Is there way of breaking down a very long equation without multiline?

Question

I have been trying to break up this long equation (see below) to fit into the page. It is quite long and I am wondering how I can break it up into different parts. There is something wrong with the \multiline function in my version, so I want to avoid using that.

\begin{equation}
        \begin{aligned}
        V^{j} \left ( q_{c},q_{e} \right ) \equiv  \max_{\sigma^{j}, c_{c}^{j}, c_{e}^{j}, y_{c}^{j}, y_{e}^{j}} \left \{ \delta^{j} u(c^{j}) - g(y^{j}) + W\left ( \frac{\phi}{\gamma_{c}}[q_{c}-c_{c}^{j}+y_{c}^{j}], \frac{\psi}{\gamma_{e}}[\sigma^{j} (R q_{e}-\kappa^{j}-c_{e}^{j}+y_{e}^{j}) + (1-\sigma^{j}) (q_{e}-c_{e}^{j}+y_{e}^{j}) ] \right ) + \lambda_{c}^{j} (q_{c}-c_{c}^{j}) + \lambda_{e}^{j} (Rq_{e}-\kappa^{j}-c_{e}^{j})
        \right \},\label{eqn:17}
    \end{aligned}
\end{equation}\\

The output I am getting:

I am looking for an output that is like

but under the maximization problem with the main brackets.

Here are the relevant packages:

\documentclass[a4paper,12pt]{article}
\usepackage[margin=1in]{geometry}
\usepackage{amsmath,amssymb,amsfonts}
\usepackage{mathtools}
\usepackage{graphicx,amsmath,stackengine,scalerel}
\newcommand\qunderline[1]{\ThisStyle{%
        \ensurestackMath{\stackengine{-1pt}{\SavedStyle#1}
            {\SavedStyle\underline{\hphantom{#1}}}{U}{c}{F}{F}{S}}}%
}
\usepackage{xfrac}
\usepackage{nicefrac}
\usepackage{accents}

Answer 1

If you use multline rather than multiline as the name of the environment, you should be fine with just two line breaks in the long formula.

Because of the line breaks, you can't use \left and \right all that well. Instead, do use explicit sizing directives such as \bigl, \Bigl, and \biggl (and their corresponding closing counterparts).

The horizontal line in the following screenshot is there just to illustrate the width of the textblock.

\documentclass{article}
\usepackage{amsmath} % for 'multline' env. and '\substack' macro

\begin{document}
\hrule % just to illustrate width of text block
\begin{multline} \label{eqn:17}
V^{j}(q_{c},q_{e}) \equiv  
\max_{\substack{\sigma^{j}, c_{c}^{j}, c_{e}^{j},\\ y_{c}^{j}, y_{e}^{j}}}
\biggl \{ \delta^{j} u(c^{j}) - g(y^{j}) 
+ W\Bigl( \tfrac{\phi}{\gamma_{c}} \bigl[q_{c}-c_{c}^{j}+y_{c}^{j}\bigl]\,,\\ 
\tfrac{\psi}{\gamma_{e}}
\bigl[ \sigma^{j} (R q_{e}-\kappa^{j}-c_{e}^{j}+y_{e}^{j}) 
+ (1-\sigma^{j}) (q_{e}-c_{e}^{j}+y_{e}^{j}) \bigr] \Bigr ) \\
+ \lambda_{c}^{j} (q_{c}-c_{c}^{j}) + \lambda_{e}^{j} (Rq_{e}-\kappa^{j}-c_{e}^{j})
\biggr \}\,.
\end{multline}
\end{document}

Answer 2

• In aligned environment math terms are not break in multi lines. Consequently your equation spill out of page
• Even you break equation on three parts, it is still to long, it protrude right text border and consequently the equation number is pushed below of equation.
• A possible solution is to use smaller font size in equation, for example by employ \medmath command defined in the nccmath package

\documentclass[a4paper,12pt]{article}
\usepackage[margin=1in]{geometry}
\usepackage{nccmath}

\usepackage{lipsum} % for dummy text filler

\begin{document}
\lipsum[66]
\begin{equation}\label{eqn:17}
    \medmath{
    \begin{aligned}
V^{j}( q_{c},q_{e}) 
    & \equiv  \max_{\substack{\sigma^{j}, c_{c}^{j}, c_{e}^{j},\\ 
                             y_{c}^{j}, y_{e}^{j}}}
    \biggl\{ \delta^{j} u(c^{j}) - g(y^{j})     \\
    &\quad {} +  \beta W \left( 
        \frac{\phi}{\gamma_{c}}\bigl[q_{c} - c_{c}^{j} + y_{c}^{j}\bigr], \frac{\psi}{\gamma_{e}}\bigl[\sigma^{j} (R q_{e} -\kappa^{j} - c_{e}^{j} +y_{e}^{j}) + (1-\sigma^{j}) (q_{e}-c_{e}^{j}+y_{e}^{j}) \bigr]
                        \right) \\
    &\quad {} +  \lambda_{c}^{j} (q_{c}-c_{c}^{j}) + \lambda_{e}^{j} (Rq_{e}-\kappa^{j}-c_{e}^{j})
    \biggr\},
    \end{aligned}
            }
\end{equation}
some more text, see \eqref{eqn:17}
\end{document}

Off-topic In your preamble amsmath is still load twice (actually three times because mathtools load it too). More correct is (considering new nccmath):

\documentclass[a4paper,12pt]{article}
\usepackage[margin=1in]{geometry}
\usepackage{nccmath,amssymb,amsfonts}
\usepackage{mathtools}
\usepackage{graphicx,stackengine,scalerel}
\newcommand\qunderline[1]{\ThisStyle{%
        \ensurestackMath{\stackengine{-1pt}{\SavedStyle#1}
            {\SavedStyle\underline{\hphantom{#1}}}{U}{c}{F}{F}{S}}}%
}
\usepackage{xfrac}
\usepackage{nicefrac}
\usepackage{accents}