function y = findvh(vh,LAMBDA,G,Z,MU,P0)
%y = findvh(vh,LAMBDA,G,Z,MU,P0) evaluates the first-order conditions of the Ramsey problem w.r.t. v and h. These focs are solved with fsolved in the program simu.m
%Inputs: vh (a 2-element vector containing values for v and h), LAMBDA (the multiplier in the implementability constraint of the Ramsey problem), G and Z, the values taken by the exogenous gov't purchases and techno shocks, and P0, an indicator variable taken the value 1 if the period is 0 and zero otherwise. 
%Output: y (a 2-element vector showing how far from zero the focs are, zero being the solution)
%(c) Stephanie Schmitt-Grohe and Martin Uribe


[BETA,THETA,D,ETA,B,A,gl,gh,phig,zl,zh,phiz,ALFA]=param(MU);

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

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

V = Vs + (Vmax-Vs) * abs(vh(1)) / (1+abs(vh(1))); %Vs + abs(vh(1)-Vs); 

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



S=A*V+B/V-2*sqrt(A*B);
C = (Z*H - G) / (1+ALFA*S); %consmption
SP=A-B/V^2;
GAMA=1+S+V*SP;
SPP=2*B/V^3;
GAMAP=2*A;
R=1/(1-V^2*SP);
RP=2*A*V*R^2;
PHI = (1+(1-1/R)/V)/GAMA + ALFA*S/GAMA;
PHIP = (-SP*GAMA + 2*SP*S + V*SPP*S)/(GAMA^2) + ALFA*(SP*GAMA-S*GAMAP)/GAMA^2 ;

UC=1/C;
UCC=-1/C^2;
UH=-THETA/(1-H);
UHH=-THETA/(1-H)^2;
UCH=0;
UHC=UCH;

MU = (UC *(1+LAMBDA * PHI) + LAMBDA * (UCC*C*PHI+UHC*H+UCC*Z*H/GAMA/ETA - UCC/GAMA * P0 * D)) / (1+ALFA*S);

y(1) = LAMBDA * UC *C * PHIP - LAMBDA *  UC * GAMAP / GAMA^2 * (Z * H / ETA - P0 * D) - MU * C * ALFA * SP; 

y(2) = UH + LAMBDA * ( UCH*C * PHI + UH + H * UHH + UCH * Z *H/ GAMA / ETA + UC * Z / GAMA / ETA - UCH/GAMA *P0 * D) + Z * MU;