can someone one please help to write this formula in latex
\begin{equation}
\max\limits_{{P^{\circ}_t(j)}} E_{t}\sum_{s=0}^{\infty}\zeta^s M_{t,t+s}
\left[P^{\circ}_{t+s}(j)-\mathcal{MC}_{t+s}(j)\right]Y_{t+s}(j)
\end{equation}
I take it the main issue is the typesetting of the curly braces around the material immediately below "max". Just change
\max_{{P^{\circ}_t(j)}}
to
\max_{\{P^{\circ}_t(j)\}}
Remember that in order to typeset curly braces, you must type \{ and \}, not just { and }.
No need for the \limits directive, by the way.
To fully reproduce the equation shown in the screenshot, you also need to provide \mid t items in two of the subscripts.
\documentclass{article}
\begin{document}
\begin{equation}
\max_{\{P^{\circ}_t(j)\}} E_{t} \sum_{s=0}^{\infty} \zeta^s M_{t,t+s}
\left[ P^{\circ}_{t+s\mid t}(j) - \mathcal{MC}_{t+s}(j) \right] Y_{t+s\mid t}(j)
\end{equation}
\end{document}
\maxin inline math mode or in display math mode? In both the OP's use case and in my answer,\maxis used in display math mode -- in which case it's not necessary to use\limits. If, in contrast,\maxis used inline math mode, then\limitsis indeed needed if the objective is to place the argument below "max". – Mico Oct 19 '20 at 18:56casesenvironment\textstyle, aka inline math style, is in use. – Mico Oct 20 '20 at 16:04\limits– Nagabhushan S N Jan 17 '21 at 16:26