\documentclass[a4paper,12pt,leqno]{report}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\begin{document}
\begin{equation}
\theta P_t + \sum_{j=1}^{\infty}
\left(\frac{1-\delta}{1+\rho_t^{t+j}}\right)^j
\frac{1}{1-\delta}
\left\{
\begin{array}{c}
r_{t+j} (1-\phi)(1-\theta)P_t + \tau (1+g)^{j-1} P_t \\
-\delta\left[P_{t+j} - (1-\theta) P_t\right]
\end{array}
\right\}
\end{equation}
\renewcommand{\theequation}{2'}
\begin{equation}
P_{t} \left( \frac{\theta_{\rho_{t}}+(1-\theta)(1-\varphi)r-g+\tau+g(1-\theta)(1-\delta) \frac{\rho_{t}-(1-\varphi)r}{\rho_{t}+\delta}}{\rho_{t}+\delta+g\delta-g} \right).
\end{equation}
\renewcommand{\theequation}{2''}
\begin{equation}
\frac{R_{t}}{P_{t}} =\theta\rho_{t}+(1-\theta)(1-\varphi)r-g+\tau+g(1-\theta)(1-\delta)\frac{\rho_{t}-(1-\varphi)r}{\rho_{t}+\delta}.
\end{equation}
\renewcommand{\theequation}{\theequation}
\footnotesize
\begin{equation}
\frac{R_{t}}{P_{t}}=\theta\hat{\rho}(\hat{r})-\varphi\pi+(1-\theta)(1-\varphi) \hat{r} -\hat{g}+\tau+(\hat{g}+\pi)(1-\theta)(1-\delta)\frac{\hat{\rho}(\hat{r})-(1-\varphi) \hat{r}}{\hat{\rho}(\hat{r})+(1-\varphi)\pi+\delta}.
\end{equation}
\normalsize