Week 5 class example - Lazear AER 2000.ipynb

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    "Given:\n",
    "\n",
    "$$ e = f(X,A) $$\n",
    "\n",
    "Fixing $e = \\bar{e}$\n",
    "\n",
    "Derive:\n",
    "\n",
    "$$ \\frac{\\partial X}{\\partial A} = -\\frac{f_2}{f_1}$$"
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    "\\begin{align}\n",
    "    \\frac{d \\bar{e}}{d A} &= \\frac{\\partial f(X,A)}{\\partial X} \\frac{\\partial X}{\\partial A} + \\frac{\\partial f(X,A)}{\\partial A}\n",
    "\\end{align}"
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   "source": [
    "\\begin{align}\n",
    "    \\underbrace{\\frac{d \\bar{e}}{d A}}_{=0} &= \\underbrace{\\frac{\\partial f(X,A)}{\\partial X}}_{f_1} \\frac{\\partial X}{\\partial A} + \\underbrace{\\frac{\\partial f(X,A)}{\\partial A}}_{f_2} \\\\\n",
    "    f_1\\frac{\\partial X}{\\partial A} &= -f_2\n",
    "\\end{align}"
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