Latex Econ Model

Step 2: Use Standard Notation

Follow economics conventions:

• Utility: $U$, $u$, or $v$
• Production: $F$, $f$, or $Y$
• Prices: $p$, $w$, $r$
• Quantities: $q$, $x$, $y$
• Time subscripts: $t$, $t+1$
• Greek letters for parameters: $\alpha$, $\beta$, $\gamma$, $\delta$

Step 3: Structure the Model

Organize as:

1. Environment - Agents, goods, time horizon
2. Preferences/Technology - Utility functions, production functions
3. Constraints - Budget, resource, incentive compatibility
4. Equilibrium concept - Definition and conditions
5. Solution - First-order conditions, closed-form solutions

Example Output

\documentclass{article}
\usepackage{amsmath, amssymb, amsthm}
\usepackage{mathtools}

% Theorem environments
\newtheorem{definition}{Definition}
\newtheorem{proposition}{Proposition}
\newtheorem{lemma}{Lemma}

% Custom commands for economics
\newcommand{\E}{\mathbb{E}}          % Expectation
\newcommand{\R}{\mathbb{R}}          % Real numbers
\newcommand{\pd}[2]{\frac{\partial #1}{\partial #2}}  % Partial derivative

\begin{document}

\section{A Simple Consumer Problem}

\subsection{Environment}

Consider a consumer who lives for two periods, $t \in \{1, 2\}$. The consumer has preferences over consumption $c_t$ represented by the utility function:
%
\begin{equation}
    U(c_1, c_2) = u(c_1) + \beta u(c_2)
\end{equation}
%
where $\beta \in (0,1)$ is the discount factor and $u(\cdot)$ is strictly increasing and strictly concave.

\subsection{Constraints}

The consumer earns income $y_1$ in period 1 and $y_2$ in period 2. She can save at gross interest rate $R = 1 + r$. The budget constraints are:
%
\begin{align}
    c_1 + s &= y_1 \label{eq:bc1}\\
    c_2 &= y_2 + Rs \label{eq:bc2}
\end{align}
%
where $s$ denotes savings. Combining \eqref{eq:bc1} and \eqref{eq:bc2} yields the intertemporal budget constraint:
%
\begin{equation}
    c_1 + \frac{c_2}{R} = y_1 + \frac{y_2}{R} \equiv W
\end{equation}

\subsection{Optimization Problem}

The consumer solves:
%
\begin{equation}
    \max_{c_1, c_2} \quad u(c_1) + \beta u(c_2) 
    \quad \text{s.t.} \quad c_1 + \frac{c_2}{R} = W
\end{equation}

\subsection{Solution}

The Lagrangian is:
%
\begin{equation}
    \mathcal{L} = u(c_1) + \beta u(c_2) + \lambda\left(W - c_1 - \frac{c_2}{R}\right)
\end{equation}

First-order conditions:
%
\begin{align}
    \pd{\mathcal{L}}{c_1} &= u'(c_1) - \lambda = 0 \\
    \pd{\mathcal{L}}{c_2} &= \beta u'(c_2) - \frac{\lambda}{R} = 0
\end{align}

Combining these yields the \textbf{Euler equation}:
%
\begin{equation}
    \boxed{u'(c_1) = \beta R \cdot u'(c_2)}
\end{equation}

\begin{proposition}[Consumption Smoothing]
If $\beta R = 1$, then $c_1^* = c_2^*$ (perfect consumption smoothing).
\end{proposition}

\begin{proof}
When $\beta R = 1$, the Euler equation becomes $u'(c_1) = u'(c_2)$. Since $u$ is strictly concave, $u'$ is strictly decreasing, which implies $c_1 = c_2$.
\end{proof}

%====================================
\section{A Firm's Dynamic Problem}
%====================================

Consider a firm that maximizes the present value of profits:
%
\begin{equation}
    \max_{\{k_{t+1}, n_t\}_{t=0}^{\infty}} \sum_{t=0}^{\infty} \beta^t \left[ F(k_t, n_t) - w_t n_t - I_t \right]
\end{equation}
%
subject to the capital accumulation equation:
%
\begin{equation}
    k_{t+1} = (1 - \delta) k_t + I_t
\end{equation}

The Bellman equation is:
%
\begin{equation}
    V(k) = \max_{k', n} \left\{ F(k, n) - wn - k' + (1-\delta)k + \beta V(k') \right\}
\end{equation}

\end{document}

LaTeX Packages to Include

% Essential packages for economics papers
\usepackage{amsmath}    % Enhanced math environments
\usepackage{amssymb}    % Mathematical symbols
\usepackage{amsthm}     % Theorem environments
\usepackage{mathtools}  % Extensions to amsmath
\usepackage{bm}         % Bold math symbols
\usepackage{dsfont}     % \mathds for indicator functions

Useful Custom Commands

% Expectation and probability
\newcommand{\E}{\mathbb{E}}
\newcommand{\Var}{\text{Var}}
\newcommand{\Cov}{\text{Cov}}
\newcommand{\Prob}{\mathbb{P}}

% Indicator function
\newcommand{\ind}{\mathds{1}}

% Partial derivatives
\newcommand{\pd}[2]{\frac{\partial #1}{\partial #2}}
\newcommand{\pdd}[2]{\frac{\partial^2 #1}{\partial #2^2}}

% Argmax/argmin
\DeclareMathOperator*{\argmax}{arg\,max}
\DeclareMathOperator*{\argmin}{arg\,min}

% Blackboard bold
\newcommand{\R}{\mathbb{R}}
\newcommand{\N}{\mathbb{N}}
\newcommand{\Z}{\mathbb{Z}}

Best Practices

1. Use align environment for multiline equations
2. Label important equations with \label{} and reference with \eqref{}
3. Use \text{} for words in equations (not bare text)
4. Box key results with \boxed{}
5. Define custom commands for repeated notation
6. Use consistent subscript conventions ($t$ for time, $i$ for individuals)

Common Pitfalls

• ❌ Using * for multiplication (use \cdot or implicit multiplication)
• ❌ Forgetting \left( and \right) for auto-sizing brackets
• ❌ Inconsistent notation across the paper
• ❌ Not aligning equations at = signs
• ❌ Using $$ ... $$ instead of proper environments

References

• AMS-LaTeX User's Guide
• The Not So Short Introduction to LaTeX
• Mathpix - Convert handwritten equations to LaTeX

Changelog

v1.0.0

• Initial release with consumer, firm, and game theory templates