diff --git a/Week 12-Persistence and Switching Costs/switching_costs1.tex b/Week 12-Persistence and Switching Costs/switching_costs1.tex
index 98f4297..d107a81 100644
--- a/Week 12-Persistence and Switching Costs/switching_costs1.tex	
+++ b/Week 12-Persistence and Switching Costs/switching_costs1.tex	
@@ -209,7 +209,7 @@
 \begin{itemize}
 \item Solve a dynamic programming problem like in Cabral (2008).
 \item If we have just auto-correlation and no switching costs, there is NO harvesting incentive.
-\item If we have switching costs than there is.
+\item If we have switching costs than there is (SOMETHING MISSING HERE).
 \item Very small switching costs can make markets MORE competitive.
 \end{itemize}
 
diff --git a/Week 12-Persistence and Switching Costs/switching_costs2.tex b/Week 12-Persistence and Switching Costs/switching_costs2.tex
index 8c05a00..260cd16 100644
--- a/Week 12-Persistence and Switching Costs/switching_costs2.tex	
+++ b/Week 12-Persistence and Switching Costs/switching_costs2.tex	
@@ -246,7 +246,7 @@
 Use what Einav, Finkelstein, and Levin (2010) call a ``realized'' empirical utility model and assume that $U_{kjt}$ has the following von-Neuman Morgenstern (v-NM) expected utility formulation
 \begin{align*}
 U_{k j t}&=\int_{0}^{\infty}  u_{k}\left(W_{k}, O O P, P_{k j t}, 1_{k j, t-1}\right) f_{k j t}(O O P) d O O P\\
-u_{k}(x)&=-\frac{1}{\gamma_{k}\left(\symbf{X}_{k}^{A}\right)} e^{-\gamma_{k}\left(\symbf{x}_{k}^{A}\right)_{x}}
+u_{k}(x)&=-\frac{1}{\gamma_{k}\left(\symbf{X}_{k}^{A}\right)} e^{-\gamma_{k}\left(\symbf{x}_{k}^{A}\right) \cdot {x}}
 \end{align*}
 \begin{itemize}
 \item $k$ is a family unit,  $j$ is an insurance plan,  $t$ is a year $(t_0,t_1,t_2)$.
@@ -264,7 +264,7 @@
 \item $P_{k j t}$ is the price for insurance plan $j$ to family $k$.
 \item $OOP$ is a draw from the distribution of $f(OOP)$ expenses: depends on the plan.
 \item $\eta\left(\symbf{X}_{k t}^{B}, Y_{k}\right) 1_{k j, t-1}$ is the switching cost which depends on demographics $\symbf{X}_{k t}^{B}$.
-\item $\delta_{k}(Y_k)$ is the family specific intercept for high-deductible plan $(Y_k)$ is family dummy.
+\item $\delta_{k}(Y_k)$ is the family specific intercept for high-deductible plan $(Y_k)$ is family dummy (ie., unit $k$ is family or single).
 \item $\alpha H_{k, t-1} 1_{250}$ is interaction between 90th percentile spenders and most generous plan.
 \end{itemize}
 \end{frame}
@@ -316,7 +316,7 @@
 
 \item Switching costs:%
 \begin{align*}
-\eta (X_{k}^{B},Y_{k})=\eta _{0}+\eta _{1}X_{kt}^{B}+\eta _{2}Y_{k}
+\eta (X_{kt}^{B},Y_{k})=\eta _{0}+\eta _{1}X_{kt}^{B}+\eta _{2}Y_{k}
 \end{align*}
 
 \item Probit error, $\varepsilon _{kjt}$ distributed iid with parms $(\mu
@@ -448,7 +448,7 @@
 \item What is a switching cost?
 \begin{itemize}
 \item Transaction costs (then SC=0 when no switch)
-\item Learning costs  -  effort needed to learn about new planŐs features.
+\item Learning costs  -  effort needed to learn about new planÕs features.
 \item Product compatibility - important if network changes (need to make new relationship-specific investments)
 \item Fixed re-optimization costs - some cost to changing beliefs from status quo
 \item Inertial and psychological costs