Untitled1.ipynb

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    "## Neoclassical growth model\n",
    "\n",
    "Consider the neoclassical growth model with leisure\n",
    "\n",
    "$$\n",
    "\\max_{c_t,l_t}E_0\\sum_{t=1}^\\infty \\beta^{t-1}\\frac{(c_t^\\theta(1-l_t)^{1-\\theta})^{1-\\tau}}{1-\\tau}\n",
    "$$\n",
    "subject to the resource constraint\n",
    "$$\n",
    "c_t + i_t = e^{z_t}k_t^\\alpha l_t^{1-\\alpha}\n",
    "$$\n",
    "the law of motion for capital\n",
    "$$\n",
    "k_{t+1} = i_t + (1-\\delta)k_t\n",
    "$$\n",
    "and the stochastic process for productivity\n",
    "$$\n",
    "z_t = \\rho z_{t-1}+\\epsilon_t\n",
    "$$\n",
    "where $epsilon_t \\sim N(0,\\sigma^2)$"
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