{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "\n", "\n", "# *Numerical Methods for Economists: Lab Assignment The Solow (1956) Model*\n", "\n", "In this lab assignment you will analyze a version of the Solow model with a [constant elasticity of substituion (CES)](http://en.wikipedia.org/wiki/Constant_elasticity_of_substitution) production function and attempt to \"explain\" observed patterns in capital's share in the U.S. between 1950-2011.\n", "\n", "A CES production function looks as follows...\n", "\n", "\\begin{equation}\n", " Y(t) = \\bigg[\\alpha K(t)^{\\rho} + (1-\\alpha) (A(t)L(t))^{\\rho}\\bigg]^{\\frac{1}{\\rho}} \\tag{1.2}\n", "\\end{equation}\n", "\n", "where $0 < \\alpha < 1$ and $-\\infty < \\rho < 1$. The parameter $\\rho = \\frac{\\sigma - 1}{\\sigma}$ where $\\sigma$ is the elasticity of substitution between factors of production. The CES production technology is popular because it nests several interesing special cases. In particular, if factors of production are perfect substitutes (i.e., $\\sigma = +\\infty \\implies \\rho = 1$), then output is just a linear combination of the inputs.\n", "\n", "\\begin{equation}\n", " \\lim_{\\rho \\rightarrow 1} Y(t) = \\alpha K(t) + (1-\\alpha)A(t)L(t) \\tag{1.3}\n", "\\end{equation}\n", " \n", "On the other hand, if factors of production are perfect complements (i.e., $\\sigma = 0 \\implies \\rho = -\\infty$), then we recover the [Leontief production function](http://en.wikipedia.org/wiki/Leontief_production_function).\n", " \n", "\\begin{equation}\n", " \\lim_{\\rho \\rightarrow -\\infty} Y(t) = \\min\\left\\{\\alpha K(t), (1-\\alpha) A(t)L(t)\\right\\} \\tag{1.4}\n", "\\end{equation}\n", "\n", "Finally, if the elasticity of substitution is unitary (i.e., $\\sigma=1 \\implies \\rho=0$), then output is [Cobb-Douglas](http://en.wikipedia.org/wiki/Cobb%E2%80%93Douglas_production_function).\n", "\n", "\\begin{equation}\n", " \\lim_{\\rho \\rightarrow 0} Y(t) = K(t)^{\\alpha}(A(t)L(t))^{1-\\alpha} \\tag{1.5}\n", "\\end{equation}" ] }, { "cell_type": "code", "collapsed": false, "input": [ "%load_ext autoreload" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 7 }, { "cell_type": "code", "collapsed": false, "input": [ "%autoreload 2" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 8 }, { "cell_type": "code", "collapsed": false, "input": [ "import numpy as np\n", "import pandas as pd\n", "from scipy import integrate, linalg, optimize\n", "import matplotlib as mpl\n", "import matplotlib.pyplot as plt\n", "\n", "# for the first few labs we will be working with models of growth\n", "import growth\n", "import pwt" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 9 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### (5 points) Part a) \n", "\n", "Show that the CES production function as defined by equation 1.2 exhibits constant returns to scale." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Answer:\n", "Constant returns to scale requires that multiplying both factors of production by some fixed constant $c > 0$, causes output to change by the same factor.\n", "\n", "\\begin{align}\n", " F(cK, cAL) =& \\bigg[\\alpha (cK(t))^{\\rho} + (1-\\alpha) (cA(t)L(t))^{\\rho}\\bigg]^{\\frac{1}{\\rho}} \\\\\n", " =& \\bigg[\\alpha c^{\\rho}K(t)^{\\rho} + (1-\\alpha) c^{\\rho}(A(t)L(t))^{\\rho}\\bigg]^{\\frac{1}{\\rho}} \\\\\n", " =& \\bigg[c^{\\rho}\\bigg(\\alpha K(t)^{\\rho} + (1-\\alpha) (A(t)L(t))^{\\rho}\\bigg)\\bigg]^{\\frac{1}{\\rho}} \\\\\n", " =& c\\bigg[\\alpha K(t)^{\\rho} + (1-\\alpha) (A(t)L(t))^{\\rho}\\bigg]^{\\frac{1}{\\rho}} \\\\\n", " =& cF(K, AL)\n", "\\end{align}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### (10 points) Part b)\n", "Derive the intensive forms for both the general CES production function as defined by equation 1.2 and for its Cobb-Douglas special case defined by equation 1.5. Show that both of these intensive production functions are concave." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Answer:\n", "\n", "The intensive form of the general CES production function is...\n", "\n", "\\begin{align}\n", "y(t) = \\frac{Y(t)}{A(t)L(t)} =& \\frac{1}{A(t)L(t)}\\bigg[\\alpha K(t)^{\\rho} + (1-\\alpha) (A(t)L(t))^{\\rho}\\bigg]^{\\frac{1}{\\rho}} \\\\\n", "=& \\bigg[\\frac{\\alpha K(t)^{\\rho} + (1-\\alpha) (A(t)L(t))^{\\rho}}{(A(t)L(t))^{\\rho}}\\bigg]^{\\frac{1}{\\rho}} \\\\\n", "=& \\bigg[\\alpha \\frac{K(t)^{\\rho}}{(A(t)L(t))^{\\rho}} + (1-\\alpha) \\frac{(A(t)L(t))^{\\rho}}{(A(t)L(t))^{\\rho}}\\bigg]^{\\frac{1}{\\rho}} \\\\\n", "=& \\bigg[\\alpha \\bigg(\\frac{K(t)}{A(t)L(t)}\\bigg)^{\\rho} + (1-\\alpha)\\bigg]^{\\frac{1}{\\rho}} \\\\\n", "=& \\bigg[\\alpha k(t)^{\\rho} + (1-\\alpha)\\bigg]^{\\frac{1}{\\rho}}\n", "\\end{align}\n", "\n", "The intensive form of the Codd-Douglas special case is...\n", "\n", "\\begin{align}\n", "y(t) = \\frac{Y(t)}{A(t)L(t)} =& \\frac{1}{A(t)L(t)}K(t)^{\\alpha}(A(t)L(t))^{1-\\alpha} \\\\\n", "=& K(t)^{\\alpha}(A(t)L(t))^{-\\alpha} \\\\\n", "=& \\bigg(\\frac{K(t)}{A(t)L(t)}\\bigg)^{\\alpha} \\\\\n", "= & k(t)^{\\alpha}\n", "\\end{align}\n", "\n", "Concavity requires that $f'(k) > 0$ and $f''(k) < 0$. For the intensive form of the general CES production function these derivatives are messy!\n", "\n", "\\begin{align}\n", " f'(k) = \\frac{\\partial y(t)}{\\partial k(t)} =& \\alpha k(t)^{\\rho-1}\\bigg[\\alpha k(t)^{\\rho} + (1-\\alpha)\\bigg]^{\\frac{1}{\\rho} - 1} > 0 \\\\\n", " f''(k) = \\frac{\\partial^2 y(t)}{\\partial k(t)^2} =& \\alpha k(t)^{\\rho-1} \\frac{\\partial}{\\partial k}\\bigg(\\bigg[\\alpha k(t)^{\\rho} + (1-\\alpha)\\bigg]^{\\frac{1}{\\rho} - 1}\\bigg) + \\frac{\\partial}{\\partial k}\\bigg(\\alpha k(t)^{\\rho-1}\\bigg)\\bigg[\\alpha k(t)^{\\rho} + (1-\\alpha)\\bigg]^{\\frac{1}{\\rho} - 1} \\\\\n", " =& \\alpha k(t)^{\\rho-1} \\frac{\\partial}{\\partial k}\\bigg(\\bigg[\\alpha k(t)^{\\rho} + (1-\\alpha)\\bigg]^{\\frac{1}{\\rho} - 1}\\bigg) + \\bigg(\\alpha(\\rho - 1)k(t)^{\\rho-2}\\bigg)\\bigg[\\alpha k(t)^{\\rho} + (1-\\alpha)\\bigg]^{\\frac{1}{\\rho} - 1} \\\\\n", " =& \\alpha k(t)^{\\rho-1}\\bigg(\\bigg(\\alpha \\rho k(t)^{\\rho-1}\\bigg)\\bigg(\\frac{1}{\\rho} - 1\\bigg)\\bigg[\\alpha k(t)^{\\rho} + (1-\\alpha)\\bigg]^{\\frac{1}{\\rho} - 2}\\bigg) + \\bigg(\\alpha(\\rho - 1)k(t)^{\\rho-2}\\bigg)\\bigg[\\alpha k(t)^{\\rho} + (1-\\alpha)\\bigg]^{\\frac{1}{\\rho} - 1} \\\\\n", " =& \\alpha k(t)^{\\rho-1}\\bigg(\\bigg(\\alpha k(t)^{\\rho-1}\\bigg)\\bigg(1 - \\rho\\bigg)\\bigg[\\alpha k(t)^{\\rho} + (1-\\alpha)\\bigg]^{\\frac{1}{\\rho} - 2}\\bigg) + \\bigg(\\alpha(\\rho - 1)k(t)^{\\rho-2}\\bigg)\\bigg[\\alpha k(t)^{\\rho} + (1-\\alpha)\\bigg]^{\\frac{1}{\\rho} - 1} \\\\\n", " =& \\bigg(\\bigg(\\alpha k(t)^{\\rho-1}\\bigg)^2\\bigg(1 - \\rho\\bigg)\\bigg[\\alpha k(t)^{\\rho} + (1-\\alpha)\\bigg]^{\\frac{1}{\\rho} - 2}\\bigg) - \\bigg(\\alpha(1 -\\rho)k(t)^{\\rho-2}\\bigg)\\bigg[\\alpha k(t)^{\\rho} + (1-\\alpha)\\bigg]^{\\frac{1}{\\rho} - 1} \\\\\n", " =& (1 -\\rho)\\bigg[\\alpha k(t)^{\\rho} + (1-\\alpha)\\bigg]^{\\frac{1}{\\rho} - 2}\\bigg(\\bigg(\\alpha k(t)^{\\rho-1}\\bigg)^2 - \\bigg(\\alpha k(t)^{\\rho-2}\\bigg)\\bigg[\\alpha k(t)^{\\rho} + (1-\\alpha)\\bigg]\\bigg) \\\\\n", " =& (1 -\\rho)\\bigg[\\alpha k(t)^{\\rho} + (1-\\alpha)\\bigg]^{\\frac{1}{\\rho} - 2}\\bigg(\\alpha^2 k(t)^{2\\rho-2} - \\alpha^2 k(t)^{2\\rho-2} - (1-\\alpha)\\bigg(\\alpha k(t)^{\\rho-2}\\bigg)\\bigg) \\\\\n", " =& -(1 -\\rho)(1-\\alpha)\\bigg(\\alpha k(t)^{\\rho-2}\\bigg)\\bigg[\\alpha k(t)^{\\rho} + (1-\\alpha)\\bigg]^{\\frac{1}{\\rho} - 2} < 0\\\\\n", "\\end{align}\n", "\n", "For the Cobb-Douglas special case, the derivatives are much nicer.\n", "\n", "\\begin{align}\n", "f'(k) =& \\alpha k(t)^{\\alpha-1} > 0 \\\\\n", "f''(k) =& -\\alpha (1 - \\alpha) k(t)^{\\alpha-2} < 0 \\\\\n", "\\end{align}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### (5 points) Part c)\n", "\n", "Using your results from part b, complete the Python function below which defines output (per person/effective person) in terms of capital (per person/effective person) and model parameters." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# you were given the following incomplete code...\n", "def ces_output(t, k, params):\n", " \"\"\"\n", " Intensive form for a CES production \n", " function.\n", "\n", " Arguments:\n", "\n", " t: (array-like) Time.\n", " k: (array-like) Capital (per person/effective person).\n", " params: (dict) Dictionary of parameter values.\n", " \n", " Returns:\n", "\n", " y: (array-like) Output (per person/ effective person)\n", "\n", " \"\"\"\n", " # extract params\n", " alpha = params['alpha']\n", " sigma = params['sigma']\n", " rho = # INSERT CODE HERE DEFINING RHO IN TERMS OF SIGMA!\n", " \n", " # nest Cobb-Douglas technology as special case\n", " if rho == 0:\n", " y = # INSERT CODE HERE!\n", " else:\n", " y = # INSERT CODE HERE!\n", " \n", " return y" ], "language": "python", "metadata": {}, "outputs": [] }, { "cell_type": "code", "collapsed": false, "input": [ "# which should be completed as follows...\n", "def ces_output(t, k, params):\n", " \"\"\"\n", " Intensive form for a CES production function.\n", "\n", " Arguments:\n", "\n", " t: (array-like) Time.\n", " k: (array-like) Capital (per person/effective person).\n", " params: (dict) Dictionary of parameter values.\n", " \n", " Returns:\n", "\n", " y: (array-like) Output (per person/ effective person)\n", "\n", " \"\"\"\n", " # extract params\n", " alpha = params['alpha']\n", " sigma = params['sigma']\n", " rho = (sigma - 1) / sigma\n", " \n", " # nest Cobb-Douglas technology as special case\n", " if rho == 0:\n", " y = k**alpha\n", " else:\n", " y = (alpha * k**rho + (1-alpha))**(1 / rho)\n", " \n", " return y" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### (5 points) Part d)\n", "\n", "Using your results from part b, complete the Python function below which defines the marginal product of capital (per person/effective person) in terms of capital (per person/effective person) and model parameters." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# you were given the following incomplete code...\n", "def marginal_product_capital(t, k, params):\n", " \"\"\"\n", " Marginal product of capital with CES production function.\n", "\n", " Arguments:\n", "\n", " t: (array-like) Time.\n", " k: (array-like) Capital (per person/effective person).\n", " params: (dict) Dictionary of parameter values.\n", " \n", " Returns:\n", "\n", " mpk: (array-like) Derivative of output with respect to capital, k.\n", "\n", " \"\"\"\n", " # extract params\n", " alpha = params['alpha']\n", " sigma = params['sigma']\n", " rho = # INSERT CODE HERE DEFINING RHO IN TERMS OF SIGMA!\n", " \n", " # nest Cobb-Douglas technology as special case\n", " if rho == 0:\n", " mpk = # INSERT CODE HERE!\n", " else:\n", " mpk = # INSERT CODE HERE!\n", " \n", " return mpk" ], "language": "python", "metadata": {}, "outputs": [] }, { "cell_type": "code", "collapsed": false, "input": [ "# which should be completed as follows...\n", "def marginal_product_capital(t, k, params):\n", " \"\"\"\n", " Marginal product of capital with CES production function.\n", "\n", " Arguments:\n", "\n", " t: (array-like) Time.\n", " k: (array-like) Capital (per person/effective person).\n", " params: (dict) Dictionary of parameter values.\n", " \n", " Returns:\n", "\n", " mpk: (array-like) Derivative of output with respect to capital, k.\n", "\n", " \"\"\"\n", " # extract params\n", " alpha = params['alpha']\n", " sigma = params['sigma']\n", " rho = (sigma - 1) / sigma\n", " \n", " # nest Cobb-Douglas technology as special case\n", " if rho == 0:\n", " mpk = alpha * k**(alpha - 1)\n", " else:\n", " mpk = alpha * k**(rho - 1) * (alpha * k**rho + (1 - alpha))**((1 / rho) - 1)\n", " \n", " return mpk" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### (5 points) Part e)\n", "\n", "Derive the equation of motion for capital per effective worker when the general CES production function defined by equation 1.2 and for the Cobb-Douglas special case defined by equation 1.5." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Answer:\n", "\n", "The key equation of the Solow model is the equation of motion for capital per effective worker, $k(t)=\\frac{K(t)}{A(t)L(t)}$. Application of the chain rule to $k(t)$ yields\n", "\n", "\\begin{align}\n", "\t\\dot{k}(t) =& \\frac{\\dot{K}A(t)L(t) - K(t)\\left[A(t)\\dot{L}(t) + \\dot{A}(t)L(t)\\right]}{[A(t)L(t)]^2} \\notag \\\\\n", "\t =& \\frac{\\dot{K}}{A(t)L(t)} - \\frac{K(t)}{A(t)L(t)}\\left(\\frac{\\dot{L}(t)}{L(t)} + \\frac{\\dot{A}(t)}{A(t)}\\right).\n", "\\end{align}\n", "\n", "From here I need only substitute the equation of motion for capital and the expressions for the exogenous growth rates of labor and technology to obtain a first-order non-linear differential equation describing the evolution of capital per effective worker, $k(t)$.\n", "\n", "\\begin{align}\n", "\t\\dot{k}(t) =& \\frac{sY(t) - \\delta K(t)}{A(t)L(t)} - \\frac{K(t)}{A(t)L(t)}\\left(\\frac{\\dot{L}(t)}{L(t)} + \\frac{\\dot{A}(t)}{A(t)}\\right) \\notag \\\\\n", "\t=& s\\frac{Y(t)}{A(t)L(t)} - (n + g + \\delta)\\frac{K(t)}{A(t)L(t)} \\notag \\\\\n", " =& sy(t) - (n + g + \\delta)k(t) \\notag \\\\\n", "\\end{align} \n", "\n", "When the production function is CES, the equation becomes\n", "\n", "\\begin{align}\n", "\t\\dot{k}(t) =& s\\bigg[\\alpha k(t)^{\\rho} + (1-\\alpha)\\bigg]^{\\frac{1}{\\rho}} - (n + g + \\delta)k(t).\n", "\\end{align} \n", "\n", "When the production function is Cobb-Douglas, the equation becomes\n", "\n", "\\begin{align}\n", "\t\\dot{k}(t) =& sk(t)^{\\alpha} - (n + g + \\delta)k(t).\n", "\\end{align} " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### (5 points) Part f)\n", "\n", "Using your results from parts d) and e) and the Python function defining the equation of motion for capital (per person/effective person) complete the Python function which defines the Jacobian for the Solow model." ] }, { "cell_type": "code", "collapsed": false, "input": [ "def equation_of_motion_capital(t, k, params):\n", " \"\"\"\n", " Equation of motion for capital (per person/effective person).\n", "\n", " Arguments:\n", "\n", " t: (array-like) Time.\n", " k: (array-like) Capital (per person/effective person).\n", " params: (dict) Dictionary of parameter values.\n", " \n", " Returns:\n", "\n", " k_dot: (array-like) Time-derivative of capital (per person/effective \n", " person).\n", "\n", " \"\"\"\n", " # extract params\n", " s = params['s']\n", " n = params['n']\n", " g = params['g']\n", " delta = params['delta']\n", " \n", " y = ces_output(t, k, params)\n", " \n", " k_dot = s * y - (n + g + delta) * k\n", " \n", " return k_dot" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 3 }, { "cell_type": "code", "collapsed": false, "input": [ "# you where given the following incomplete code...\n", "def solow_jacobian(t, k, params):\n", " \"\"\"\n", " The Jacobian of the Solow model.\n", " \n", " Arguments:\n", "\n", " t: (array-like) Time.\n", " k: (array-like) Capital (per person/effective person).\n", " params: (dict) Dictionary of parameter values.\n", " \n", " Returns:\n", "\n", " jac: (array-like) Value of the derivative of the equation of \n", " motion for capital (per worker/effective worker) with \n", " respect to k.\n", "\n", " \"\"\"\n", " # extract params\n", " s = params['s']\n", " n = params['n']\n", " g = params['g']\n", " delta = params['delta']\n", "\n", " mpk = #INSERT YOUR CODE HERE\n", " \n", " k_dot = s * mpk - (n + g + delta)\n", " \n", " return k_dot" ], "language": "python", "metadata": {}, "outputs": [] }, { "cell_type": "code", "collapsed": false, "input": [ "# which should have been completed as follows...\n", "def solow_jacobian(t, k, params):\n", " \"\"\"\n", " The Jacobian of the Solow model.\n", " \n", " Arguments:\n", "\n", " t: (array-like) Time.\n", " k: (array-like) Capital (per person/effective person).\n", " params: (dict) Dictionary of parameter values.\n", " \n", " Returns:\n", "\n", " jac: (array-like) Value of the derivative of the equation of \n", " motion for capital (per worker/effective worker) with \n", " respect to k.\n", "\n", " \"\"\"\n", " # extract params\n", " s = params['s']\n", " n = params['n']\n", " g = params['g']\n", " delta = params['delta']\n", "\n", " mpk = marginal_product_capital(t, k, params) \n", " \n", " k_dot = s * mpk - (n + g + delta)\n", " \n", " return k_dot" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### (5 points) Part g)\n", "\n", "In the cell below, create a Python dictionary called `default_params` using the following values: $\\alpha$ = 0.33, $\\delta$ = 0.04, $\\sigma$ = 1.0, $g$ = 0.02, $n$ = 0.01, $s$ = 0.15, $L(0)$=1.0, $A(0)$=1.0." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# INSERT CODE HERE!" ], "language": "python", "metadata": {}, "outputs": [] }, { "cell_type": "code", "collapsed": false, "input": [ "# my solution...\n", "default_params = {'alpha':0.5, 'delta':0.04, 'sigma':1.05, 'g':0.02, \n", " 'n':0.01, 's':0.15, 'A0':1.0, 'L0':1.0} " ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 60 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### (5 points) Part h)\n", "In the cell below, create instance of the `SolowModel` class called `model` using the results from parts c), d), f) and g)." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# INSERT CODE HERE!" ], "language": "python", "metadata": {}, "outputs": [] }, { "cell_type": "code", "collapsed": false, "input": [ "# my solution...\n", "model = growth.SolowModel(output=ces_output, \n", " mpk=marginal_product_capital,\n", " k_dot=equation_of_motion_capital, \n", " jacobian=solow_jacobian,\n", " params=default_params)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 61 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### (10 points) Part i)\n", "\n", "Derive an analytic expression for the steady state value of capital (per person/effective person) using your result from part e) and use your result to complete the Python function in the cell below defining the analytic steady state value for $k$ as a function of model parameters." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Answer:\n", "When the production function is CES, the steady state value for capital (per person/effective person) is\n", "\n", "\\begin{align}\n", "0 =& s\\bigg[\\alpha k^{*\\rho} + (1-\\alpha)\\bigg]^{\\frac{1}{\\rho}} - (n + g + \\delta)k^* \\\\\n", "s\\bigg[\\alpha k^{*\\rho} + (1-\\alpha)\\bigg]^{\\frac{1}{\\rho}} =& (n + g + \\delta)k^* \\\\\n", "s^{\\rho}\\bigg[\\alpha k^{*\\rho} + (1-\\alpha)\\bigg] =& (n + g + \\delta)^{\\rho}k^{*\\rho} \\\\\n", "\\alpha s^{\\rho} k^{*\\rho} + (1-\\alpha)s^{\\rho} =& (n + g + \\delta)^{\\rho}k^{*\\rho} \\\\\n", "(1-\\alpha)s^{\\rho} =& (n + g + \\delta)^{\\rho}k^{*\\rho} - \\alpha s^{\\rho} k^{*\\rho} \\\\\n", "(1-\\alpha)s^{\\rho} =& \\bigg((n + g + \\delta)^{\\rho} - \\alpha s^{\\rho}\\bigg) k^{*\\rho} \\\\\n", "k^{*\\rho} =& \\frac{(1-\\alpha)s^{\\rho}}{(n + g + \\delta)^{\\rho} - \\alpha s^{\\rho}} \\\\\n", "k^* =& \\left(\\frac{(1-\\alpha)s^{\\rho}}{(n + g + \\delta)^{\\rho} - \\alpha s^{\\rho}}\\right)^{\\frac{1}{\\rho}} \\\\\n", "\\end{align}\n", "\n", "Note that in order for $k^* > 0$ we require that the parameter $\\alpha$ satisfies\n", "\n", "\\begin{align}\n", "\\alpha < \\bigg(\\frac{n+g+\\delta}{s}\\bigg)^{\\rho}.\n", "\\end{align}\n", "\n", "When the production function is Cobb-Douglas, the steady state value for capital (per person/effective person) is\n", "\n", "\\begin{align}\n", "0 =& sk^{*\\alpha} - (n + g + \\delta)k^* \\\\\n", "sk^{*\\alpha} =& (n + g + \\delta)k^* \\\\\n", "sk^{*\\alpha-1} =& (n + g + \\delta) \\\\\n", "k^{*\\alpha-1} =& \\frac{n + g + \\delta}{s} \\\\\n", "k^* =& \\left(\\frac{s}{n + g + \\delta}\\right)^{\\frac{1}{1-\\alpha}}\n", "\\end{align} " ] }, { "cell_type": "code", "collapsed": false, "input": [ "### you were given the following incomplete code...\n", "def analytic_k_star(params): \n", " \"\"\"Steady-state level of capital (per person/effective person).\"\"\"\n", " # extract params\n", " s = params['s']\n", " n = params['n']\n", " g = params['g']\n", " alpha = params['alpha']\n", " delta = params['delta']\n", " sigma = params['sigma']\n", " rho = # INSERT CODE HERE DEFINING RHO IN TERMS OF SIGMA!\n", " \n", " # nest Cobb-Douglas technology as special case\n", " if rho == 0:\n", " k_star = # INSERT CODE HERE!\n", " else:\n", " k_star = # INSERT CODE HERE!\n", " \n", " return k_star" ], "language": "python", "metadata": {}, "outputs": [] }, { "cell_type": "code", "collapsed": false, "input": [ "### which should be completed as follows...\n", "def analytic_k_star(params): \n", " \"\"\"Steady-state level of capital (per person/effective person).\"\"\"\n", " # extract params\n", " s = params['s']\n", " n = params['n']\n", " g = params['g']\n", " alpha = params['alpha']\n", " delta = params['delta']\n", " sigma = params['sigma']\n", " rho = (sigma - 1) / sigma\n", " \n", " # nest Cobb-Douglas as special case\n", " if rho == 0:\n", " k_star = (s / (n + g + delta))**(1 / (1 - alpha))\n", " else:\n", " k_star = (((1 - alpha) * s**rho) / ((n + g + delta)**rho - alpha * s**rho))**(1 / rho)\n", " \n", " return k_star" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 11 }, { "cell_type": "code", "collapsed": false, "input": [ "def isfinite_k_star(params):\n", " \"\"\"Returns true if parameters are consistent with a finite k*.\"\"\"\n", " # extract params\n", " s = params['s']\n", " n = params['n']\n", " g = params['g']\n", " alpha = params['alpha']\n", " delta = params['delta']\n", " sigma = params['sigma']\n", " rho = (sigma - 1) / sigma\n", " \n", " return alpha < ((n + g + delta) / s)**rho" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 12 }, { "cell_type": "code", "collapsed": false, "input": [ "isfinite_k_star(default_params)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 13, "text": [ "True" ] } ], "prompt_number": 13 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### (5 points) Part j)\n", "\n", "Using the code from the lab session as a guide, create a Python dictionary called `solow_steady_state_funcs` containing your result from part i) and add it to the model." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# INSERT YOUR CODE HERE!!" ], "language": "python", "metadata": {}, "outputs": [] }, { "cell_type": "code", "collapsed": false, "input": [ "# create a dictionary of steady state expressions...\n", "solow_steady_state_funcs = {'k_star':analytic_k_star}\n", "\n", "# add the dictionary of functions to the model\n", "model.steady_state.set_functions(solow_steady_state_funcs)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 62 }, { "cell_type": "code", "collapsed": false, "input": [ "# compute the steady state values\n", "model.steady_state.set_values()" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 63 }, { "cell_type": "code", "collapsed": false, "input": [ "# compare this result to the one you obtained from part i\n", "model.steady_state.values" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 64, "text": [ "{'k_star': 4.72555503663348}" ] } ], "prompt_number": 64 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Execute the code in the cell below to calibrate the model for the U.S. using data from the Penn World Tables." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# calibrate the model!\n", "growth.calibrate_ces(model, 'USA', x0=[0.75, 1.01], method='Nelder-Mead', bounds=None)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Optimization terminated successfully.\n", " Current function value: 0.624288\n", " Iterations: 62\n", " Function evaluations: 145\n" ] } ], "prompt_number": 84 }, { "cell_type": "code", "collapsed": false, "input": [ "# display the parameters...\n", "model.params" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 85, "text": [ "{'A0': 121.54997789817465,\n", " 'L0': 61.971196530271804,\n", " 'alpha': 0.91456643533201798,\n", " 'delta': 0.03761163,\n", " 'g': 0.03629411526782518,\n", " 'n': 0.015525562239498985,\n", " 's': 0.20732178,\n", " 'sigma': 0.78943070081394473}" ] } ], "prompt_number": 85 }, { "cell_type": "code", "collapsed": false, "input": [ "# check that k_star is finite!\n", "isfinite_k_star(model.params)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 86, "text": [ "True" ] } ], "prompt_number": 86 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### (5 points) Part k)\n", "\n", "Using the code examples from the lab as a guide, generate a plot of the Solow diagram demonstrating how the output, actual investment, and breakeven investment curves shift as a result of a 50% *increase* in $\\sigma$ (i.e., the elasticity of substitution between capital and effective labor). Explain why, and in which direction, each curve shifts. Discuss the impact on the steady state levels of capital, output, and consumption per effective person." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# here is the code for generating the plot...\n", "plt.figure(figsize=(8,6))\n", "model.plot_solow_diagram(gridmax=300, N=1000, param='sigma', shock=1.05, reset=True) \n", "plt.show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAfcAAAGYCAYAAABf16uoAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nBEEQUwySO0EQBEFMMUjuBEEQBDHF+H+hKnQtJrLSAgAAAABJRU5ErkJggg==\n", "text": [ "