%
% ex5F is a matlab function that defines the eulers
% at the 'steady-state' for a simplified Kydland and Prescott model 
%

function [q] = ex5F(x,gamma,alpha,psi,sigma,delta,beta,thetabar)

% ----- define marginal utilities ----- %

muc = x(1)^(-gamma) ;

mul = psi*(1-x(2))^(-sigma) ; 


% ----- define marginal products ----- % 
 
mpn = (1-alpha)*thetabar*x(3)^(alpha)*x(2)^(1-alpha-1) ;

mpk = (alpha)*thetabar*x(3)^(alpha-1)*x(2)^(1-alpha) ;

% ----- define eulers ----- %

r1 = muc - beta*muc*(mpk+(1-delta)) ;

r2 = mul - muc*mpn ;

% ----- define resource constraint ------ %

r3 = thetabar*x(3)^(alpha)*x(2)^(1-alpha)  - x(1) + (1-delta)*x(3) - x(3);

% ----- define the equations to be returned ----- %

q = [r1,r2,r3];