{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "#### [**NICOLAS CACHANOSKY**](http://www.ncachanosky.com) | Department of Economics | Metropolitan State University of Denver | ncachano@msudenver.edu" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# A SIMPLE RAMSEY MODEL\n", "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This note illustrates how to code a simple Ramsey model in Python. The purpose of the note is to walk through Python applications, not to offer a detailed discussion of Ramsey model or to show best coding practices. The note also assumes familiarity with Ramsey model and a beginner experience with Python.\n", "\n", "For a more complete and detailed discussion of Python applications see the material in [Quant Econ](https://quantecon.org/).\n", "\n", "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## TABLE OF CONTENTS\n", "1. [Description of the model](#1.-DESCRIPTION-OF-THE-MODEL)\n", "2. [The respresentative household](#2.-THE-REPRESENTATIVE-HOUSEHOLD)\n", "3. [The Representative Firm](#3.-THE-REPRESENTATIVE-FIRM)\n", "4. [Equilibrium](#4.-EQUILIBRIUM)\n", "5. [The code](#5.-THE-CODE)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1. DESCRIPTION OF THE MODEL" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A known issue with the Solow model is that the savings rate is exogenous (and constant). This means the ratio of consumption to income $Y/C$ is also constant. While the Solow model can be useful to highlight some features of long-run growth, this assumption also limits the applicability of this model. Yet, the Solow model can be interpreted as a specIal case of Ramsey model (or Ramsey-Kass-Koopmans model). Ramsey model can be considered as the building block of macro models with a household that optimizes its utility and, therefore, endogenously sets the savings rate.\n", "\n", "This note presents a \"simple\" Ramsey model (it offers a simplified discussion, does not discuss shocks, and does not add other features). For a more complete and detailed discussion see an advanced macroeconomics textbook. \n", "\n", "The model is populated by a representative household that maximizes its utility and by a representative firm that maximizes its profits. The model assumes a competitive market (no monopoly power, agents are price takers, etc.) The household provides labor services to the firm in exchange of a wage. The wage can be used to consume goods or save and accumulate assets. The model assumes a closed economy with no government. Finally, the model is presented in continuous (rather than discrete) time. A \"dot\" on top of a variable denotes its instantaneous time-change $(\\dot x (t) = \\frac{\\partial x}{\\partial t})$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 2. THE REPRESENTATIVE HOUSEHOLD" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Assume a large number of identicial infinitely-lived households. Because these households are identical, we can use a **representative** household to populate the model. The assumptions that this households are infinitely lived captures a continuum of generations. The representative household has $L(t)$ individuals with a population growth rate of $n$. Therefore, $L(t) = L(0) \\cdot e^{nt}$\n", "\n", "## 2.1. THE HOUSEHOLD UTILITY\n", "\n", "The household utility $(U)$ is the present value of the utility (felicity function) of all household individuals $(u(c))$.\n", "\n", "\$$\n", " U = \\int_{0}^{\\infty} u[c(t)] \\cdot e^{nt} \\cdot \\underbrace{e^{-\\rho t}}_{L(t)} \\cdot dt = \\int_{0}^{\\infty} u[c(t)] \\cdot e^{(n-\\rho)t} \\cdot dt\n", "\$$\n", "\n", "where $\\rho > 0$ is the time preference of the household individual and where $n -\\rho >0$. Also, $u(c)$ is concave $(u^{'}(c) > 0, u^{''}(c) < 0)$ and satisfies the Inada conditions $(u^{'}(c) \\to \\infty \\text{ as } c \\to 0 \\text{, and } u^{'}(c) \\to 0 \\text{ as } c \\to \\infty$.\n", "\n", "The parameter $\\rho$ can be interpreted as the time preference of the household or as capturing a discount of the future generation by the present generations. If $\\rho = 1$, then present generation assigns equal \"value\" to the next generatio (i.e. parents with respect to their kids). If $\\rho < 0$, then the present generation is altruistic and values the utility of the next generation more than their own.\n", "\n", "## 2.2. THE HOUSEHOLD BUDGET CONSTRAINT\n", "\n", "The household budget constrained is composed of assets $(\\Lambda)$ and wages $(w)$. The non-consumed wage becames an increase in assets. At some period in time, assets can be negative, which means that in that period the household has a net debt. Assets have a rate of return of $r$. Therefore, the stock of assets increase by the return of the assets plus wages, and decrease by the amount of consumption. Since population growths at rate $n$, the change in household's assets can be represented as follows.\n", "\n", "\$$\n", " \\frac{d\\Lambda}{dt} = r(t) \\cdot \\Lambda(t) + w(t)L(t) - C(t)\n", "\$$\n", "\n", "\n", "Dividing by $L(t)$ we get the change in assets per capita $(a)$ (and dropping the $t$ variable for notation simplicity):\n", "\n", "\\begin{align}\n", " \\dot{\\left(\\frac{A}{L} \\right)} &= \\frac{\\dot{A}L - A \\dot{L}}{L^2} \\\\\n", " \\dot{a} &= \\frac{\\dot{A}}{L} - \\frac{A}{L}n \\\\\n", " \\dot{a} &= ra + w - c - na \\\\\n", " \\dot{a} &= (r - n)a + w - c\n", "\\end{align}\n", "\n", "To avoid the situation where the household borrows money indifenetely, the model also imposses a \"no Ponzi game condition\". Intuitively, at the end of the household life $(T)$, assets have to be at least zero $a(T) \\geq 0$. A household may have debt at any point in time, but at the end of its lifetime all debts are paid. The present value of the assets have to be asymptotically nonnegative.\n", "\n", "\$$\n", " \\lim\\limits_{t \\to \\infty} a(t) e^{-\\tilde{r}(t)} \\geq 0\n", "\$$\n", "\n", "where $\\tilde{r}(t) = \\int_{0}^{t} (r(\\tau) - n) d\\tau$. This expression means that any moment $\\tau \\in (0, \\infty)$, the present value of $a$ cannot be negative. Note that $\\tilde{r}$ is taking into consideration the growht rate of the household as well $n$. In a more simple notation, this condition can be written as $\\lim\\limits_{t \\to \\infty} a(t) \\geq 0$.\n", "\n", "## 2.3. THE HOUSEHOLD OPTIMIZATION PROBLEM\n", "\n", "The household is facing a dynamic optimization problem. It needs to set the path of consumption that maximizes the present value of its life utility. The optimization problem can be described with the following equations (where $n - \\rho > 0$).\n", "\n", "\\begin{align}\n", " \\max_{c(t)} U &= \\int_{t=0}^{\\infty} u[c(t)] \\cdot e^{-(n-\\rho)t} \\\\\n", " \\text{subject to:} \\\\\n", " \\dot{a} &= (r(t) - n)a(t) + w(t) - c(t) \\\\\n", " a(0) &= a_{0} \\\\\n", " \\lim\\limits_{t \\to \\infty}a(t) &\\geq 0 \\\\\n", " \\text{transversality condition:} \\\\\n", " \\lim\\limits_{t \\to \\infty} \\mu(t) \\cdot a(t) = 0\n", "\\end{align}\n", "\n", "The optimization problem is given an initial asset value of $a_0$ and a terminal condition for which assets cannot be negative. Let $\\mathscr{H}$ be the present-value Hamiltonian:\n", "\n", "\$$\n", " \\mathscr{H} = e^{-(\\rho - n)t} \\cdot u[c(t)] + \\mu(t) \\cdot \\left[r(t) - n)a(t) + w(t) - c(t) \\right] \n", "\$$\n", "\n", "where $\\mu(t)$ is the present-value shadow price. Since the household faces an optimization problem at each moment $t$, the shadow price may vary over time as well. The \"transversality condition\" states that in the limit, either the shadow price or the assets have to be zero. \n", "\n", "The first-order-conditions (FOC) of the hamiltonian are:\n", "\n", "\\begin{align}\n", " \\frac{\\partial \\mathscr{H}}{\\partial c} &= e^{-(\\rho - n)t} \\cdot u'_{c} - \\mu(t) = 0 \\\\\n", " \\frac{\\partial\\mathscr{H}}{\\partial\\mu} &= (r(t) - n)a(t) + w(t) - c(t) = \\dot{a} \\\\\n", " \\frac{\\partial \\mathscr{H}}{\\partial a} &= - (r(t) - n)\\cdot \\mu (t) = \\dot{\\mu}(t)\n", "\\end{align}\n", "\n", "Now we proceed to use the first equation to get $\\dot{\\mu}(t)$.\n", "\n", "\\begin{align}\n", " \\mu(t) &= e^{-(\\rho - n)t} \\cdot u'_{c} \\\\\n", " \\dot{\\mu}(t) &= -(\\rho - n) \\cdot e^{-(\\rho - n)t} \\cdot u'_{c} + e^{-(\\rho - n)t} \\cdot u''_c \\cdot \\dot{c}\n", "\\end{align} \n", "\n", "Make now two substitutions: (1) The first FOC in the third FOC, and (2) this last derivative in the third FOC as well.\n", "\n", "\\begin{align}\n", " -[r(t) -n] \\cdot \\mu(t) &= -(\\rho - n) \\cdot e^{-(\\rho - n)t} \\cdot u'(c) + e^{-(\\rho - n)t} \\cdot u''(c) \\cdot \\dot{c} \\\\[10pt]\n", " -[r(t) -n] \\cdot e^{-(\\rho - n)t} \\cdot u'(c) &= e^{-(\\rho - n)t} \\left[-(\\rho - n) \\cdot u'(c) + u''(c) \\cdot \\dot{c} \\right] \\\\[10pt]\n", " -[r(t) -n] \\cdot u'(c) &= -(\\rho - n) \\cdot u'(c) + u''(c) \\cdot \\dot{c} \\\\[10pt]\n", " r(t) &= \\rho - \\frac{u''(c)\\cdot c}{u'(c)} \\cdot \\frac{\\dot{c}}{c}\n", "\\end{align}\n", " \n", "The last equation is the **Euler equation**, which defines the path for $c$ given the rate of return $r(t)$. Recall that $u''(c)<0$ and therefore $\\frac{u''(c)c}{u'(c)}>0$. The right-hand side of the equation can be interpreted as the \"rate of return of consumption.\" Consumers would like to smooth consumption in time. Therefore, the rate of return $(r)$ has to be equal to the time preference $(\\rho)$ minus the change of consumption over time. Or, put it differently, if $r = \\rho$, then consumption will be flat. There is no opportunity to increase utility by moving consumption over time (extend a loan and postpone consumption or take a debt and advance consumption). Consumers will be willing to postpone consumption if $r$ is sufficiently above $\\rho$. The required compensation to postpone consumption is the second term in the righ-hand side of the equation.\n", "\n", "\\begin{align}\n", " r &= \\rho \\to \\frac{\\dot{c}}{c} = 0 \\\\\n", " r &> \\rho \\to \\frac{\\dot{c}}{c} > 0 \\text{ (saving today: postpone present consumption)} \\\\\n", " r &< \\rho \\to \\frac{\\dot{c}}{c} < 0 \\text{ (consuming today: advance future consumption)}\n", "\\end{align}\n", "\n", "The Euler equation also includes the elasticity of marginal utility: $\\frac{u''(c)\\cdot c}{u'(c)}$. For $r$ and $\\frac{\\dot{c}}{c}$ to be constant, this elasticity of marginal utility has to be constant. A common practice is to assume a CRRA (constant relative risk aversion) utility function that depicts constant intertemporal elasticity of substitution (CIES).\n", "\n", "\$$\n", " u(c) = \\frac{c^{1-\\theta}-1}{1-\\theta}\n", "\$$\n", "\n", "where $\\theta > 0$ is the coefficient of relative risk aversion. The $1 - \\theta$ denominator assures the function will keep its desired properties of the function $(u'>0, u''<0)$ even if $\\theta > 1$ (see below). The inclution of the term $-1/(1-\\theta)$ is for convenience; when $\\theta \\to 1$ then the CRRA function becomes $(u(c) = log(c))$. Consider now the first and second derivative of the CRRA function and the elasticity of substitution $(\\sigma)$.\n", "\n", "\\begin{align}\n", " u'(c) &= c^{-\\theta} > 0 \\\\\n", " u''(c) &= -\\theta \\cdot c^{-(\\theta + 1)} < 0 \\\\\n", " \\sigma &= \\left[ \\frac{u''(c) \\cdot c}{u'(c)} \\right]^{-1} = \\left[\\frac{\\theta \\cdot c^{-(\\theta + 1)} \\cdot c}{c^{-\\theta}} \\right]^{-1} = \\frac{1}{\\theta}\n", "\\end{align}\n", "\n", "Then, the Euler equation from the household maximization problem becomes\n", "\n", "\\begin{align}\n", " r(t) &= \\rho - \\frac{u''(c)\\cdot c}{u'(c)} \\cdot \\frac{\\dot{c}}{c} \\\\\n", " r(t) &= \\rho - \\theta \\cdot \\frac{\\dot{c}}{c} \\\\\n", "\\end{align}\n", "\n", "We can rewrite the Euler equation to more conveniently depict the consumption path that maximizes the household utility.\n", "\n", "\$$\n", " \\frac{\\dot{c}}{c} = \\frac{1}{\\theta} \\cdot \\left(r(t) - \\rho \\right)\n", "\$$\n", "\n", "This is one of the two equations that describes Ramsey model. The second equation is derived from the firms profit maximization problem (next section).\n", "\n", "---\n", "\n", "The following code plots the utility function for different levels of $\\theta$. The function also allows for $\\theta = 1$, in such case the utility function becomes the log of consumption." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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