21/replication_package/Tables/A1_theory_table.tex

\begin{table}[h!] \begin{adjustbox}{max width=1.2\textwidth} \begin{threeparttable} 
\caption{Doctor's Expected Utility from Different Prescription Choices} 
\label{tab:Doctor's-expected-utility} {
\begin{tabular}{|c|c|c|}
\hline 
 & {\footnotesize{}Utility from treatment use} & {\footnotesize{}Utility loss from gatekeeping cost}\tabularnewline
\hline 
% No treatment
\hline 
\multicolumn{3}{|l|}{{\footnotesize{}No treatment}}\tabularnewline
\hline 
{\footnotesize{}(1) C \& DV} & {\footnotesize{}0} & {\footnotesize{}$-g\int_{L_{P}}U_{l}(\pi,P)dF(\pi|\gamma,\eta)-g\int_{H_{P}}U_{v}(\pi)dF(\pi|\gamma,\eta)$}\tabularnewline
\hline 
{\footnotesize{}(2) PV} & {\footnotesize{}0} & {\footnotesize{}$-g\int_{L_{0}}U_{l}(\pi,0)dF(\pi|\gamma,\eta)-g\int_{H_{0}}U_{v}(\pi)dF(\pi|\gamma,\eta)$}\tabularnewline
\hline 
% Severe treatment
\multicolumn{3}{|l|}{{\footnotesize{}Severe treatment}}\tabularnewline
\hline 
{\footnotesize{}(3) C \& DV} & {\footnotesize{}$P(\pi\in L2_{P}\cup H_{P})V_{v}(\hat{\pi})$} & {\footnotesize{}$-g\int_{L1_{P}}U_{l}(\pi,P)dF(\pi|\gamma,\eta)-g\int_{L2_{P}}\left[U_{l}(\pi,P)-U_{v}(\pi)\right]dF(\pi|\gamma,\eta)$}\tabularnewline
\hline 
{\footnotesize{}(4) PV} & {\footnotesize{}$P(\pi\in L2_{0}\cup H_{0})V_{v}(\hat{\pi})$} & {\footnotesize{}$-g\int_{L1_{0}}U_{l}(\pi,0)dF(\pi|\gamma,\eta)-g\int_{L2_{0}}\left[U_{l}(\pi,0)-U_{v}(\pi)\right]dF(\pi|\gamma,\eta)$}\tabularnewline
\hline 
% Simple treatment
\multicolumn{3}{|l|}{{\footnotesize{}Simple treatment}}\tabularnewline
\hline 
{\footnotesize{}(5) C \& (DV/no voucher)} & {\footnotesize{}$P(\pi\in L_{P}\cup H_{P})V_{l}(\hat{\pi},P)$} & {\footnotesize{}$-g\int_{H_{P}}\left[U_{v}(\pi)-U_{l}(\pi,P)\right]dF(\pi|\gamma,\eta)$}\tabularnewline
\hline 
{\footnotesize{}(6) (PV \& DV)/voucher} & {\footnotesize{}$P(\pi\in L_{0}\cup H_{0})V_{l}(\hat{\pi},0)$} & {\footnotesize{}$-g\int_{H_{0}}\left[U_{v}(\pi)-U_{l}(\pi,0)\right]dF(\pi|\gamma,\eta)$}\tabularnewline
\hline 
\multirow{2}{*}{{\footnotesize{}(7) PV/no voucher}} & \multirow{2}{*}{{\footnotesize{}$P(\pi\in L_{P}\cup H_{P})V_{l}(\hat{\pi},P)$}} & {\footnotesize{}$-g\int_{L1_{0}\backslash L1_{P}}U_{l}(\pi,0)dF(\pi |\gamma,\eta)-g\int_{L1_{P}\cup L2_{0}}\left[U_{l}(\pi,0)-U_{l}(\pi,P)\right]dF(\pi |\gamma,\eta)$}\tabularnewline
 &  & {\footnotesize{}$-g\int_{H_{0}}\left[U_{v}(\pi)-U_{l}(\pi,P)\right]dF(\pi|\gamma,\eta)$}\tabularnewline
\hline 
% Choice
\multicolumn{3}{|l|}{{\footnotesize{}Patient choice between simple and severe treatment}}\tabularnewline
\hline 
{\footnotesize{}(8) C \& (DV/no voucher)} & {\footnotesize{}$P(\pi\in L_{P})V_{l}(\hat{\pi},P)+P(\pi\in H_{P})V_{v}(\hat{\pi})$} & 0
\tabularnewline
\hline 
{\footnotesize{}(9) C \& (PV \& DV/voucher)} & {\footnotesize{}$P(\pi\in L_{0})V_{l}(\hat{\pi},0)+P(\pi\in H_{0})V_{v}(\hat{\pi})$} & 0
\tabularnewline
\hline 
\multirow{2}{*}{{\footnotesize{}(10) PV/no voucher}} & \multirow{2}{*}{{\footnotesize{}$P(\pi\in L_{P})V_{l}(\hat{\pi},P)+P(\pi\in H_{P})V_{v}(\hat{\pi})$}} & 
{\footnotesize{}$-g\int_{L_{0}}U_{l}(\pi,0)dF(\pi|\gamma,\eta)$}\tabularnewline
 &  & {\footnotesize{}$+g\int_{L_{P}}U_{l}(\pi,P)dF(\pi|\gamma,\eta)+g\int_{H_{P}\backslash H_0}U_{v}(\pi)dF(\pi |\gamma,\eta)$}\tabularnewline
\hline 

\end{tabular}
} \begin{tablenotes}[flushleft] \small                  
\item \emph{Notes}: C denotes control, DV denotes voucher given to doctor, PV denotes voucher given to patient. "No voucher" and "voucher" indicate if the doctor offers the subsidy when prescribing simple treatment.              
 \end{tablenotes} \end{threeparttable} \end{adjustbox} \end{table}