+A*v+B/v-2*(A*B)^(1/2))*c-g)*(yf/v*(1-v^2*(A-B/v^2))/c/BETTA+1+A*v+B/v-2*(A*B)^(1/2)))+la*BETTA*(THETA/(1+yf/v-yf/v*(1-v^2*(A-B/v^2))/BETTA-(1+A*v+B/v-2*(A*B)^(1/2))*c-g)^2*(-yf/v+yf/v*(1-v^2*(A-B/v^2))/BETTA+(1+A*v+B/v-2*(A*B)^(1/2))*c+g)*yf/v*(1-v^2*(A-B/v^2))/c/BETTA+THETA*yf/v*(1-v^2*(A-B/v^2))/c/BETTA/(1+yf/v-yf/v*(1-v^2*(A-B/v^2))/BETTA-(1+A*v+B/v-2*(A*B)^(1/2))*c-g));

y(2) = Lcs;