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latex-econ-model by meleantonio/awesome-econ-ai-stuff
npx skills add https://github.com/meleantonio/awesome-econ-ai-stuff --skill latex-econ-model此技能帮助经济学家使用 LaTeX 编写和排版经济模型,确保数学符号正确、格式一致并符合学术惯例。涵盖效用最大化、均衡条件、动态规划和博弈论模型。
询问用户:
遵循经济学惯例:
按以下方式组织:
\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}
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% 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
% 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}}
align 环境 处理多行公式\label{} 标记重要公式 并用 \eqref{} 引用\text{} 包裹文字(不要直接使用纯文本)\boxed{} 框出关键结果* 表示乘法(应使用 \cdot 或隐式乘法)\left( 和 \right) 来自动调整括号大小= 符号处对齐$$ ... $$ 而不是合适的环境48
301
2026年1月27日
opencode43
codex42
github-copilot40
gemini-cli39
cursor38
claude-code36
This skill helps economists write and typeset economic models in LaTeX with proper mathematical notation, consistent formatting, and academic conventions. It covers utility maximization, equilibrium conditions, dynamic programming, and game theory models.
Ask the user:
Follow economics conventions:
Organize as:
\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}
% 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
% 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}}
align environment for multiline equations\label{} and reference with \eqref{}\text{} for words in equations (not bare text)\boxed{}* for multiplication (use \cdot or implicit multiplication)\left( and \right) for auto-sizing brackets= signs$$ ... $$ instead of proper environmentsWeekly Installs
48
Repository
GitHub Stars
301
First Seen
Jan 27, 2026
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MCP图像生成技能:使用Gemini AI为营销、UI设计、演示文稿创建高质量图像
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