{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "(bcg_complete_mkts_final)=\n", "```{raw} html\n", "
\n", " \n", " \"QuantEcon\"\n", " \n", "
\n", "```\n", "\n", "# Irrelevance of Capital Structures with Complete Markets\n", "\n", "```{contents} Contents\n", ":depth: 2\n", "```\n", "\n", "In addition to what's in Anaconda, this lecture will need the following libraries:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "tags": [ "hide-output" ] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Requirement already up-to-date: quantecon in /Users/matthewmckay/anaconda3/envs/quantecon/lib/python3.8/site-packages (0.4.8)\r\n", "Requirement already satisfied, skipping upgrade: numpy in /Users/matthewmckay/anaconda3/envs/quantecon/lib/python3.8/site-packages (from quantecon) (1.18.5)\r\n", "Requirement already satisfied, skipping upgrade: sympy in /Users/matthewmckay/anaconda3/envs/quantecon/lib/python3.8/site-packages (from quantecon) (1.6.1)\r\n", "Requirement already satisfied, skipping upgrade: requests in /Users/matthewmckay/anaconda3/envs/quantecon/lib/python3.8/site-packages (from quantecon) (2.24.0)\r\n", "Requirement already satisfied, skipping upgrade: numba>=0.38 in /Users/matthewmckay/anaconda3/envs/quantecon/lib/python3.8/site-packages (from quantecon) (0.50.1)\r\n", "Requirement already satisfied, skipping upgrade: scipy>=1.0.0 in /Users/matthewmckay/anaconda3/envs/quantecon/lib/python3.8/site-packages (from quantecon) (1.5.0)\r\n", "Requirement already satisfied, skipping upgrade: mpmath>=0.19 in /Users/matthewmckay/anaconda3/envs/quantecon/lib/python3.8/site-packages (from sympy->quantecon) (1.1.0)\r\n", "Requirement already satisfied, skipping upgrade: idna<3,>=2.5 in /Users/matthewmckay/anaconda3/envs/quantecon/lib/python3.8/site-packages (from requests->quantecon) (2.10)\r\n", "Requirement already satisfied, skipping upgrade: certifi>=2017.4.17 in /Users/matthewmckay/anaconda3/envs/quantecon/lib/python3.8/site-packages (from requests->quantecon) (2020.6.20)\r\n", "Requirement already satisfied, skipping upgrade: urllib3!=1.25.0,!=1.25.1,<1.26,>=1.21.1 in /Users/matthewmckay/anaconda3/envs/quantecon/lib/python3.8/site-packages (from requests->quantecon) (1.25.9)\r\n", "Requirement already satisfied, skipping upgrade: chardet<4,>=3.0.2 in /Users/matthewmckay/anaconda3/envs/quantecon/lib/python3.8/site-packages (from requests->quantecon) (3.0.4)\r\n", "Requirement already satisfied, skipping upgrade: llvmlite<0.34,>=0.33.0.dev0 in /Users/matthewmckay/anaconda3/envs/quantecon/lib/python3.8/site-packages (from numba>=0.38->quantecon) (0.33.0+1.g022ab0f)\r\n", "Requirement already satisfied, skipping upgrade: setuptools in /Users/matthewmckay/anaconda3/envs/quantecon/lib/python3.8/site-packages (from numba>=0.38->quantecon) (49.2.0.post20200714)\r\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Requirement already satisfied: interpolation in /Users/matthewmckay/anaconda3/envs/quantecon/lib/python3.8/site-packages (2.1.6)\r\n", "Requirement already satisfied: tempita>=0.5.2 in /Users/matthewmckay/anaconda3/envs/quantecon/lib/python3.8/site-packages (from interpolation) (0.5.2)\r\n", "Requirement already satisfied: numpy>=1.18.1 in /Users/matthewmckay/anaconda3/envs/quantecon/lib/python3.8/site-packages (from interpolation) (1.18.5)\r\n", "Requirement already satisfied: scipy>=1.4.1 in /Users/matthewmckay/anaconda3/envs/quantecon/lib/python3.8/site-packages (from interpolation) (1.5.0)\r\n", "Requirement already satisfied: numba>=0.47 in /Users/matthewmckay/anaconda3/envs/quantecon/lib/python3.8/site-packages (from interpolation) (0.50.1)\r\n", "Requirement already satisfied: llvmlite<0.34,>=0.33.0.dev0 in /Users/matthewmckay/anaconda3/envs/quantecon/lib/python3.8/site-packages (from numba>=0.47->interpolation) (0.33.0+1.g022ab0f)\r\n", "Requirement already satisfied: setuptools in /Users/matthewmckay/anaconda3/envs/quantecon/lib/python3.8/site-packages (from numba>=0.47->interpolation) (49.2.0.post20200714)\r\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Collecting package metadata (current_repodata.json): - " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\\ " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b| " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b/ " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b- " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\\ " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b| " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b/ " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b- " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\\ " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b| " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b/ " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b- " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\\ " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b| " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b/ " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b- " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\\ " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b| " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b/ " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b- " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\\ " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b| " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b/ " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b- " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\\ " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b| " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b/ " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b- " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\\ " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b| " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b/ " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b- " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\\ " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b| " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b/ " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b- " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\\ " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b| " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b/ " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b- " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\\ " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b| " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b/ " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b- " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\\ " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b| " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b/ " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b- " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\\ " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b| " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b/ " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b- " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\\ " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b| " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b/ " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b- " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\\ " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b| " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\bdone\r\n", "Solving environment: - " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\\ " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b| " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b/ " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b- " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\\ " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b| " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b/ " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b- " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\\ " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b| " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b/ " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b- " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\\ " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b| " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b/ " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b- " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\\ " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b| " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b/ " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b- " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\\ " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b| " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b/ " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b- " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\\ " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b| " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b/ " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b- " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\\ " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b| " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\bdone\r\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\r\n", "\r\n", "==> WARNING: A newer version of conda exists. <==\r\n", " current version: 4.8.5\r\n", " latest version: 4.9.0\r\n", "\r\n", "Please update conda by running\r\n", "\r\n", " $ conda update -n base conda\r\n", "\r\n", "\r\n", "\r\n", "# All requested packages already installed.\r\n", "\r\n" ] } ], "source": [ "!pip install --upgrade quantecon\n", "!pip install interpolation\n", "!conda install -y -c plotly plotly plotly-orca" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Introduction\n", "\n", "This is a prolegomenon to another lecture {doc}`BCG_incomplete_mkts ` about a model with\n", "incomplete markets authored by Bisin, Clementi, and Gottardi {cite}`BCG_2018`.\n", "\n", "We adopt specifications of preferences and technologies very close to\n", "Bisin, Clemente, and Gottardi’s but unlike them assume that there are complete\n", "markets in one-period Arrow securities.\n", "\n", "This simplification of BCG’s setup helps us by\n", "\n", "- creating a benchmark economy to compare with outcomes in BCG’s\n", " incomplete markets economy\n", "- creating a good guess for initial values of some equilibrium objects\n", " to be computed in BCG’s incomplete markets economy via an iterative\n", " algorithm\n", "- illustrating classic complete markets outcomes that include\n", " - indeterminacy of consumers’ portfolio choices\n", " - indeterminacy of firms' financial structures that underlies a\n", " Modigliani-Miller theorem {cite}`Modigliani_Miller_1958`\n", "- introducing `Big K, little k` issues in a simple context that will\n", " recur in the BCG incomplete markets environment\n", "\n", "A Big K, little k analysis also played roles in [this quantecon lecture](https://python.quantecon.org/cass_koopmans.html) as well as\n", "[here](https://python.quantecon.org/rational_expectations.html) and {doc}`here `.\n", "\n", "### Setup\n", "\n", "The economy lasts for two periods, $t=0, 1$.\n", "\n", "There are two types of consumers named $i=1,2$.\n", "\n", "A scalar random variable $\\epsilon$ with probability density $g(\\epsilon)$ affects both\n", "\n", "- the return in period $1$ from investing\n", " $k \\geq 0$ in physical capital in period $0$.\n", "- exogenous period $1$ endowments of the consumption good for\n", " agents of types $i =1$ and $i=2$.\n", "\n", "Type $i=1$ and $i=2$ agents’ period $1$ endowments are\n", "correlated with the return on physical capital in different ways.\n", "\n", "We discuss two arrangements:\n", "\n", "- a command economy in which a benevolent planner chooses $k$ and\n", " allocates goods to the two types of consumers in each period and each random\n", " second period state\n", "- a competitive equilibrium with markets in claims on physical capital\n", " and a complete set (possibly a continuum) of one-period Arrow\n", " securities that pay period $1$ consumption goods contingent on\n", " the realization of random variable $\\epsilon$.\n", "\n", "### Endowments\n", "\n", "There is a single consumption good in period $0$ and at each\n", "random state $\\epsilon$ in period $1$.\n", "\n", "Economy-wide endowments in periods $0$ and $1$ are\n", "\n", "$$\n", "\\begin{aligned}\n", "w_0 & \\cr\n", "w_1(\\epsilon) & \\textrm{ in state }\\epsilon\n", "\\end{aligned}\n", "$$\n", "\n", "Soon we’ll explain how aggregate endowments are divided between\n", "type $i=1$ and type $i=2$ consumers.\n", "\n", "We don’t need to do that in order to describe a social planning problem.\n", "\n", "### Technology:\n", "\n", "Where $\\alpha \\in (0,1)$ and $A >0$\n", "\n", "$$\n", "\\begin{aligned}\n", " c_0^1 + c_0^2 + k & = w_0^1 + w_0^2 \\cr\n", " c_1^1(\\epsilon) + c_1^2(\\epsilon) & = w_1^1(\\epsilon) + w_1^2(\\epsilon) + e^\\epsilon A k^\\alpha, \\quad k \\geq 0\n", "\\end{aligned}\n", "$$\n", "\n", "### Preferences:\n", "\n", "A consumer of type $i$ orders period $0$ consumption\n", "$c_0^i$ and state $\\epsilon$, period $1$ consumption\n", "$c^i_1(\\epsilon)$ by\n", "\n", "$$\n", "u^i = u(c_0^i) + \\beta \\int u(c_1^i(\\epsilon)) g (\\epsilon) d \\epsilon, \\quad i = 1,2\n", "$$\n", "\n", "$\\beta \\in (0,1)$ and the one-period utility function is\n", "\n", "$$\n", "u(c) = \\begin{cases}\n", "\\frac{c^{1 -\\gamma}} { 1 - \\gamma} & \\textrm{if } \\gamma \\neq 1 \\\\\n", "\\log c & \\textrm{if } \\gamma = 1\n", "\\end{cases}\n", "$$\n", "\n", "### Parameterizations\n", "\n", "Following BCG, we shall employ the following parameterizations:\n", "\n", "$$\n", "\\begin{aligned}\n", "\\epsilon & \\sim {\\mathcal N}(\\mu, \\sigma^2) \\cr\n", "u(c) & = \\frac{c^{1-\\gamma}}{1 - \\gamma} \\cr\n", "w_1^i(\\epsilon) & = e^{- \\chi_i \\mu - .5 \\chi_i^2 \\sigma^2 + \\chi_i \\epsilon} , \\quad \\chi_i \\in [0,1]\n", "\\end{aligned}\n", "$$\n", "\n", "Sometimes instead of asuming $\\epsilon \\sim g(\\epsilon) = {\\mathcal N}(0,\\sigma^2)$,\n", "we’ll assume that $g(\\cdot)$ is a probability\n", "mass function that serves as a discrete approximation to a standardized\n", "normal density.\n", "\n", "### Pareto criterion and planning problem\n", "\n", "The planner’s objective function is\n", "\n", "$$\n", "\\textrm{obj} = \\phi_1 u^1 + \\phi_2 u^2 , \\quad \\phi_i \\geq 0, \\quad \\phi_1 + \\phi_2 = 1\n", "$$\n", "\n", "where $\\phi_i \\geq 0$ is a Pareto weight that the planner attaches\n", "to a consumer of type $i$.\n", "\n", "We form the following Lagrangian for the planner’s problem:\n", "\n", "$$\n", "\\begin{aligned} L & = \\sum_{i=1}^2 \\phi_i \\left[ u(c_0^i) + \\beta \\int u(c_1^i(\\epsilon)) g (\\epsilon) d \\epsilon \\right] \\cr\n", " & + \\lambda_0 \\left[ w_0^1 + w_0^2 - k - c_0^1 - c_0^2 \\right] \\cr\n", " & + \\beta \\int \\lambda_1(\\epsilon) \\left[ w_1^1(\\epsilon) + w_1^2(\\epsilon) + e^\\epsilon A k^\\alpha -\n", " c_1^1(\\epsilon) - c_1^2(\\epsilon)\\right] g(\\epsilon) d\\epsilon\n", "\\end{aligned}\n", "$$\n", "\n", "First-order necessary optimality conditions for the planning problem are:\n", "\n", "$$\n", "\\begin{aligned}\n", "c_0^1: \\quad & \\phi_1 u'(c_0^1) - \\lambda_0 = 0 \\cr\n", "c_0^2: \\quad & \\phi_2 u'(c_0^2) - \\lambda_0 = 0 \\cr\n", "c_1^1(\\epsilon): \\quad & \\phi_1 \\beta u'(c_1^1(\\epsilon)) g(\\epsilon) - \\beta \\lambda_1 (\\epsilon) g (\\epsilon) = 0 \\cr\n", "c_1^2(\\epsilon):\\quad & \\phi_2 \\beta u'(c_1^2(\\epsilon)) g(\\epsilon) - \\beta \\lambda_1 (\\epsilon) g (\\epsilon) = 0 \\cr\n", "k: \\quad & -\\lambda_0 + \\beta \\alpha A k^{\\alpha -1} \\int \\lambda_1(\\epsilon) e^\\epsilon g(\\epsilon) d \\epsilon = 0\n", "\\end{aligned}\n", "$$\n", "\n", "The first four equations imply that\n", "\n", "$$\n", "\\begin{aligned}\n", "\\frac{u'(c_1^1(\\epsilon))}{u'(c_0^1))} & = \\frac{u'(c_1^2(\\epsilon))}{u'(c_0^2))} = \\frac{\\lambda_1(\\epsilon)}{\\lambda_0} \\cr\n", "\\frac{u'(c_0^1)}{u'(c_0^2)} & = \\frac{u'(c_1^1(\\epsilon))}{u'(c_1^2(\\epsilon))} = \\frac{\\phi_2}{\\phi_1}\n", "\\end{aligned}\n", "$$\n", "\n", "These together with the fifth first-order condition for the planner\n", "imply the following equation that determines an optimal choice of\n", "capital\n", "\n", "$$\n", "1 = \\beta \\alpha A k^{\\alpha -1} \\int \\frac{u'(c_1^i(\\epsilon))}{u'(c_0^i)} e^\\epsilon g(\\epsilon) d \\epsilon\n", "$$\n", "\n", "for $i = 1,2$.\n", "\n", "### Helpful observations and bookkeeping\n", "\n", "Evidently,\n", "\n", "$$\n", "u'(c) = c^{-\\gamma}\n", "$$\n", "\n", "and\n", "\n", "$$\n", "\\frac{u'(c^1)}{u'(c^2)} = \\left(\\frac{c^1}{c^2}\\right)^{-\\gamma} = \\frac{\\phi_2}{\\phi_1}\n", "$$\n", "\n", "where it is to be understood that this equation holds for $c^1 = c^1_0$ and $c^2 = c^2_0$ and also\n", "for $c^1 = c^1(\\epsilon)$ and $c^2 = c^2(\\epsilon)$ for all $\\epsilon$.\n", "\n", "With the same understanding, it follows that\n", "\n", "$$\n", "\\left(\\frac{c^1}{c^2}\\right) = \\left(\\frac{\\phi_2}{\\phi_1}\\right)^{- \\gamma^{-1}}\n", "$$\n", "\n", "Let $c= c^1 + c^2$.\n", "\n", "It follows from the preceding equation that\n", "\n", "$$\n", "\\begin{aligned}\n", " c^1 & = \\eta c \\cr\n", " c^2 & = (1 -\\eta) c\n", "\\end{aligned}\n", "$$\n", "\n", "where $\\eta \\in [0,1]$ is a function of $\\phi_1$ and\n", "$\\gamma$.\n", "\n", "Consequently, we can write the planner’s first-order condition for\n", "$k$ as\n", "\n", "$$\n", "1 = \\beta \\alpha A k^{\\alpha -1} \\int \\left( \\frac{w_1(\\epsilon) + A k^\\alpha e^\\epsilon}\n", " {w_0 - k } \\right)^{-\\gamma} e^\\epsilon g(\\epsilon) d \\epsilon\n", "$$\n", "\n", "which is one equation to be solved for $k \\geq 0$.\n", "\n", "Anticipating a `Big K, little k` idea widely used in macroeconomics,\n", "to be discussed in detail below, let $K$ be the value of $k$\n", "that solves the preceding equation so that\n", "\n", "```{math}\n", ":label: focke\n", "\n", "1 = \\beta \\alpha A K^{\\alpha -1} \\int \\left( \\frac{w_1(\\epsilon) + A K^\\alpha e^\\epsilon}\n", " {w_0 - K } \\right)^{-\\gamma} g(\\epsilon) e^\\epsilon d \\epsilon\n", "```\n", "\n", "The associated optimal consumption allocation is\n", "\n", "$$\n", "\\begin{aligned}\n", "C_0 & = w_0 - K \\cr\n", "C_1(\\epsilon) & = w_1(\\epsilon) + A K^\\alpha e^\\epsilon \\cr\n", "c_0^1 & = \\eta C_0 \\cr\n", "c_0^2 & = (1 - \\eta) C_0 \\cr\n", "c_1^1(\\epsilon) & = \\eta C_1 (\\epsilon) \\cr\n", "c_1^2 (\\epsilon) & = (1 - \\eta) C_1(\\epsilon)\n", "\\end{aligned}\n", "$$\n", "\n", "where $\\eta \\in [0,1]$ is the consumption share parameter\n", "mentioned above that is a function of the Pareto weight $\\phi_1$\n", "and the utility curvature parameter $\\gamma$.\n", "\n", "#### Remarks\n", "\n", "The relative Pareto weight parameter $\\eta$ does not appear in\n", "equation {eq}`focke` that determines $K$.\n", "\n", "Neither does it influence $C_0$ or $C_1(\\epsilon)$, which\n", "depend solely on $K$.\n", "\n", "The role of $\\eta$ is to determine how to allocate total\n", "consumption between the two types of consumers.\n", "\n", "Thus, the planner’s choice of $K$ does not interact with how it wants to allocate consumption.\n", "\n", "## Competitive equilibrium\n", "\n", "We now describe a competitive equilibrium for an economy that has\n", "specifications of consumer preferences, technology, and aggregate\n", "endowments that are identical to those in the preceding planning\n", "problem.\n", "\n", "While prices do not appear in the planning problem – only quantities do –\n", "prices play an important role in a competitive equilibrium.\n", "\n", "To understand how the planning economy is related to a competitive\n", "equilibrium, we now turn to the `Big K, little k` distinction.\n", "\n", "### Measures of agents and firms\n", "\n", "We follow BCG in assuming that there are unit measures of\n", "\n", "- consumers of type $i=1$\n", "- consumers of type $i=2$\n", "- firms with access to the production technology that converts\n", " $k$ units of time $0$ good into\n", " $A k^\\alpha e^\\epsilon$ units of the time $1$ good in\n", " random state $\\epsilon$\n", "\n", "Thus, let $\\omega \\in [0,1]$ index a particular consumer of type\n", "$i$.\n", "\n", "Then define Big $C^i$ as\n", "\n", "$$\n", "C^i = \\int_0^1 c^i(\\omega) d \\, \\omega\n", "$$\n", "\n", "In the same spirit, let $\\zeta \\in [0,1]$ index a particular firm.\n", "Then define Big $K$ as\n", "\n", "$$\n", "K = \\int_0^1 k(\\zeta) d \\, \\zeta\n", "$$\n", "\n", "The assumption that there are continua of our three types of\n", "agents plays an important role making each individual agent into a\n", "powerless **price taker**:\n", "\n", "- an individual consumer chooses its own (infinesimal) part\n", " $c^i(\\omega)$ of $C^i$ taking prices as given\n", "- an individual firm chooses its own (infinitesmimal) part\n", " $k(\\zeta)$ of $K$ taking prices as\n", "- equilibrium prices depend on the `Big K, Big C` objects\n", " $K$ and $C$\n", "\n", "Nevertheless, in equilibrium, $K = k, C^i = c^i$\n", "\n", "The assumption about measures of agents is thus a powerful device for\n", "making a host of competitive agents take as given equilibrium prices\n", "that are determined by the independent decisions of hosts of agents who behave just like they do.\n", "\n", "#### Ownership\n", "\n", "Consumers of type $i$ own the following exogenous quantities of\n", "the consumption good in periods $0$ and $1$:\n", "\n", "$$\n", "\\begin{aligned}\n", " w_0^i, & \\quad i = 1,2 \\cr\n", " w_1^i(\\epsilon) & \\quad i = 1,2\n", "\\end{aligned}\n", "$$\n", "\n", "where\n", "\n", "$$\n", "\\begin{aligned}\n", "\\sum_i w_0^i & = w_0 \\cr\n", "\\sum_i w_1^i(\\epsilon) & = w_1(\\epsilon)\n", "\\end{aligned}\n", "$$\n", "\n", "Consumers also own shares in a firm that operates the technology for converting\n", "nonnegative amounts of the time $0$ consumption good one-for-one\n", "into a capital good $k$ that produces\n", "$A k^\\alpha e^\\epsilon$ units of the time $1$ consumption good\n", "in time $1$ state $\\epsilon$.\n", "\n", "Consumers of types $i=1,2$ are endowed with $\\theta_0^i$\n", "shares of a firm and\n", "\n", "$$\n", "\\theta_0^1 + \\theta_0^2 = 1\n", "$$\n", "\n", "#### Asset markets\n", "\n", "At time $0$, consumers trade the following assets with other consumers\n", "and with firms:\n", "\n", "- equities (also known as stocks) issued by firms\n", "- one-period Arrow securities that pay one unit of consumption at time\n", " $1$ when the shock $\\epsilon$ assumes a particular value\n", "\n", "Later, we’ll allow the firm to issue bonds too, but\n", "not now.\n", "\n", "### Objects appearing in a competitive equilibrium\n", "\n", "Let\n", "\n", "- $a^i(\\epsilon)$ be consumer $i$ ’s purchases of claims\n", " on time $1$ consumption in state $\\epsilon$\n", "- $q(\\epsilon)$ be a pricing kernel for one-period Arrow\n", " securities\n", "- $\\theta_0^i \\geq 0$ be consumer $i$'s intial share of\n", " the firm, $\\sum_i \\theta_0^i =1$\n", "- $\\theta^i$ be the fraction of a firm’s shares purchased by\n", " consumer $i$ at time $t=0$\n", "- $- \\bar a^i(\\epsilon; \\theta^i)$ be debt limits constraining consumer $i$ ' s issues of claims\n", " on time $1$ consumption in state $\\epsilon$\n", "- $V$ be the value of the representative firm\n", "- $\\tilde V$ be the value of equity issued by the representative\n", " firm\n", "- $K, C_0$ be two scalars and $C_1(\\epsilon)$ a function\n", " that we use to construct a guess about an equilibrium pricing kernel\n", " for Arrow securities\n", "\n", "We proceed to describe constrained optimum problems faced by\n", "consumers and a representative firm in a competitive equilibrium.\n", "\n", "### A representative firm’s problem\n", "\n", "A representative firm takes Arrow security prices $q(\\epsilon)$ as\n", "given.\n", "\n", "The firm purchases capital $k \\geq 0$ from consumers at time\n", "$0$ and finances itself by issuing equity at time $0$.\n", "\n", "The firm produces time $1$ goods $A k^\\alpha e^\\epsilon$ in\n", "state $\\epsilon$ and pays all of these `earnings` to owners of its\n", "equity.\n", "\n", "The value of a firm's equity at time $0$ can be computed by multiplying\n", "its state-contingent earnings by their Arrow securities prices and then\n", "adding over all contingencies:\n", "\n", "$$\n", "\\tilde V = \\int A k^\\alpha e^\\epsilon q(\\epsilon) d \\epsilon\n", "$$\n", "\n", "Owners of a firm want it to choose $k$ to maximize\n", "\n", "$$\n", "V = - k + \\int A k^\\alpha e^\\epsilon q(\\epsilon) d \\epsilon\n", "$$\n", "\n", "The firm's first-order necessary condition for an optimal $k$ is\n", "\n", "$$\n", "- 1 + \\alpha A k^{\\alpha -1} \\int e^\\epsilon q(\\epsilon) d \\epsilon = 0\n", "$$\n", "\n", "The time $0$ value of a representative firm is\n", "\n", "$$\n", "V = - k + \\tilde V\n", "$$\n", "\n", "The right side equals the value of equity minus the cost of the time $0$ goods\n", "that it purchases and uses as capital.\n", "\n", "### A consumer’s problem\n", "\n", "We now pose a consumer’s problem in a competitive equilibrium.\n", "\n", "As a price taker, each consumer faces a given Arrow securities pricing kernel\n", "$q(\\epsilon)$, a given value of a firm $V$ that has chosen capital stock $k$, a price of\n", "equity $\\tilde V$, and prospective next period random dividends $A k^\\alpha e^\\epsilon$.\n", "\n", "Consumer $i$ also confronts a state-by-state borrowing limit that restricts quantities of Arrow securities that he can issue.\n", "\n", "If we evaluate consumer $i$'s time $1$ budget constraint at zero consumption $c^i_1(\\epsilon) = 0$ and solve for $-a^i(\\epsilon)$\n", "we obtain\n", "\n", "```{math}\n", ":label: debtlimit\n", "\n", "-\\bar a^i(\\epsilon;\\theta^i) = w_1^i(\\epsilon) +\\theta^i A k^\\alpha e^\\epsilon\n", "```\n", "\n", "The quantity $- \\bar a^i(\\epsilon;\\theta^i)$ is the maximum amount that it is feasible for consumer $i$ to repay to\n", "his Arrow security creditors at time $1$ in state $\\epsilon$.\n", "\n", "To arrange trading with one-period Arrow securities, we must impose on agent $i$ the state-by-state debt limits\n", "\n", "$$\n", "-a^i(\\epsilon) \\leq - \\bar a^i(\\epsilon;\\theta^i)\n", "$$\n", "\n", "Notice that consumer $i$'s borrowing limit defined in {eq}`debtlimit` depends on\n", "\n", "* his endowment $w_1^i(\\epsilon)$ at time $1$ in state $\\epsilon$\n", "* his share $\\theta^i$ of a representive firm's dividends\n", "\n", "These constitute the two sources of **collateral** that back the consumer's issues of Arrow securities that pay off in state $\\epsilon$\n", "\n", "Consumer $i$ chooses a scalar $c_0^i$ and a function\n", "$c_1^i(\\epsilon)$ to maximize\n", "\n", "$$\n", "u(c_0^i) + \\beta \\int u(c_1^i(\\epsilon)) g (\\epsilon) d \\epsilon\n", "$$\n", "\n", "subject to his state-by-state debt limits and time $0$ and time $1$ budget constraints\n", "\n", "$$\n", "\\begin{aligned}\n", "c_0^i & \\leq w_0^i +\\theta_0^i V - \\int q(\\epsilon) a^i(\\epsilon) d \\epsilon - \\theta^i \\tilde V \\cr\n", "c_1^i(\\epsilon) & \\leq w_1^i(\\epsilon) +\\theta^i A k^\\alpha e^\\epsilon + a^i(\\epsilon)\n", "\\end{aligned}\n", "$$\n", "\n", "Attach Lagrange multiplier $\\lambda_0^i$ to the budget constraint\n", "at time $0$, scaled Lagrange multiplier\n", "$\\beta \\lambda_1^i(\\epsilon) g(\\epsilon)$ to the budget constraint\n", "at time $1$ and state $\\epsilon$, and scaled Lagrange multiplier\n", "$\\beta \\phi_1^i(\\epsilon) g(\\epsilon)$ to the debt limit at time $1$ and state $\\epsilon$,\n", "then form the Lagrangian\n", "\n", "$$\n", "\\begin{aligned}\n", "L^i & = u(c_0^i) + \\beta \\int u(c^i_1(\\epsilon)) g(\\epsilon) d \\epsilon \\cr\n", " & + \\lambda_0^i [ w_0^i + \\theta_0^i - \\int q(\\epsilon) a^i(\\epsilon) d \\epsilon -\n", " \\theta^i \\tilde V - c_0^i ] \\cr\n", " & + \\beta \\int \\lambda_1^i(\\epsilon) [ w_1^i(\\epsilon) + \\theta^i A k^\\alpha e^\\epsilon\n", " + a^i(\\epsilon) c_1^i(\\epsilon) ] g(\\epsilon) d \\epsilon \\cr\n", " & + \\beta \\int \\phi_1^i(\\epsilon) [ - \\bar a^i(\\epsilon; \\theta^i) + a^i(\\epsilon) ] g(\\epsilon) d \\epsilon\n", "\\end{aligned}\n", "$$\n", "\n", "Off corners, first-order necessary conditions for an optimum with respect to\n", "$c_0^i, c_1^i(\\epsilon),$ and $a^i(\\epsilon)$ are\n", "\n", "$$\n", "\\begin{aligned}\n", "c_0^i: \\quad & u'(c_0^i) - \\lambda_0^i = 0 \\cr\n", "c_1^i(\\epsilon): \\quad & \\beta u'(c_1^i(\\epsilon)) g(\\epsilon) - \\beta \\lambda_1^i(\\epsilon) g(\\epsilon) = 0 \\cr\n", "a^i(\\epsilon): \\quad & -\\lambda_0^i q(\\epsilon) + \\beta \\lambda_1^i(\\epsilon) = 0\n", "\\end{aligned}\n", "$$\n", "\n", "These equations imply that consumer $i$ adjusts its consumption\n", "plan to satisfy\n", "\n", "```{math}\n", ":label: qgeqn\n", "\n", "q(\\epsilon) = \\beta \\left( \\frac{u'(c_1^i(\\epsilon))}{u'(c_0^i)} \\right) g(\\epsilon)\n", "```\n", "\n", "To deduce a restriction on equilibrium prices, we\n", "solve the period $1$ budget constraint to express\n", "$a^i(\\epsilon)$ as\n", "\n", "$$\n", "a^i(\\epsilon) = c_1^i(\\epsilon) - w_1^i(\\epsilon) - \\theta^i A k^\\alpha e^\\epsilon\n", "$$\n", "\n", "then substitute the expression on the right side into the time $0$\n", "budget constraint and rearrange to get the single intertemporal budget\n", "constraint\n", "\n", "```{math}\n", ":label: noarb\n", "\n", "w_0^i + \\theta_0^i V + \\int w_1^i(\\epsilon) q(\\epsilon) d \\epsilon + \\theta^i \\left[ A k^\\alpha \\int e^\\epsilon q(\\epsilon) d \\epsilon - \\tilde V \\right]\n", "\\geq c_0^i + \\int c_1^i(\\epsilon) q(\\epsilon) d \\epsilon\n", "```\n", "\n", "The right side of inequality {eq}`noarb` is the present value\n", "of consumer $i$’s consumption while the left side is the present\n", "value of consumer $i$’s endowment when consumer $i$ buys\n", "$\\theta^i$ shares of equity.\n", "\n", "From inequality {eq}`noarb`, we deduce two\n", "findings.\n", "\n", "**1. No arbitrage profits condition:**\n", "\n", "Unless\n", "\n", "```{math}\n", ":label: tilde\n", "\n", "\\tilde V = A k^\\alpha \\int e^\\epsilon q (\\epsilon) d \\epsilon\n", "```\n", "\n", "an **arbitrage** opportunity would be open.\n", "\n", "If\n", "\n", "$$\n", "\\tilde V > A k^\\alpha \\int e^\\epsilon q (\\epsilon) d \\epsilon\n", "$$\n", "\n", "the consumer could afford an arbitrarily high present value of consumption by setting $\\theta^i$ to an arbitrarily large **negative**\n", "number.\n", "\n", "If\n", "\n", "$$\n", "\\tilde V < A k^\\alpha \\int e^\\epsilon q (\\epsilon) d \\epsilon\n", "$$\n", "\n", "the consumer could afford an arbitrarily high present value of\n", "consumption by setting $\\theta^i$ to be arbitrarily large **positive**\n", "number.\n", "\n", "Since resources are finite, there can exist no such arbitrage\n", "opportunity in a competitive equilibrium.\n", "\n", "Therefore, it must be true\n", "that the following no arbitrage condition prevails:\n", "\n", "```{math}\n", ":label: tildeV20\n", "\n", "\\tilde V = \\int A k^\\alpha e^\\epsilon q(\\epsilon;K) d \\epsilon\n", "```\n", "\n", "Equation {eq}`tildeV20` asserts that the value of equity\n", "equals the value of the state-contingent dividends\n", "$Ak^\\alpha e^\\epsilon$ evaluated at the Arrow security prices\n", "$q(\\epsilon; K)$ that we have expressed as a function of $K$.\n", "\n", "We'll say more about this equation later.\n", "\n", "**2. Indeterminacy of portfolio**\n", "\n", "When the no-arbitrage pricing equation {eq}`tildeV20`\n", "prevails, a consumer of type $i$’s choice $\\theta^i$ of equity is\n", "indeterminate.\n", "\n", "Consumer of type $i$ can offset any choice of\n", "$\\theta^i$ by setting an appropriate schedule $a^i(\\epsilon)$ for purchasing state-contingent\n", "securities.\n", "\n", "### Computing competitive equilibrium prices and quantities\n", "\n", "Having computed an allocation that solves the planning problem, we can\n", "readily compute a competitive equilibrium via the following steps that,\n", "as we’ll see, relies heavily on the `Big K, little k`,\n", "`Big C, little c` logic mentioned earlier:\n", "\n", "- a competitive equilbrium allocation equals the allocation chosen by\n", " the planner\n", "- competitive equilibrium prices and the value of a firm’s equity are encoded in shadow prices from the planning problem that\n", " depend on Big $K$ and Big $C$.\n", "\n", "To substantiate that this procedure is valid, we proceed as follows.\n", "\n", "With $K$ in hand, we make the following guess for competitive\n", "equilibrium Arrow securities prices\n", "\n", "```{math}\n", ":label: arrowprices\n", "\n", "q(\\epsilon;K) = \\beta \\left( \\frac{u'\\left( w_1(\\epsilon) + A K^\\alpha e^\\epsilon\\right)} {u'(w_0 - K )} \\right)^{-\\gamma}\n", "```\n", "\n", "To confirm the guess, we begin by considering its consequences for the firm’s choice of $k$.\n", "\n", "With Arrow securities prices {eq}`arrowprices`, the firm’s\n", "first-order necessary condition for choosing $k$ becomes\n", "\n", "```{math}\n", ":label: kK\n", "\n", "-1 + \\alpha A k^{\\alpha -1} \\int e^\\epsilon q(\\epsilon;K) d \\epsilon = 0\n", "```\n", "\n", "which can be verified to be satisfied if the firm sets\n", "\n", "$$\n", "k = K\n", "$$\n", "\n", "because by setting $k=K$ equation {eq}`kK` becomes\n", "equivalent with the planner’s first-order condition\n", "{eq}`focke` for setting $K$.\n", "\n", "To pose a consumer’s problem in a competitive equilibrium, we require\n", "not only the above guess for the Arrow securities pricing kernel\n", "$q(\\epsilon)$ but the value of equity $\\tilde V$:\n", "\n", "```{math}\n", ":label: tildeV2\n", "\n", "\\tilde V = \\int A K^\\alpha e^\\epsilon q(\\epsilon;K) d \\epsilon\n", "```\n", "\n", "Let $\\tilde V$ be the value of equity implied by Arrow securities\n", "price function {eq}`arrowprices` and formula\n", "{eq}`tildeV2`.\n", "\n", "At the Arrow securities prices $q(\\epsilon)$ given by {eq}`arrowprices`\n", "and equity value $\\tilde V$ given by {eq}`tildeV2`,\n", "consumer $i=1,2$ choose consumption allocations and portolios\n", "that satisfy the first-order necessary conditions\n", "\n", "$$\n", "\\beta \\left( \\frac{u'(c_1^i(\\epsilon))}{u'(c_0^i)} \\right) g(\\epsilon) = q(\\epsilon;K)\n", "$$\n", "\n", "It can be verified directly that the following choices satisfy these\n", "equations\n", "\n", "$$\n", "\\begin{aligned}\n", "c_0^1 + c_0^2 & = C_0 = w_0 - K \\cr\n", "c_0^1(\\epsilon) + c_0^2(\\epsilon) & = C_1(\\epsilon) = w_1(\\epsilon) + A k^\\alpha e ^\\epsilon \\cr\n", "\\frac{c_1^2(\\epsilon)}{c_1^1(\\epsilon)} & = \\frac{c_0^2}{c_0^1} = \\frac{1-\\eta}{\\eta}\n", "\\end{aligned}\n", "$$\n", "\n", "for an $\\eta \\in (0,1)$ that depends on consumers’\n", "endowments\n", "$[w_0^1, w_0^2, w_1^1(\\epsilon), w_1^2(\\epsilon), \\theta_0^1, \\theta_0^2 ]$.\n", "\n", "**Remark:** Multiple arrangements of endowments\n", "$[w_0^1, w_0^2, w_1^1(\\epsilon), w_1^2(\\epsilon), \\theta_0^1, \\theta_0^2 ]$\n", "associated with the same distribution of wealth $\\eta$. Can you explain why?\n", "**Hint:** Think about the portfolio indeterminacy finding above.\n", "\n", "### Modigliani-Miller theorem\n", "\n", "We now allow a firm to issue both bonds and equity.\n", "\n", "Payouts from equity and bonds, respectively, are\n", "\n", "$$\n", "\\begin{aligned}\n", "d^e(k,b;\\epsilon) &= \\max \\left\\{ e^\\epsilon A k^\\alpha - b, 0 \\right\\} \\\\\n", "d^b(k,b;\\epsilon) &= \\min \\left\\{ \\frac{e^\\epsilon A k^\\alpha}{b}, 1 \\right\\}\n", "\\end{aligned}\n", "$$\n", "\n", "Thus, one unit of the bond pays one unit of consumption at time\n", "$1$ in state $\\epsilon$ if\n", "$A k^\\alpha e^\\epsilon - b \\geq 0$, which is true when\n", "$\\epsilon \\geq \\epsilon^* = \\log \\frac{b}{Ak^\\alpha}$, and pays\n", "$\\frac{A k^\\alpha e^\\epsilon}{b}$ units of time $1$\n", "consumption in state $\\epsilon$ when\n", "$\\epsilon < \\epsilon^*$.\n", "\n", "The value of the firm is now the sum of equity plus the value of bonds,\n", "which we denote\n", "\n", "$$\n", "\\tilde V + b p(k,b)\n", "$$\n", "\n", "where $p(k,b)$ is the price of one unit of the bond when a firm\n", "with $k$ units of physical capital issues $b$ bonds.\n", "\n", "We continue to assume that there are complete markets in Arrow\n", "securities with pricing kernel $q(\\epsilon)$.\n", "\n", "A version of the no-arbitrage-in-equilibrium argument that we presented\n", "earlier implies that the value of equity and the price of bonds are\n", "\n", "$$\n", "\\begin{aligned}\n", "\\tilde V & = A k^\\alpha \\int_{\\epsilon^*}^\\infty e^\\epsilon q(\\epsilon) d \\epsilon - b \\int_{\\epsilon^*}^\\infty q(\\epsilon) d \\epsilon\\cr\n", "p(k, b) & = \\frac{A k^\\alpha}{b} \\int_{-\\infty}^{\\epsilon^*} e^\\epsilon q(\\epsilon) d \\epsilon\n", " + \\int_{\\epsilon^*}^\\infty q(\\epsilon) d \\epsilon\n", "\\end{aligned}\n", "$$\n", "\n", "Consequently, the value of the firm is\n", "\n", "$$\n", "\\tilde V + p(k,b) b = A k^\\alpha \\int_{-\\infty}^\\infty e^\\epsilon q(\\epsilon) d \\epsilon,\n", "$$\n", "\n", "which is the same expression that we obtained above when we assumed that\n", "the firm issued only equity.\n", "\n", "We thus obtain a version of the celebrated Modigliani-Miller theorem {cite}`Modigliani_Miller_1958`\n", "about firms’ finance:\n", "\n", "**Modigliani-Miller theorem:**\n", "\n", "- The value of a firm is independent the mix of equity and bonds that\n", " it uses to finance its physical capital.\n", "- The firms’s decision about how much physical capital to purchase does\n", " not depend on whether it finances those purchases by issuing bonds\n", " or equity\n", "- The firm’s choice of whether to finance itself by issuing equity or\n", " bonds is indeterminant\n", "\n", "Please note the role of the assumption of complete markets in Arrow\n", "securities in substantiating these claims.\n", "\n", "In {doc}`Equilibrium Capital Structures with Incomplete Markets `, we will assume that markets are (very)\n", "incomplete – we’ll shut down markets in almost all Arrow securities.\n", "\n", "That will pull the rug from underneath the Modigliani-Miller theorem.\n", "\n", "## Code\n", "\n", "We create a class object `BCG_complete_markets` to compute\n", "equilibrium allocations of the complete market BCG model given a list\n", "of parameter values.\n", "\n", "It consists of 4 functions that do the following things:\n", "\n", "> \n", "\n", "* `opt_k` computes the planner's optimal capital $K$\n", " - First, create a grid for capital.\n", " - Then for each value of capital stock in the grid, compute the left side of the planner's\n", " first-order necessary condition for $k$, that is,\n", " \n", " $$\n", " \\beta \\alpha A K^{\\alpha -1} \\int \\left( \\frac{w_1(\\epsilon) + A K^\\alpha e^\\epsilon}{w_0 - K } \\right)^{-\\gamma} e^\\epsilon g(\\epsilon) d \\epsilon - 1 =0\n", " $$\n", " \n", " - Find $k$ that solves this equation.\n", "* `q` computes Arrow security prices as a function of the productivity shock $\\epsilon$ and capital $K$:\n", " \n", " $$\n", " q(\\epsilon;K) = \\beta \\left( \\frac{u'\\left( w_1(\\epsilon) + A K^\\alpha e^\\epsilon\\right)} {u'(w_0 - K )} \\right)\n", " $$\n", " \n", "* `V` solves for the firm value given capital $k$:\n", " \n", " $$\n", " V = - k + \\int A k^\\alpha e^\\epsilon q(\\epsilon; K) d \\epsilon\n", " $$\n", " \n", "* `opt_c` computes optimal consumptions $c^i_0$, and $c^i(\\epsilon)$:\n", " - The function first computes weight $\\eta$ using the\n", " budget constraint for agent 1:\n", " \n", " $$\n", " w_0^1 + \\theta_0^1 V + \\int w_1^1(\\epsilon) q(\\epsilon) d \\epsilon\n", " = c_0^1 + \\int c_1^1(\\epsilon) q(\\epsilon) d \\epsilon\n", " = \\eta \\left( C_0 + \\int C_1(\\epsilon) q(\\epsilon) d \\epsilon \\right)\n", " $$\n", " where\n", " \n", " $$\n", " \\begin{aligned}\n", " C_0 & = w_0 - K \\cr\n", " C_1(\\epsilon) & = w_1(\\epsilon) + A K^\\alpha e^\\epsilon \\cr\n", " \\end{aligned}\n", " $$\n", " \n", " - It computes consumption for each agent as\n", "* $$\n", " \\begin{aligned}\n", " c_0^1 & = \\eta C_0 \\cr\n", " c_0^2 & = (1 - \\eta) C_0 \\cr\n", " c_1^1(\\epsilon) & = \\eta C_1 (\\epsilon) \\cr\n", " c_1^2 (\\epsilon) & = (1 - \\eta) C_1(\\epsilon)\n", " \\end{aligned}\n", " $$\n", " \n", "\n", "The list of parameters includes:\n", "\n", "- $\\chi_1$, $\\chi_2$: Correlation parameters for agents 1\n", " and 2. Default values are 0 and 0.9, respectively.\n", "- $w^1_0$, $w^2_0$: Initial endowments. Default values are 1.\n", "- $\\theta^1_0$, $\\theta^2_0$: Consumers’ initial shares of\n", " a representative firm. Default values are 0.5.\n", "- $\\psi$: CRRA risk parameter. Default value is 3.\n", "- $\\alpha$: Returns to scale production function parameter.\n", " Default value is 0.6.\n", "- $A$: Productivity of technology. Default value is 2.5.\n", "- $\\mu$, $\\sigma$: Mean and standard deviation of the log of the shock.\n", " Default values are -0.025 and 0.4, respectively.\n", "- $\\beta$: time preference discount factor. Default value is .96.\n", "- `nb_points_integ`: number of points used for integration through\n", " Gauss-Hermite quadrature: default value is 10" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import pandas as pd\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from scipy.stats import norm\n", "from numba import njit, prange\n", "from quantecon.optimize import root_finding\n", "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "#=========== Class: BCG for complete markets ===========#\n", "class BCG_complete_markets:\n", "\n", " # init method or constructor\n", " def __init__(self,\n", " 𝜒1 = 0,\n", " 𝜒2 = 0.9,\n", " w10 = 1,\n", " w20 = 1,\n", " 𝜃10 = 0.5,\n", " 𝜃20 = 0.5,\n", " 𝜓 = 3,\n", " 𝛼 = 0.6,\n", " A = 2.5,\n", " 𝜇 = -0.025,\n", " 𝜎 = 0.4,\n", " 𝛽 = 0.96,\n", " nb_points_integ = 10):\n", "\n", " #=========== Setup ===========#\n", " # Risk parameters\n", " self.𝜒1 = 𝜒1\n", " self.𝜒2 = 𝜒2\n", "\n", " # Other parameters\n", " self.𝜓 = 𝜓\n", " self.𝛼 = 𝛼\n", " self.A = A\n", " self.𝜇 = 𝜇\n", " self.𝜎 = 𝜎\n", " self.𝛽 = 𝛽\n", "\n", " # Utility\n", " self.u = lambda c: (c**(1-𝜓)) / (1-𝜓)\n", "\n", " # Production\n", " self.f = njit(lambda k: A * (k ** 𝛼))\n", " self.Y = lambda 𝜖, k: np.exp(𝜖) * self.f(k)\n", "\n", " # Initial endowments\n", " self.w10 = w10\n", " self.w20 = w20\n", " self.w0 = w10 + w20\n", "\n", " # Initial holdings\n", " self.𝜃10 = 𝜃10\n", " self.𝜃20 = 𝜃20\n", "\n", " # Endowments at t=1\n", " w11 = njit(lambda 𝜖: np.exp(-𝜒1*𝜇 - 0.5*(𝜒1**2)*(𝜎**2) + 𝜒1*𝜖))\n", " w21 = njit(lambda 𝜖: np.exp(-𝜒2*𝜇 - 0.5*(𝜒2**2)*(𝜎**2) + 𝜒2*𝜖))\n", " self.w11 = w11\n", " self.w21 = w21\n", "\n", " self.w1 = njit(lambda 𝜖: w11(𝜖) + w21(𝜖))\n", "\n", " # Normal PDF\n", " self.g = lambda x: norm.pdf(x, loc=𝜇, scale=𝜎)\n", "\n", " # Integration\n", " x, self.weights = np.polynomial.hermite.hermgauss(nb_points_integ)\n", " self.points_integral = np.sqrt(2) * 𝜎 * x + 𝜇\n", "\n", " self.k_foc = k_foc_factory(self)\n", "\n", " #=========== Optimal k ===========#\n", " # Function: solve for optimal k\n", " def opt_k(self, plot=False):\n", " w0 = self.w0\n", "\n", " # Grid for k\n", " kgrid = np.linspace(1e-4, w0-1e-4, 100)\n", "\n", " # get FONC values for each k in the grid\n", " kfoc_list = [];\n", " for k in kgrid:\n", " kfoc = self.k_foc(k, self.𝜒1, self.𝜒2)\n", " kfoc_list.append(kfoc)\n", "\n", " # Plot FONC for k\n", " if plot:\n", " fig, ax = plt.subplots(figsize=(8,7))\n", " ax.plot(kgrid, kfoc_list, color='blue', label=r'FONC for k')\n", " ax.axhline(0, color='red', linestyle='--')\n", " ax.legend()\n", " ax.set_xlabel(r'k')\n", " plt.show()\n", "\n", " # Find k that solves the FONC\n", " kk = root_finding.newton_secant(self.k_foc, 1e-2, args=(self.𝜒1, self.𝜒2)).root\n", "\n", " return kk\n", "\n", " #=========== Arrow security price ===========#\n", " # Function: Compute Arrow security price\n", " def q(self,𝜖,k):\n", " 𝛽 = self.𝛽\n", " 𝜓 = self.𝜓\n", " w0 = self.w0\n", " w1 = self.w1\n", " fk = self.f(k)\n", " g = self.g\n", "\n", " return 𝛽 * ((w1(𝜖) + np.exp(𝜖)*fk) / (w0 - k))**(-𝜓)\n", "\n", "\n", " #=========== Firm value V ===========#\n", " # Function: compute firm value V\n", " def V(self, k):\n", " q = self.q\n", " fk = self.f(k)\n", " weights = self.weights\n", " integ = lambda 𝜖: np.exp(𝜖) * fk * q(𝜖, k)\n", "\n", " return -k + np.sum(weights * integ(self.points_integral)) / np.sqrt(np.pi)\n", "\n", " #=========== Optimal c ===========#\n", " # Function: Compute optimal consumption choices c\n", " def opt_c(self, k=None, plot=False):\n", " w1 = self.w1\n", " w0 = self.w0\n", " w10 = self.w10\n", " w11 = self.w11\n", " 𝜃10 = self.𝜃10\n", " Y = self.Y\n", " q = self.q\n", " V = self.V\n", " weights = self.weights\n", "\n", " if k is None:\n", " k = self.opt_k()\n", "\n", " # Solve for the ratio of consumption 𝜂 from the intertemporal B.C.\n", " fk = self.f(k)\n", "\n", " c1 = lambda 𝜖: (w1(𝜖) + np.exp(𝜖)*fk)*q(𝜖,k)\n", " denom = np.sum(weights * c1(self.points_integral)) / np.sqrt(np.pi) + (w0 - k)\n", "\n", " w11q = lambda 𝜖: w11(𝜖)*q(𝜖,k)\n", " num = w10 + 𝜃10 * V(k) + np.sum(weights * w11q(self.points_integral)) / np.sqrt(np.pi)\n", "\n", " 𝜂 = num / denom\n", "\n", " # Consumption choices\n", " c10 = 𝜂 * (w0 - k)\n", " c20 = (1-𝜂) * (w0 - k)\n", " c11 = lambda 𝜖: 𝜂 * (w1(𝜖)+Y(𝜖,k))\n", " c21 = lambda 𝜖: (1-𝜂) * (w1(𝜖)+Y(𝜖,k))\n", "\n", " return c10, c20, c11, c21\n", "\n", "\n", "def k_foc_factory(model):\n", " 𝜓 = model.𝜓\n", " f = model.f\n", " 𝛽 = model.𝛽\n", " 𝛼 = model.𝛼\n", " A = model.A\n", " 𝜓 = model.𝜓\n", " w0 = model.w0\n", " 𝜇 = model.𝜇\n", " 𝜎 = model.𝜎\n", "\n", " weights = model.weights\n", " points_integral = model.points_integral\n", "\n", " w11 = njit(lambda 𝜖, 𝜒1, : np.exp(-𝜒1*𝜇 - 0.5*(𝜒1**2)*(𝜎**2) + 𝜒1*𝜖))\n", " w21 = njit(lambda 𝜖, 𝜒2: np.exp(-𝜒2*𝜇 - 0.5*(𝜒2**2)*(𝜎**2) + 𝜒2*𝜖))\n", " w1 = njit(lambda 𝜖, 𝜒1, 𝜒2: w11(𝜖, 𝜒1) + w21(𝜖, 𝜒2))\n", "\n", " @njit\n", " def integrand(𝜖, 𝜒1, 𝜒2, k=1e-4):\n", " fk = f(k)\n", " return (w1(𝜖, 𝜒1, 𝜒2) + np.exp(𝜖) * fk) ** (-𝜓) * np.exp(𝜖)\n", "\n", " @njit\n", " def k_foc(k, 𝜒1, 𝜒2):\n", " int_k = np.sum(weights * integrand(points_integral, 𝜒1, 𝜒2, k=k)) / np.sqrt(np.pi)\n", "\n", " mul = 𝛽 * 𝛼 * A * k ** (𝛼 - 1) / ((w0 - k) ** (-𝜓))\n", " val = mul * int_k - 1\n", "\n", " return val\n", "\n", " return k_foc" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Examples\n", "\n", "Below we provide some examples of how to use `BCG_complete markets`.\n", "\n", "#### 1st example\n", "\n", "In the first example, we set up instances of BCG complete markets\n", "models.\n", "\n", "We can use either default parameter values or set parameter values as we\n", "want.\n", "\n", "The two instances of the BCG complete markets model, `mdl1` and\n", "`mdl2`, represent the model with default parameter settings and with agent 2’s income correlation altered to be $\\chi_2 = -0.9$,\n", "respectively." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "# Example: BCG model for complete markets\n", "mdl1 = BCG_complete_markets()\n", "mdl2 = BCG_complete_markets(𝜒2=-0.9)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let’s plot the agents’ time-1 endowments with respect to shocks to see\n", "the difference in the two models:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "filenames": { "image/png": "/Users/matthewmckay/repos-collab/phd-macro-theory-book/_build/jupyter_execute/BCG_complete_mkts_8_0.png" }, "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#==== Figure 1: HH endowments and firm productivity ====#\n", "# Realizations of innovation from -3 to 3\n", "epsgrid = np.linspace(-1,1,1000)\n", "\n", "\n", "fig, ax = plt.subplots(1,2,figsize=(15,7))\n", "ax[0].plot(epsgrid, mdl1.w11(epsgrid), color='black', label='Agent 1\\'s endowment')\n", "ax[0].plot(epsgrid, mdl1.w21(epsgrid), color='blue', label='Agent 2\\'s endowment')\n", "ax[0].plot(epsgrid, mdl1.Y(epsgrid,1), color='red', label=r'Production with $k=1$')\n", "ax[0].set_xlim([-1,1])\n", "ax[0].set_ylim([0,7])\n", "ax[0].set_xlabel(r'$\\epsilon$',fontsize=12)\n", "ax[0].set_title(r'Model with $\\chi_1 = 0$, $\\chi_2 = 0.9$')\n", "ax[0].legend()\n", "ax[0].grid()\n", "\n", "ax[1].plot(epsgrid, mdl2.w11(epsgrid), color='black', label='Agent 1\\'s endowment')\n", "ax[1].plot(epsgrid, mdl2.w21(epsgrid), color='blue', label='Agent 2\\'s endowment')\n", "ax[1].plot(epsgrid, mdl2.Y(epsgrid,1), color='red', label=r'Production with $k=1$')\n", "ax[1].set_xlim([-1,1])\n", "ax[1].set_ylim([0,7])\n", "ax[1].set_xlabel(r'$\\epsilon$',fontsize=12)\n", "ax[1].set_title(r'Model with $\\chi_1 = 0$, $\\chi_2 = -0.9$')\n", "ax[1].legend()\n", "ax[1].grid()\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let’s also compare the optimal capital stock, $k$, and optimal\n", "time-0 consumption of agent 2, $c^2_0$, for the two models:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The optimal k for model 1: 0.14235\n", "The optimal k for model 2: 0.13791\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "The optimal c20 for model 1: 0.90205\n", "The optimal c20 for model 2: 0.92862\n" ] } ], "source": [ "# Print optimal k\n", "kk_1 = mdl1.opt_k()\n", "kk_2 = mdl2.opt_k()\n", "\n", "print('The optimal k for model 1: {:.5f}'.format(kk_1))\n", "print('The optimal k for model 2: {:.5f}'.format(kk_2))\n", "\n", "# Print optimal time-0 consumption for agent 2\n", "c20_1 = mdl1.opt_c(k=kk_1)[1]\n", "c20_2 = mdl2.opt_c(k=kk_2)[1]\n", "\n", "print('The optimal c20 for model 1: {:.5f}'.format(c20_1))\n", "print('The optimal c20 for model 2: {:.5f}'.format(c20_2))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 2nd example\n", "\n", "In the second example, we illustrate how the optimal choice of $k$\n", "is influenced by the correlation parameter $\\chi_i$.\n", "\n", "We will need to install the `plotly` package for 3D illustration. See\n", "[https://plotly.com/python/getting-started/](https://plotly.com/python/getting-started/) for further instructions." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "# Mesh grid of 𝜒\n", "N = 30\n", "𝜒1grid, 𝜒2grid = np.meshgrid(np.linspace(-1,1,N),\n", " np.linspace(-1,1,N))\n", "\n", "k_foc = k_foc_factory(mdl1)\n", "\n", "# Create grid for k\n", "kgrid = np.zeros_like(𝜒1grid)\n", "\n", "w0 = mdl1.w0\n", "\n", "@njit(parallel=True)\n", "def fill_k_grid(kgrid):\n", " # Loop: Compute optimal k and\n", " for i in prange(N):\n", " for j in prange(N):\n", " X1 = 𝜒1grid[i, j]\n", " X2 = 𝜒2grid[i, j]\n", " k = root_finding.newton_secant(k_foc, 1e-2, args=(X1, X2)).root\n", " kgrid[i, j] = k" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 2.17 s, sys: 10.8 ms, total: 2.19 s\n", "Wall time: 2.15 s\n" ] } ], "source": [ "%%time\n", "fill_k_grid(kgrid)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 44.4 ms, sys: 720 µs, total: 45.1 ms\n", "Wall time: 8.23 ms\n" ] } ], "source": [ "%%time\n", "# Second-run\n", "fill_k_grid(kgrid)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "" ] }, "execution_count": 10, "metadata": { "filenames": { "image/png": "/Users/matthewmckay/repos-collab/phd-macro-theory-book/_build/jupyter_execute/BCG_complete_mkts_15_0.png" } }, "output_type": "execute_result" } ], "source": [ "#=== Example: Plot optimal k with different correlations ===#\n", "\n", "from IPython.display import Image\n", "# Import plotly\n", "import plotly.graph_objs as go\n", "\n", "# Plot optimal k\n", "fig = go.Figure(data=[go.Surface(x=𝜒1grid, y=𝜒2grid, z=kgrid)])\n", "fig.update_layout(scene = dict(xaxis_title='x - 𝜒1',\n", " yaxis_title='y - 𝜒2',\n", " zaxis_title='z - k',\n", " aspectratio=dict(x=1,y=1,z=1)))\n", "fig.update_layout(width=500,\n", " height=500,\n", " margin=dict(l=50, r=50, b=65, t=90))\n", "fig.update_layout(scene_camera=dict(eye=dict(x=2, y=-2, z=1.5)))\n", "\n", "# Export to PNG file\n", "Image(fig.to_image(format=\"png\"))\n", "# fig.show() will provide interactive plot when running\n", "# notebook locally" ] } ], "metadata": { "jupytext": { "text_representation": { "extension": ".md", "format_name": "myst" } }, "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.3" }, "source_map": [ 10, 29, 36, 880, 890, 1076, 1094, 1098, 1103, 1131, 1136, 1150, 1160, 1184, 1189, 1195 ] }, "nbformat": 4, "nbformat_minor": 4 }