\documentclass[a4paper,11pt]{article}
\title{CEE New Keynesian model}
\author{Eric Scheffel}
\begin{document}
\maketitle

\section{Variable Legend}

\begin{table}[h]
		\begin{tabular}[c]{l@{\extracolsep{25pt}}l}
			$z=$ techn. shock & $qq=$ Tobin's q \\
			$r=$ gross nom. interest & $\tilde{p}=$ rel. price opt. firms \\
			$r^k=$ rental rate capital & $\tilde{\mu}=$ inverse of wage markup \\
			$mc=$ marginal cost final good & $s=$ dist. between ouput and total prod. \\
			$\tilde{h}=$ hours supplied by wage optimizers & $h^d=$ labour demand \\
			$\tilde{s}=$ dist. b. hours supplied and used & $k=$ aggr. capital \\
			$h=$ no. of hours supplied & $iv=$ investment \\
			$w=$ real wage & $\tilde{w}=$ wage charged by wage optimizers \\
			$y^d=$ aggr. demand & $g=$ gov. spending \\
			$m^h=$ r. balanc. held by hh & $c=$ consumption \\
			$\lambda=$ marg. util. of income & $\Pi=$ inflation \\
			$u=$ capital utilization & $f^1=$ wage recursion param 1 \\
			$f^2=$ wage recursion param 2 & $x^1=$ price recursion param 1 \\
			$x^2=$ price recursion param 2 & $exp\_vf=$ exp of value func \\
			$cb=$ p. cons. state & $ivb=$ p. investment state \\
			$rb=$ p. nom. interest state & $\Pi b=$ p. inflation state \\
			$yb^d=$ p. output state & $wb=$ p. wage state

		\end{tabular}
\end{table}

What are the first-order non-linear conditions that are entered?
\section{The non-linear FOCs}

Investment
\begin{equation}
-k_{t+1}+\left(1-\delta\right)k_t+qi_t=0;
\end{equation}
Marginal utility of consumption
\begin{equation}
-\lambda_t+\frac{1}{\left(c_t-B c_{t-1}\right)}-\beta \frac{B}{\left(c_{t+1}-B c_t\right)}=0;
\end{equation}
\begin{equation}
-\lambda q_t+\beta \lambda_{t+1}\left(r_{t+1}^k u_{t+1}-a_{t+1}+q_{t+1}\left(1-\delta\right)\right)=0;
\end{equation}





\end{document}
