Fixed typo in Euler equation due to conditional operator

exam/endterm_exam_WS2425.tex

@@ -18,7 +18,7 @@
 \begin{document}
 
 \title{Quantitative Macroeconomics}
-\author{Endterm Exam\\Version 1.0}
+\author{Endterm Exam\\Version 1.0.1}
 \date{Winter 2024/2025}
 
 \maketitle
@@ -38,6 +38,20 @@ \section*{General information}
 	\item If there are any questions, do not hesitate to contact Willi Mutschler.
 \end{itemize}
 
+\section*{Changelog}
+\begin{itemize}
+\item \textbf{Version 1.0.1:} Rearranged first equation in exercise 2.2, because the conditional expectation operator is not correctly applied \emph{mathematically}.
+Old equation:
+\begin{align*}
+E_t\left[ \frac{C_{i,t+1}}{C_{i,t}} \right] = \beta E_t\left[1-\delta + R_{t+1}\right]
+\end{align*}
+Corrected equation:
+\begin{align*}
+1 = \beta E_t\left[ \frac{C_{i,t}}{C_{i,t+1}} \left(1-\delta + R_{t+1}\right)\right]
+\end{align*}
+This has no effect on the underlying codes, as Dynare automatically puts all terms on one side of the equation and then applies the conditional expectation operator.
+\end{itemize}
+
 \newpage
 
 \section[Historical Decomposition]{Historical Decomposition}
@@ -171,7 +185,7 @@ \section{RBC model with leisure and non-Ricardian agents}
 
 \item Show that the first-order conditions of the agents are given by
 \begin{align*}
-E_t\left[\frac{C_{i,t+1}}{C_{i,t}}\right] = \beta E_t\left[1-\delta + R_{t+1}\right],
+1 = \beta E_t\left[ \frac{C_{i,t}}{C_{i,t+1}} \left(1-\delta + R_{t+1}\right)\right],
 &&
 W_t = \frac{1-\gamma}{\gamma} \frac{C_{i,t}}{1-L_{i,t}},
 \\