ipynb/barry_ke-applied_computational_economics_and_finance_part_2.ipynb

{
    "cells": [
        {
            "cell_type": "code",
            "execution_count": 1,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "Warning: Function psi has the same name as a MATLAB builtin. We suggest you rename the function to avoid a potential name conflict.\n",
                        "> In path (line 109)\n",
                        "  In addpath (line 86)\n",
                        "\n"
                    ]
                }
            ],
            "source": [
                "addpath('C:\\Users\\barry\\Documents\\Academics\\Quantecon-Notes\\functions')\n",
                "addpath('C:\\Users\\barry\\Documents\\Academics\\Quantecon-Notes\\functions\\CEtools')\n",
                "addpath('C:\\Users\\barry\\Documents\\Academics\\Quantecon-Notes\\functions\\CEtools\\public')\n",
                "cd 'C:\\Users\\barry\\Documents\\Academics\\Quantecon-Notes\\functions'"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "# Chapter 7: Discrete Time Discrete State Dynamic Models\n",
                "\n",
                "In every period $t$, and agent observes the state of an economic process $s_t$, takes an action $x_t$, and earns reward $f(x_t,s_t)$. Action space: $X$\n",
                "\n",
                "State space: $S$ follows a controlled Markov probability law: \n",
                "\n",
                "$$\n",
                "Pr(s_{t+1} = s'|x_t = x, s_t = s) = P(s'|x,s)\n",
                "$$\n",
                "\n",
                "The agent seeks a policy $\\{x_t^*\\}_{t=1}^T$ where prescribes $x_t = x_t^*(s_t)$ be taken at each state in each time so to maximize utility:\n",
                "\n",
                "$$\n",
                "\\max_{\\{x_t^*\\}_{t=1}^T} E[\\sum_{t=0}^T \\delta^t f(x_t, s_t)]\n",
                "$$\n",
                "\n",
                "Dynamic programming: decompose multiperiod model to a sequence of two period model. Principle of Optimality (Richard Bellman):\n",
                "\n",
                ">An optimal policy has the property that, whatever the initial state and decision are, the remaining decisions must consistitute an optimal policy with regard to the state resulting from the first decision\n",
                "\n",
                "Bellman equation:\n",
                "\n",
                "$$\n",
                "V_t(s) = \\max_{x\\in X(s)} [f(x,s) + \\delta \\sum_{s'\\in S}P(s'|x,s)V_{t+1}(s')]\n",
                "$$\n",
                "\n",
                "If the decision problem has an infinite horizon, the value function will not depend on time $t$, and the Bellman equation will become the vector fixed point equation\n",
                "\n",
                "$$\n",
                "V(s) = \\max_{x\\in X(s)} [f(x,s) + \\delta \\sum_{s'\\in S}P(s'|x,s)V(s')]\n",
                "$$\n",
                "\n",
                "## Solution Algorithm\n",
                "\n",
                "States: $S = \\{1,2,\\cdots n\\}$. Actions: $X = \\{1,2,\\cdots n\\}$. Let $v\\in R^n$ be an arbitrary value vector. $v_i \\in R = \\text{value in state }i$. Let $x\\in X^n$ denote an arbitrary policy vector, and $x_i \\in X = \\text{action in state }i$\n",
                "\n",
                "For each policy $x\\in X^n$, let $f(x)$ denote the n-vector reward $f_i(x) = \\text{reward when }x_i \\text{ taken at state }i$. $P_{ij}(x) = \\text{probability of jump from state }i\\text{ to }j\\text{, given }x_i\\text{ is taken}$\n",
                "\n",
                "In recursive vector equation,\n",
                "$$\n",
                "v_t = \\max_{x} [f(x) + \\delta P(x)v_{t+1}]\n",
                "$$\n",
                "\n",
                "### Algorithm: Backward Induction (finite horizon)\n",
                "\n",
                "0. Initialization: Specify reward $f$, transition probability $P$, discount factor $\\delta$, terminal period $T$, and end value $v_{T+1}$\n",
                "1. Recursive step: given $v_{t+1}$, compute $v_t$ and $x_t$:\n",
                "$$\n",
                "\\begin{aligned}\n",
                "v_t &\\leftarrow \\max_{x}[f(x) + \\delta P(x)v_{t+1}] \\\\\n",
                "x_t &\\leftarrow \\arg\\max_{x} [f(x) + \\delta P(x) v_{t+1}]\n",
                "\\end{aligned}\n",
                "$$\n",
                "\n",
                "### Algorithm: Function Iteration (infinite horizon)\n",
                "\n",
                "0. Specify $f, P, \\delta$ and initial guess of $v=v_0$\n",
                "1. Update value function \n",
                "$$v \\leftarrow \\max_x[f(x) + \\delta P(x) v]$$\n",
                "2. Terminates if $||\\Delta v||$ is small and set $$x \\leftarrow \\arg\\max_{x} [f(x) + \\delta P(x) v]$$\n",
                "\n",
                "### Algorithm: Policy Iteration (infinite horizon)\n",
                "\n",
                "0. Specify $f, P, \\delta$ and initial guess of $v=v_0$\n",
                "1. Update policy function \n",
                "$$x \\leftarrow \\arg\\max_x[f(x) + \\delta P(x) v]$$\n",
                "and updates value function\n",
                "$$\n",
                "v\\leftarrow (I - \\delta P(x))^{-1}f(x)\n",
                "$$\n",
                "2. Terminates if $||\\Delta v||$ is small\n",
                "\n",
                "## Examples\n",
                "\n",
                "### Mine Management\n",
                "\n",
                "Determine the optimal ore extraction schedule for a mine that will be shut down after $T$ years. Price: $p$ per ton. Cost of extracting $x$ tons: $c = x^2/(1+s)$, where $s$ is the amount remaining in the mine at the beginning of the year. Currently it has $\\bar{s}$ in mine. Assuming the amount of ore must be an integer. \n",
                "\n",
                "Intratemporal reward: $f(s,x) = px - x^2/(1+s)$. So bellman equation\n",
                "\n",
                "$$\n",
                "V_t(s) = \\max_{x = 0,1,\\cdots} [px-x^2/(1+s) + \\delta V_{t+1}(s-x)\n",
                "$$\n",
                "subject to $T_{T+1}(s) = 0$"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 101,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "\n"
                    ]
                }
            ],
            "source": [
                " delta = 0.9; p = 1; sbar = 10; S = (0:sbar); %vector of states\n",
                " n = length(S); X = (0:sbar)'; %vector of actions\n",
                " m = length(X);\n",
                " \n",
                " f = zeros(n,m);\n",
                " for k = 1:m\n",
                "     f(:,k) = p*X(k) - (X(k)^2)./(1+S);\n",
                "     f(X(k)>S, k) = -inf;\n",
                "end\n",
                "g = zeros(n,m);\n",
                "for k = 1:m\n",
                "    j = max(0, S-X(k))+1;\n",
                "    g(:,k) = j;\n",
                "end\n"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 43,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "\n"
                    ]
                }
            ],
            "source": [
                "model.reward = f;\n",
                "model.transfunc = g;\n",
                "model.discount = delta;\n",
                "model.horizon = 10;"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 44,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "Solve Bellman equation via backward recursion\n",
                        "\n"
                    ]
                }
            ],
            "source": [
                "\n",
                "[vi,xi, pstari] = ddpsolve(model);"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 37,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "\n"
                    ]
                },
                {
                    "data": {
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\n",
                        "text/plain": [
                            "<IPython.core.display.Image object>"
                        ]
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "figure(1); plot(S, X(xi));\n",
                "xlabel('Stock'); ylabel('Optimal Extraction');"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 45,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "\n"
                    ]
                },
                {
                    "data": {
                        "image/png": 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\n",
                        "text/plain": [
                            "<IPython.core.display.Image object>"
                        ]
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "s1 = length(S); nyrs = 10;\n",
                "sipath = ddpsimul(pstari, s1, nyrs, xi);\n",
                "figure(2)\n",
                "plot(0:nyrs, S(sipath))"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "### Asset Replacement\n",
                "\n",
                "At the beginning of each year, a manufacturer must decide whether to continue operating with asset or replace it. Asset with $a$ years old gives $p(a)$ profit. It can be used up to $n$ years. The cost of new one is $c$. \n",
                "\n",
                "Infinite horizon deterministic model. State variable $a = \\{1,2,\\cdots n\\}$. Action variable $x = [(keep, replace), replace]$ ([$a <n$, $a = n$]). The state transitoin function $g(a,x) = a+1$ if $x = keep$, and $1$ if $x = replace$. Reward function $f(a,x) = p(a)$ if $x = keep$, and $f(a,x) = p(0) - c$ if replace. \n",
                "\n",
                "Value function\n",
                "$$\n",
                "V(a) = \\max_{x \\in X(a)} [f(a,x) + \\delta V(g(a,x))] = \\max [p(a) + \\delta V(a+1), p(0)-c + \\delta V(1)]\n",
                "$$\n",
                "\n",
                "### Option Pricing\n",
                "\n",
                "In Cox-Ross-Rubinstein binomial option pricing model, the price follows two-state discrete jump process. If stock is at price $p$ at time $t$, then in $t+1$ the price will be $pu$ with probability $q$ and $p/u$ with probability $1-q$, where $u = \\exp{\\sigma \\sqrt{\\Delta t}}, q = \\frac{1}{2} + \\frac{\\sqrt{\\Delta t}}{2\\sigma}(r - \\frac{1}{2}\\sigma^2), \\delta = \\exp{-r\\Delta t}$\n",
                "\n",
                "If current price is $p_0$ and strike price is $\\bar{p}$, expiration is $T$, the state space is $p \\in S = \\{p_0u^i|i = -N-1, -N, \\cdots N, N+1\\}$. The action space is $x = \\{keep, exercise\\}$, the transition probability is \n",
                "$$\n",
                "P(p'|x,p) = \\begin{cases}q \\text{  if }p' = pu. \\\\\n",
                "1-q \\text{  if }p' = p/u.\\\\\n",
                "0 \n",
                "\\end{cases}\n",
                "$$\n",
                "\n",
                "The reward function is \n",
                "$$\n",
                "f(x,p) = \\begin{cases}0 \\text{  if keep}. \\\\\n",
                "\\bar{p} - p \\text{  if exercise}.\\\\\n",
                "0 \n",
                "\\end{cases}\n",
                "$$\n",
                "\n",
                "Value function\n",
                "$$\n",
                "V_t(p) = \\max[\\bar{p} - p, \\delta (q V_{t+1}(pu) + (1-q) V_{t+1}(p/u))]\n",
                "$$"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 191,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "\n"
                    ]
                }
            ],
            "source": [
                "clear all\n",
                "T = 0.5; sigma = 0.2; r = 0.05; strike = 2; p0 = 2; N = 100;\n",
                "tau = T/N; delta = exp(-r*tau); u = exp(sigma*sqrt(tau)); q = 0.5+tau^2*(r-(sigma^2)/2)/(2*sigma);\n",
                "p = p0*(u.^(-N:N));\n",
                "n = length(p);\n",
                "\n",
                "%probability\n",
                "%first column: reward for first option\n",
                "f = [(strike - p)' zeros(n,1)];\n",
                "\n",
                "%P is 2xnxn matrix. first nxn is transition matrix when first action is taken\n",
                "P = zeros(n,n);\n",
                "for i=1:n\n",
                " P(i, min(i+1,n),2) = q;\n",
                " P(i, max(i-1,1),2) = 1-q;\n",
                "end\n",
                "%P = sparse(P);\n",
                "P = permute(P, [3,1,2]);"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 192,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "\n"
                    ]
                }
            ],
            "source": [
                "model.reward = f;\n",
                "model.transprob = P;\n",
                "model.discount = delta;\n",
                "moel.horizon=N+1;"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 197,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "Solve Bellman equation via Newton method\n",
                        "    1    1.0e+01\n",
                        "    2    1.4e-02\n",
                        "    3    9.8e-03\n",
                        "    4    8.4e-03\n",
                        "    5    7.6e-03\n",
                        "    6    7.1e-03\n",
                        "    7    6.7e-03\n",
                        "    8    6.3e-03\n",
                        "Warning: Failure to converge in ddpsolve\n",
                        "> In ddpsolve (line 106)\n",
                        "\n"
                    ]
                }
            ],
            "source": [
                "[v,x] = ddpsolve(model);"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 199,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "\n"
                    ]
                },
                {
                    "data": {
                        "image/png": 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\n",
                        "text/plain": [
                            "<IPython.core.display.Image object>"
                        ]
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "plot(p, v(:,1)); axis([0 strike*2 -inf inf])"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "\n",
                "\n",
                "# Chapter 8: Discrete Time Continuous State Dynamic Models\n",
                "\n",
                "1. Centralized decision making (option pricing, industry entry, asset replacement)\n",
                "2. Strategic gaming among a small number of participants (international trade, factory expansion, risk sharing)\n",
                "3. Partial and general equilibrium model of collective, decentralized economic behavior. \n",
                "\n",
                "## Model structure:\n",
                "In each period $t$, an agent observes the state of the economic process $s_t\\in S$, takes an action $x_t \\in X$, and earns a reward $f(s_t, x_t)$. The state of the economic process in period $t+1$ will depend on the state and action in period $t$ and an exogenous random shock $\\epsilon_{t+1}$ that is unknown in period $t$: $s_{t+1} = g(s_t, x_t, \\epsilon_{t+1})$. \n",
                "\n",
                "The agent seeks a policy of state-contingent actions $x_t^*:S\\rightarrow X, t=0,1,\\cdots T\\leq \\infty$, that maximizes $E_0\\sum_{t=0}^T \\delta^t f(s_t, x_t(s_t))$\n",
                "\n",
                "Bellman equation:\n",
                "$$\n",
                "V_t(s) = \\max_{x\\in X(s)}[f(s,x) + \\delta E_\\epsilon V_{t+1}(g(s,x,\\epsilon))]\n",
                "$$\n",
                "\n",
                "In infinite horizon, \n",
                "$$\n",
                "V(s) = \\max_{x\\in X(s)}[f(s,x) + \\delta E_\\epsilon V(g(s,x,\\epsilon))]\n",
                "$$\n",
                "\n",
                "## Continuous State Discrete Choice model (CSDC)\n",
                "\n",
                "Optimal stopping problem\n",
                "\n",
                "## Continuous State Continuous Choice Model (SCCC)\n",
                "\n",
                "Markov decison models with continuous state and action spaces are special because their solutions can often be characterized by \"first-order\" equilibrium conditions. \n",
                "\n",
                "The equilibrium condition involve the derivative of the value function $\\lambda(s) \\equiv V'(s)$. We call $\\lambda$ the shadow price function, which represents the marginal value of the state variable to the optimizer, or the price that the optimizer imputes to the state variable. \n",
                "\n",
                "The equilibrium condition is derived by applying KKT and Envelope Theorems to the optimization problem embedded in Bellman equation. \n",
                "\n",
                "Unconstrained KKT: \n",
                "$$\n",
                "f_x(s,x) + \\delta E_\\epsilon [V'(g(s,x,\\epsilon))g_x(s,x,\\epsilon)] = f_x(s,x) + \\delta E_\\epsilon [\\lambda(g(s,x,\\epsilon))g_x(s,x,\\epsilon)] = 0\n",
                "$$\n",
                "Envelope Theorem: \n",
                "$$\n",
                "f_s(s,x) + \\delta E_\\epsilon [\\lambda (g(s,x,\\epsilon))g_s(s,x,\\epsilon)] = \\lambda(s)\n",
                "$$\n",
                "\n",
                "If the state transition only depends on the action of the agent, then $g_s = 0$, and we can substitute the expression derived using the Envelope theorem into the KKT and eliminate $\\lambda$:\n",
                "\n",
                "$$\n",
                "f_x(s,x(s)) + \\delta E_\\epsilon [f_s(g(s,x(s),\\epsilon),x(g(s,x(s),\\epsilon)))g_x(s,x(s), \\epsilon)] = 0\n",
                "$$\n",
                "which is called the Euler equation\n",
                "\n",
                "## Linear-Quadratic Control\n",
                "\n",
                "LQ control problem is an unconstrained Markov decision model with a quadratic reward function\n",
                "$$\n",
                "f(s,x) = F_0 + F_s s+F_x x + \\frac{1}{2}s^T F_{ss} s + s^T F_{sx}x + \\frac{1}{2}x^TF_{xx}x\n",
                "$$\n",
                "and a linear state transition function\n",
                "$$\n",
                "g(s,x,\\epsilon) = G_0 + G_s s + G_x x + \\epsilon\n",
                "$$\n",
                "\n",
                "It is a continuous state Markov decision model with a finite-dimensional solution. The optimal policy and shadow price functions for the infinite horizon linear-quadratic control moel are both linear in state variable:\n",
                "\n",
                "$$\n",
                "x(s) = \\Gamma_0 + \\Gamma_s s\n",
                "$$\n",
                "$$\n",
                "\\lambda(s) = \\Lambda_0 + \\Lambda_s s\n",
                "$$\n",
                "\n",
                "## Dynamic Games\n",
                "\n",
                "Discrete time continuous state Markov $m$-agent game: in each period, each agent $i$ observes the stte of an economic process $s\\in S$, takes an action $x_i \\in X$, and earns a reward $f_i(s,x_i, x_{-i})$ that depends on what other people have done. The state of the economic process is a jointly controlled Markov process. \n",
                "\n",
                "Noncooperative Markov perfect equilibria (SPNE) with perfect information: $x_i^*: S\\rightarrow X, i = 1,2, \\cdots m$ such that $x_i^*$ maximizes \n",
                "\n",
                "$$\n",
                "E_0\\sum_{t=0}^T \\delta^t f_i(s_t, x_i(s_t), x_{-i}^*(s_t))\n",
                "$$\n",
                "\n",
                "The Markov perfect equilibrium for m agents is characterized by a set of m simultaneous Bellman equations:\n",
                "\n",
                "$$\n",
                "V_i(s) = \\max_{x\\in X_i(s)} [f_i(s,x,x_{-i}^*(s))+ \\delta E_\\epsilon V_i(g(s,x,x_{-i}^*(s), \\epsilon))]\n",
                "$$\n",
                "\n",
                "## Rational Expectation Model\n",
                "\n",
                "Equilibrium through the decentralized actions of individuals. Assumption: agents are rational, that their expectations are consistent with the implications of the model as whole. \n",
                "\n",
                "At beginning of period $t$, an economic system emerges in a state $s_t$. Agents observe the state of the system and produce a systematic response $x_t$ governed by an equilibrium condition that depends on the expectations of the following period's state and action, i.e. satisfies $f(s_t, x_t, E_t h(s_{t+1}, x_{t+1})) = 0$ where $f$ is equilibrium condition. State transition: $s_{t+1}  g(s_t, x_t, \\epsilon_{t+1})$. \n",
                "\n",
                "The response functoin $x(s)$ is characterized implicitly as the solution to a functional equaiton \n",
                "$$\n",
                "f(s, x(s), E[h(g(s,x(s),\\epsilon), x(g(s,x(s),\\epsilon)))]) = 0\n",
                "$$"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "## Examples \n",
                "\n",
                "**<span style=\"color:red\">When using dpsolve, don't call for resid. Only four outputs: [c,s,v,x]</span>.**\n",
                "\n",
                "**c: coefficient for basis functions. s: grid nodes. v: value functions. x: optimal action**\n",
                "\n",
                "**If ckron(x) has error, use ckronx(x,1)**\n",
                "\n",
                "**use cdprodx_new to replace cdprodx.mex**\n",
                "\n",
                "## Continuous State Discrete Choice##\n",
                "### Asset Replacement\n",
                "In each period the producer must decide if to replace an asset. In the asset's $a^{th}$ period it generates $q(a)$ up to period $\\bar{a}$. The price is $p$ and the cost $K$ for new asset is an exogenous continuous-valued Markov process $K_{t+1} = g(K_t, \\epsilon_{t+1})$. State variable: $s = K\\times a \\in (0,\\infty)\\times [0,1, \\cdots \\bar{a}]$. Control variable: $keep$ or $replace$. \n",
                "\n",
                "Reward: $f(s,a,x) = \\begin{cases} pq(0) - K \\text{  if x = 1} \\\\ pq(a) \\text{  if x = 0}\\end{cases}$\n",
                "\n",
                "Bellman equation:\n",
                "$$\n",
                "V(p,a) = \\max[pq(a) + \\delta EV(g(p,\\epsilon), a+1), pq(0)-K + \\delta EV(g(p,\\epsilon),1)]\n",
                "$$\n",
                "\n",
                "Assume $q(a) = 100-5a-0.5a^2$, and $\\bar{a} = 10$. Output price $p = 2$. Replacement cost $k_{t+1} = \\bar{k} + \\gamma(k_t - \\bar{k}) + \\epsilon_{t+1}$ where $\\epsilon_t\\sim N(0,\\sigma^2)$."
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 4,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "Created file 'C:\\Users\\barry\\Documents\\Academics\\Quantecon-Notes\\functions\\asset_replace.m'.\n"
                    ]
                }
            ],
            "source": [
                "%%file functions\\asset_replace.m\n",
                "\n",
                "function out = asset_replace(flag, s, x, e, price, kbar, gamma, abar);\n",
                "k = s(:,1); a = s(:,2);\n",
                "switch flag\n",
                "case 'f';\n",
                " out = price*(50-2.5*a-0.25*a.^2).*(1-x) + (price*50 - k).*x;\n",
                " out(a==abar & x==0)=-inf;\n",
                "\n",
                "case 'g';\n",
                " out(:,1) = kbar + gamma*(k - kbar) + e;\n",
                " out(:,2) = min(a+1, 10).*(1-x)+x;\n",
                "end"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 23,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "\n"
                    ]
                }
            ],
            "source": [
                "addpath('C:\\Users\\barry\\Documents\\Academics\\Quantecon-Notes\\functions')\n",
                "addpath('C:\\Users\\barry\\Documents\\Academics\\Quantecon-Notes\\functions\\CEtools')\n",
                "\n",
                "delta = 0.9; price = 2; kbar = 100; gamma = 0.5; sigma = 15; abar = 6;\n",
                "\n",
                "%% The function is not performing\n",
                "\n",
                "%discreteize shock: five node gaussian quadrature scheme\n",
                "m = 5;\n",
                "[e,w] = qnwnorm(m,0, sigma^2);\n",
                "\n",
                "%specify basis functions and collocation nodes:\n",
                "n = 100;\n",
                "kmin = 30;\n",
                "kmax = 190;\n",
                "fspace = fundefn('spli', n, kmin, kmax, [],[1:10]');\n",
                "snodes = funnode(fspace);\n",
                "s = gridmake(snodes);\n",
                "\n",
                "%construct action space\n",
                "x = [0;1];\n",
                "\n",
                "%pack model structure:\n",
                "model.func = 'asset_replace';\n",
                "model.discount = delta;\n",
                "model.e = e;\n",
                "model.w = w;\n",
                "model.actions = x;\n",
                "model.discretestates = 2;\n",
                "model.params = {price kbar gamma abar};\n",
                "\n",
                "%initial guess for value\n",
                "vinit = zeros(size(s,1),1);\n",
                "\n",
                "%solve model\n",
                "%[c,scoord,v,x,resid] = dpsolve(model, fspace, s);"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "### Timber Cutting\n",
                "\n",
                "The owner must decide each year whether to cut down the stand and sell it for lumber. The biomass $s$ growths at deterministic rate $s_{t+1} = g(s_t)$. The profit contribution per unit of biomass is $p$. If cut timber, need to pay cost $C$. What is the optimal timber cutting policy?\n",
                "\n",
                "Infinite horizon model with one continuous state variable $s \\in [0, \\infty)$. Choice variable $x = 1$ if cutt and $x = 0$ if not cut. Reward function \n",
                "$f(s,x) = \\begin{cases}ps - C \\text{  if x = 1} \\\\ 0 \\text{  if x = 0}\\end{cases}$\n",
                "Bellman equation:\n",
                "$$\n",
                "V(s) = max[\\delta EV(g(s)), ps - C + \\delta EV(0)]\n",
                "$$\n",
                "\n",
                "Suppose $s_{t+1} = K + \\exp{-\\alpha} (s_t - K)$ if not cut $x = 0$"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 2,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "Created file 'C:\\Users\\barry\\Documents\\Academics\\Quantecon-Notes\\functions\\timber_cutting.m'.\n"
                    ]
                }
            ],
            "source": [
                "%%file functions\\timber_cutting.m\n",
                "function out = timber_cutting(flag, s, x, e, price, C, K, alpha)\n",
                "switch flag\n",
                "case 'f'\n",
                "out = (price*s - C).*x;\n",
                "case 'g';\n",
                "out  =((K+exp(-alpha)*(s-K))).*(1-x);\n",
                "end"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 27,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "\n"
                    ]
                }
            ],
            "source": [
                "delta = 0.95; price = 1; C = 0.2; K = 0.5; alpha = 0.1;\n",
                "n = 350; fspace = fundefn('lin',n, 0, K);\n",
                "snodes = funnode(fspace);\n",
                "\n",
                "x = [0;1];\n",
                "\n",
                "model.func = 'timber_cutting';\n",
                "model.discount = delta;\n",
                "model.actions = x;\n",
                "model.params = {price C K alpha};"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 28,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "   1    3.6e-01\n",
                        "   2    1.5e-01\n",
                        "   3    7.7e-03\n",
                        "   4    7.7e-03\n",
                        "   5    1.5e-04\n",
                        "   6    1.7e-16\n",
                        "Elapsed Time =    0.02 Seconds\n",
                        "\n"
                    ]
                }
            ],
            "source": [
                "[c,s,v,x,resid] = dpsolve(model,fspace,snodes);"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 31,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "\n"
                    ]
                },
                {
                    "data": {
                        "image/png": 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\n",
                        "text/plain": [
                            "<IPython.core.display.Image object>"
                        ]
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "s = gridmake(snodes);\n",
                "plot(s,v)\n",
                "title('Value function')\n",
                "xlabel('Biomass (s)')\n",
                "ylabel('Value (v)')"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 34,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "\n"
                    ]
                },
                {
                    "data": {
                        "image/png": 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\n",
                        "text/plain": [
                            "<IPython.core.display.Image object>"
                        ]
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "plot(s,x)\n",
                "title('Optimal action')"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "### American Option Pricing\n",
                "\n",
                "In the discrete-time Black-Scholes option pricing model, the price of the commodity follows an exogenous continuous valued Markov process $p_{t+1} = g(p_t, \\epsilon_{t+1})$. What is the value of an American put at time $t$ if price is $p$, and strike price is $K$?\n",
                "\n",
                "State space: $p \\times i \\in [0,\\infty)\\times \\{0,1\\}$, where $i = 1$ if the option is already executed. Action space $x = 1$ if execute and $x = 0$ if not execute. Reward function: $f(p,i,x) = ix(K-p)$. The value function $V_t(p,i)$ is \n",
                "\n",
                "$$\n",
                "V_t(p,1) = \\max[K-p, \\delta EV(g(p,\\epsilon),1)]\n",
                "$$"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 67,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "Created file 'C:\\Users\\barry\\Documents\\Academics\\Quantecon-Notes\\functions\\american_option.m'.\n"
                    ]
                }
            ],
            "source": [
                "%%file functions\\american_option.m\n",
                "function out = american_option(flag, s, x, e, K)\n",
                "switch flag\n",
                "case 'f';\n",
                "out = (K-exp(s(:,1))).*x.*(1-s(:,2));\n",
                "case 'g';\n",
                "out = [s(:,1)+e s(:,2)|x]; % \"|\" is binary operator. Google it\n",
                "end"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 116,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "Solving for time 30\n",
                        "Solving for time 29\n",
                        "Solving for time 28\n",
                        "Solving for time 27\n",
                        "Solving for time 26\n",
                        "Solving for time 25\n",
                        "Solving for time 24\n",
                        "Solving for time 23\n",
                        "Solving for time 22\n",
                        "Solving for time 21\n",
                        "Solving for time 20\n",
                        "Solving for time 19\n",
                        "Solving for time 18\n",
                        "Solving for time 17\n",
                        "Solving for time 16\n",
                        "Solving for time 15\n",
                        "Solving for time 14\n",
                        "Solving for time 13\n",
                        "Solving for time 12\n",
                        "Solving for time 11\n",
                        "Solving for time 10\n",
                        "Solving for time 9\n",
                        "Solving for time 8\n",
                        "Solving for time 7\n",
                        "Solving for time 6\n",
                        "Solving for time 5\n",
                        "Solving for time 4\n",
                        "Solving for time 3\n",
                        "Solving for time 2\n",
                        "Solving for time 1\n",
                        "\n"
                    ]
                }
            ],
            "source": [
                "clear all\n",
                "sigma = 0.2;                                          % annual volatility\n",
                "T     = 0.5;                                          % years to expiration\n",
                "K     = 1.0;                                          % option strike price\n",
                "p0    = 1.0;                                          % current asset price \n",
                "r     = 0.1;                                          % interest rate\n",
                "\n",
                "nt = 30;\n",
                "deltat = T/(nt-1);\n",
                "beta = exp(-r*deltat);\n",
                "\n",
                "m = 10;\n",
                "[e,w] = qnwnorm(m,deltat*(r-sigma^2/2),deltat*sigma^2);\n",
                "\n",
                "x = [0;1];\n",
                "nx = length(x);\n",
                "\n",
                "clear model;\n",
                "model.func = 'american_option';\n",
                "model.horizon = nt;\n",
                "model.discount = beta;\n",
                "model.e = e;\n",
                "model.w = w;\n",
                "model.actions = x;\n",
                "model.discretestates = 2;\n",
                "model.params = {K};\n",
                "\n",
                "d = 6;\n",
                "ns = 500;\n",
                "s0 = log(p0);\n",
                "smin = s0-d*sigma*sqrt(T);\n",
                "smax = s0+d*sigma*sqrt(T);\n",
                "fspace = fundefn('lin', ns, smin, smax,[],[0;1]);\n",
                "scoord = funnode(fspace);\n",
                "s = gridmake(scoord);\n",
                "\n",
                "p = exp(s(:,1));\n",
                "v = zeros(2*ns,1);\n",
                "\n",
                "optset('dpsolve','nres',5);\n",
                "[c,s,v,x] = dpsolve(model, fspace, s,v);"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 117,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "\n"
                    ]
                },
                {
                    "data": {
                        "image/png": 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\n",
                        "text/plain": [
                            "<IPython.core.display.Image object>"
                        ]
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "%figure(1);\n",
                "p = exp(scoord{1});\n",
                "v = reshape(v,ns,2,nt+1);\n",
                "v = squeeze(v(:,1,:));\n",
                "plot(p,v(:,1),p,max(K-p,0));\n",
                "title('American Put Option Value');\n",
                "xlabel('Asset Price'); ylabel('Value');"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 118,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "\n"
                    ]
                },
                {
                    "data": {
                        "image/png": 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\n",
                        "text/plain": [
                            "<IPython.core.display.Image object>"
                        ]
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "  figure(2);\n",
                "  x = reshape(x,ns,2,nt);\n",
                "  x = squeeze(x(:,1,:)); \n",
                "  plot(linspace(T,0,nt),p(sum(x==1)))\n",
                "  title('American Put Option Optimal Exercise Boundary'); \n",
                "  xlabel('Time-to-Maturity'); ylabel('Asset Price');"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "### Industry Entry and Exit\n",
                "\n",
                "A firm operates in an uncertain profit environment. At the beginning of each period, the firm observes the profit $s$ for this period, and the firm decides whether to operate and take the profit. The short-run profit $\\pi$ is enxogenous continous Markov process $\\pi_{t+1} = g(\\pi_t, \\epsilon_{t+1})$. If it closes after a period of active, it incurs a shut down cost $K_0$. If it starts after a period of inactive, in incurs a start tup cost $K_1$.\n",
                "\n",
                "State variable: $\\pi \\times i \\in R\\times \\{0,1\\}$, where $i=0$ if it is inactive and $i=1$ if it is active. Action space: $x \\in \\{0,1\\}$ where $x = 0$ if it shuts down. Profit function: $f(\\pi,i,x) = ix\\pi + (1-i)x(\\pi-K_1) + i(1-x)(-K_0) = x\\pi - K_0 i(1-x) - K_1x(1-i)$. Value function:\n",
                "\n",
                "$$\n",
                "V_t(\\pi,i) = \\max_{x = 0,1}[\\pi x - K_0 i(1-x)-K_1x(1-i)+\\delta EV(g(\\pi,\\epsilon),x)]\n",
                "$$\n",
                "\n",
                "Suppose the profit process is $\\pi = \\bar{\\pi} + \\gamma(\\pi-\\bar{\\pi})+ \\epsilon$, where $\\epsilon \\sim N(0,\\sigma^2)$"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 137,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "Created file 'C:\\Users\\barry\\Documents\\Academics\\Quantecon-Notes\\functions\\industry_entry.m'.\n"
                    ]
                }
            ],
            "source": [
                "%%file functions\\industry_entry.m\n",
                "function out = industry_entry(flag, s,x,e,pibar,gamma,k0,k1)\n",
                "pi = s(:,1); i = s(:,2);\n",
                "switch flag\n",
                "case 'f'\n",
                "out = pi.*x - k0.*i.*(1-x)-k1.*x.*(1-i);\n",
                "case 'g'\n",
                "out = [pibar+gamma*(pi-pibar)+e x];\n",
                "end"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 22,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "   1    4.2e+02\n",
                        "   2    5.7e+01\n",
                        "   3    2.0e+01\n",
                        "   4    1.7e+01\n",
                        "   5    9.8e-01\n",
                        "   6    5.1e-13\n",
                        "Elapsed Time =    0.01 Seconds\n",
                        "Warning: extrapolating beyond smax\n",
                        "\n"
                    ]
                }
            ],
            "source": [
                "pibar = 1;\n",
                "gamma = 0.9;\n",
                "k0 = 10;\n",
                "k1 = 5;\n",
                "delta = 0.98;\n",
                "sigma = 0.9;\n",
                "\n",
                "m = 10;\n",
                "[e,w] = qnwnorm(m,0,sigma.^2);\n",
                "\n",
                "x = [0;1];\n",
                "nx = length(x);\n",
                "\n",
                "clear model;\n",
                "model.func = 'industry_entry';\n",
                "model.actions = x;\n",
                "model.e = e;\n",
                "model.w = w;\n",
                "model.discount = delta;\n",
                "model.discretestates = 2;\n",
                "model.params = {pibar gamma k0 k1};\n",
                "\n",
                "n = 100;\n",
                "pimin = pibar + min(e)/(1-gamma) - 0.1;\n",
                "pimax = pibar + max(e)/(1-gamma) - 0.1;\n",
                "fspace = fundefn('spli',n,pimin,pimax,[],[0;1]);\n",
                "scoord = funnode(fspace);\n",
                "s = gridmake(scoord);\n",
                "\n",
                "[c,s,v,x] = dpsolve(model, fspace, s);"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 24,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "\n"
                    ]
                },
                {
                    "data": {
                        "image/png": 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\n",
                        "text/plain": [
                            "<IPython.core.display.Image object>"
                        ]
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "plot(scoord{1},v)\n",
                "title('Value Function');\n",
                "legend('Inactive','Active');\n",
                "xlabel('Anticipated profit');\n",
                "ylabel('Value');"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 25,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "\n"
                    ]
                },
                {
                    "data": {
                        "image/png": 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\n",
                        "text/plain": [
                            "<IPython.core.display.Image object>"
                        ]
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "plot(scoord{1},x)\n",
                "title('Optimal action');\n",
                "legend('Inactive','Active');\n",
                "xlabel('Anticipated profit');\n",
                "ylabel('Action');"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "### Job Search\n",
                "\n",
                "At the beginning of each period, the worker observes current wage $w$. If laborer is employed, he must decide to continue to work or not. if he is not employed, he must decide to accept the job or continue to search. If he works, he gets $w$. If search, he gets unemployment benefit $u$, and if neigher works nor searches, he gets leisure benefit $v$. If the agent searches the job, his probability of finding employment for the following period is $\\pi_f$. If he works, he faces a probability $\\pi_k$ of keeping his job for the following period. How low must the wage for him to decline search if unemployed, and how low must the wage to be for him to quit if employed?\n",
                "\n",
                "State varible: $w\\in [0,\\infty)$ and $i=1$ if employed and $i=0$ if unemployed. Decision variable: $x = 1$ if employed continue or unemployed search, and $0$ otherwise. Reward function: $f(w,i,x) = wix + u(1-i)x+v(1-i)(1-x)+vi(1-x) = wix+u(1-i)x+v(1-x)$\n",
                "\n",
                "Value function:\n",
                "$$\n",
                "V(w,i) = \\max_{x = 0,1} [f(w,i,j)+\\delta E[\\pi_{ij} V(g(w,\\epsilon),1)+(1-\\pi_{ij})V(g(w,\\epsilon),0)]]\n",
                "$$\n",
                "where $\\pi_{01} = \\pi_f, \\pi_{11} = \\pi_k, \\pi_{00} = \\pi_{10} = 0$\n",
                "\n",
                "Suppose $w = \\bar{w} + \\gamma (w - \\bar{w})+\\epsilon$"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 26,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "Created file 'C:\\Users\\barry\\Documents\\Academics\\Quantecon-Notes\\functions\\job_search.m'.\n"
                    ]
                }
            ],
            "source": [
                "%%file functions\\job_search.m\n",
                "function out = job_search(flag,s,x,e,pbar,gamma,u,v);\n",
                "switch flag\n",
                "case 'f'; % REWARD FUNCTION\n",
                "  out = (x==0)*v + (x==1).*( (s(:,2)==0)*u + (s(:,2)==1).*s(:,1) );\n",
                "case 'g'; % STATE TRANSITION FUNCTION\n",
                "  out(:,1) = pbar+gamma*(s(:,1)-pbar)+e(:,1);\n",
                "  out(:,2) = (x==1).*( (s(:,2)==0).*(e(:,2)==1) + (s(:,2)==1).*(e(:,3)==1) );\n",
                "end\n"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 30,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "   1    2.0e+03\n",
                        "   2    1.0e+02\n",
                        "   3    3.3e+00\n",
                        "   4    2.5e-12\n",
                        "Elapsed Time =    0.03 Seconds\n",
                        "\n"
                    ]
                }
            ],
            "source": [
                "clear all\n",
                "  \n",
                "  u =  90;                                              % unemployment benefit\n",
                "  v =  95;                                              % benefit of pure leisure\n",
                "  pbar = 100;                                           % long-run mean wage\n",
                "  gamma = 0.50;                                         % mean reversion rate\n",
                "  pfind = 0.90;                                         % probability of finding job\n",
                "  pkeep = 0.90;                                         % probability of keeping job\n",
                "  delta = 0.95;                                         % discount factor\n",
                "  sigma = 2;                                            % standard deviation of error\n",
                "   \n",
                "% COMPUTE SHOCK DISTRIBUTION \n",
                "  m = 7;                                                % number of shocks\n",
                "  [e1,w1] = qnwnorm(m,0,sigma.^2);                      % price shocks\n",
                "  e2 = [0;1]; w2 = [1-pfind;pfind];                     % job finding shock\n",
                "  e3 = [0;1]; w3 = [1-pkeep;pkeep];                     % job keeping shock\n",
                "  e = gridmake(e1,e2,e3);                               % shock vector\n",
                "  w = ckronx({w3,w2,w1},1);                                % shock probabilities\n",
                "\n",
                "% CONSTRUCT ACTION SPACE\n",
                "  x = [0;1];\n",
                "\n",
                "% PACK MODEL STRUCTURE\n",
                "  clear model  \n",
                "  model.func = 'job_search';                                % model functions\n",
                "  model.discount = delta;                               % discount factor\n",
                "  model.e = e;                                          % shocks\n",
                "  model.w = w;                                          % probabilities\n",
                "  model.actions = x;                                    % model actions\n",
                "  model.discretestates = 2;                             % index of discrete states    \n",
                "  model.params = {pbar gamma u v};                      % other parameters\n",
                "\n",
                "% DEFINE APPROXIMATION SPACE\n",
                "  n = 150;                                              % number of price nodes\n",
                "  pmin = 60;                                            % minimum price\n",
                "  pmax = 140;                                           % maximum price\n",
                "  fspace = fundefn('spli',n,pmin,pmax,[],[0;1]);        % approximation space\n",
                "  scoord = funnode(fspace);                             % state collocation grid coordinates\n",
                "  s = gridmake(scoord);                                 % state collocation grid points\n",
                "\n",
                "% SOLVE BELLMAN EQUATION  \n",
                "  [c,s,v,x] = dpsolve(model,fspace,s);"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 34,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "\n"
                    ]
                },
                {
                    "data": {
                        "image/png": 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\n",
                        "text/plain": [
                            "<IPython.core.display.Image object>"
                        ]
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "plot(s{1},v)\n",
                "title('Value function')\n",
                "legend('Unemployed','Employed')\n",
                "xlabel('Wage')"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 35,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "\n"
                    ]
                },
                {
                    "data": {
                        "image/png": 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\n",
                        "text/plain": [
                            "<IPython.core.display.Image object>"
                        ]
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "plot(s{1},x)\n",
                "title('Optimal action')\n",
                "legend('Unemployed','Employed')\n",
                "xlabel('Wage')"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "## Continuous State Continuous Choice##"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "### Optimal Growth\n",
                "\n",
                "Each year $t$ begins with a predetermined amount of the good $s_t$, of which an amount $x_t$ is invested and the remainder is consumed. The social welfare derived from consumption is $u(s_t - x_t)$. The amount of good available in year $t+1$ is $s_{t+1} = \\gamma x_t + \\epsilon_{t+1}f(x_t)$, where $\\gamma = 1-\\delta$ is capital survival rate, $f$ is the aggregate production function, and $\\epsilon_{t+1}$ is a positive production shock with mean 1. what consumption-investment policy maximizes the sum of current and expected future welfare over an infinite horizon?\n",
                "\n",
                "State variable: $s_t \\in [0,\\infty)$\n",
                "\n",
                "Action variable: $x_t \\in [0, s_t]$\n",
                "\n",
                "State transition: $s_{t+1} = \\gamma x_t + \\epsilon_{t+1}f(x_t)$\n",
                "\n",
                "Bellman equation:\n",
                "$$\n",
                "V(s) = \\max_{0\\leq x\\leq s}[u(s-x) + \\delta EV(\\gamma x+ \\epsilon f(x)]\n",
                "$$\n",
                "\n",
                "Assuming $u'(0) = -\\infty$ and $f(0) = 0$, the constraints will never be binding at an optimum and the shadow price of the composite good $\\lambda(s)$ will satisfy the Euler equation:\n",
                "\n",
                "$$\n",
                "u'(s-t) = \\delta E[\\lambda(\\gamma x + \\epsilon f(x))(\\gamma + \\epsilon f'(x))]\n",
                "$$\n",
                "\n",
                "$$\n",
                "\\lambda (s) = u'(s-x)\n",
                "$$\n",
                "\n",
                "(recall $\\lambda$ is the derivative of V)\n",
                "\n",
                "These conditions imply that along the optimal path, \n",
                "\n",
                "$$\n",
                "u'_t = \\delta E_t [(\\gamma + \\epsilon_{t+1}f'_t)u_{t+1}']\n",
                "$$\n",
                "where $u'_t$ is the current marginal utility and $\\epsilon_{t+1}f'_t$ is the following period's marginal product of capittal. \n",
                "\n",
                "The certainty-equivalent steady-state, which is obtained by fixing the production shock $\\epsilon$ at its mean $1$, are the stock level $s^*$, investment level $x^*$, and shadow price $\\lambda^*$ that solve the nonlinear equation system \n",
                "$$\n",
                "\\begin{aligned}\n",
                "u'(s^*-x^*) &= \\delta \\lambda^*(\\gamma + f'(x^*)) \\\\\n",
                "\\lambda^* &= u'(s^* - x^*)\\\\\n",
                "s^* &= \\gamma x^* + f(x^*)\n",
                "\\end{aligned}\n",
                "$$\n",
                "\n",
                "Assume $u(c) = \\frac{c^{1-\\alpha}}{1-\\alpha}, f(x) = x^\\beta$, and iid lognormal shock $log(\\epsilon) \\sim N(0, \\sigma^2$"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 9,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "Created file 'C:\\Users\\barry\\Documents\\Academics\\Quantecon-Notes\\functions\\optimal_growth.m'.\n"
                    ]
                }
            ],
            "source": [
                "%%file functions\\optimal_growth.m\n",
                "function [out1,out2,out3] = optimal_growth(flag,s,x,e,alpha,beta,gamma)\n",
                "switch flag\n",
                "case 'b'\n",
                "out1 = zeros(size(s));\n",
                "out2 = s;\n",
                "case 'f'\n",
                "out1 = ((s-x).^(1-alpha))/(1-alpha);\n",
                "out2 = -(s-x).^(-alpha);\n",
                "out3 = -alpha*(s-x).^(-alpha-1);\n",
                "case 'g'\n",
                "out1 = gamma*x + e.*x.^beta;\n",
                "out2 = gamma+beta*e.*x.^(beta-1);\n",
                "out3 = (beta-1)*beta*e.*x.^(beta-2);\n",
                "end"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 13,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "   1    6.8e-02\n",
                        "   2    1.8e-02\n",
                        "   3    9.3e-04\n",
                        "   4    2.9e-06\n",
                        "   5    3.0e-11\n",
                        "Elapsed Time =    0.12 Seconds\n",
                        "\n"
                    ]
                }
            ],
            "source": [
                "delta = 0.9;alpha = 0.2;beta = 0.5;gamma = 0.9;sigma = 0.1;\n",
                "m = 3;\n",
                "[e,w] = qnwlogn(m,0,sigma^2);\n",
                "\n",
                "n = 10;\n",
                "smin = 5;\n",
                "smax = 10;\n",
                "fspace = fundefn('cheb',n,smin,smax);\n",
                "snodes = funnode(fspace);\n",
                "\n",
                "model.func = 'optimal_growth';\n",
                "model.discount = delta;\n",
                "model.e = e;\n",
                "model.w = w;\n",
                "model.params = {alpha beta gamma};\n",
                "\n",
                "estar = 1;\n",
                "xstar = ((1-delta*gamma)/(delta*beta))^(1/(beta-1));\n",
                "sstar = gamma*xstar + xstar^beta;\n",
                "\n",
                "[vlq, xlq] = lqapprox(model, snodes, sstar, xstar, estar);\n",
                "\n",
                "[c,s,v,x,resid] = dpsolve(model,fspace,snodes,vlq,xlq);"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 17,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "\n"
                    ]
                },
                {
                    "data": {
                        "image/png": 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\n",
                        "text/plain": [
                            "<IPython.core.display.Image object>"
                        ]
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "plot(s, x./s, snodes,xlq./snodes)"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 18,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "\n"
                    ]
                }
            ],
            "source": [
                "nyrs = 20;\n",
                "nrep = 2000;\n",
                "sinit = 5*ones(nrep,1);\n",
                "[spath, xpath] = dpsimul(model, sinit, nyrs,s,x);\n",
                "\n",
                "nsmooth = 5;\n",
                "nbin = 80;\n",
                "[ss,pi,xx] = dpstst(model, nsmooth, nbin, s,x);"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 29,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "\n"
                    ]
                },
                {
                    "data": {
                        "image/png": 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\n",
                        "text/plain": [
                            "<IPython.core.display.Image object>"
                        ]
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "plot(ss,pi)\n",
                "title(\"wealth distribution for steady state\")"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 45,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "\n"
                    ]
                },
                {
                    "data": {
                        "image/png": 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\n",
                        "text/plain": [
                            "<IPython.core.display.Image object>"
                        ]
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "plot(linspace(1,nyrs,nyrs+1),mean(spath))\n",
                "title(\"Expected wealth over time\")"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "### Public Renewable Resource Management\n",
                "\n",
                "Each year begins with a predetermined stock of the resource $s$, of which an amount $x$ is harvested at total cost $c(x)$ and sold at market clearing price $p(x)$. The stock of resource available at the beginning of each period follows a deterministic process $s_{t+1} = g(s_t - x_t)$. What is the harvest policy? What is the steady-state resource stock and how does it vary with interest rate?\n",
                "\n",
                "State variable: $s\\in[0,\\infty)$. Choice variable: $x\\in[0,s]$. Current reward: $f(x) = \\int_0^x p(\\xi)d\\xi - c(x)$. Bellman equation:\n",
                "$$\n",
                "V(s) = \\max_{0\\leq x\\leq s} [\\int_0^x p(\\xi)d\\xi -c(x)+\\delta V(g(s-x))]\n",
                "$$\n",
                "\n",
                "Assuming $p(0) = \\infty$ and $g(0) = 0$, the constraint $x=0$ or $x=s$ will never bind and Euler equations:\n",
                "\n",
                "$$\n",
                "\\begin{aligned}\n",
                "p(x) &= c'(x)+\\delta \\lambda(g(s-x))g'(s-x)\\\\\n",
                "\\lambda(s) &= \\delta \\lambda(g(s-x))g'(s-x)\\end{aligned}\n",
                "$$\n",
                "which implies\n",
                "$$\n",
                "\\begin{aligned}\n",
                "p(x) &= c'(x)+\\delta \\lambda_t\\\\\n",
                "\\lambda(s) &= \\delta \\lambda_{t+1}g'\\end{aligned}\n",
                "$$\n",
                "For steady state, it solves \n",
                "\n",
                "$$\n",
                "\\begin{aligned}\n",
                "p(x) &= c'(x)+\\delta \\lambda g'(s-x)\\\\\n",
                "\\lambda &= \\delta \\lambda g'(s-x)\\\\\n",
                "s &= g(s-x)\n",
                "\\end{aligned}\n",
                "$$\n",
                "\n",
                "Suppose $p(x) = x^{-\\gamma}$, $c(x) = kx$, and $g(s,x) = \\alpha(s-x)-0.5\\beta(s-x)^2$"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 36,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "Created file 'C:\\Users\\barry\\Documents\\Academics\\Quantecon-Notes\\functions\\public_resource.m'.\n"
                    ]
                }
            ],
            "source": [
                "%%file functions\\public_resource.m\n",
                "function [out1, out2, out3] = public_resource(flag, s,x,e,alpha, beta, gamma, k)\n",
                "switch flag\n",
                "case 'b'\n",
                "out1 = zeros(size(s));\n",
                "out2 = s;\n",
                "case 'f'\n",
                "out1 = (x.^(1-gamma))/(1-gamma)-k*x;\n",
                "out2 = x.^(-gamma)-k;\n",
                "out3 = -gamma*x.^(-gamma-1);\n",
                "case 'g'\n",
                "out1 = alpha*(s-x)-0.5*beta*(s-x).^2;\n",
                "out2 = -alpha+beta*(s-x);\n",
                "out3 = zeros(size(s)) - beta;\n",
                "end"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 108,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "\n"
                    ]
                }
            ],
            "source": [
                "clear all\n",
                "delta = 0.9;\n",
                "alpha = 4;\n",
                "beta = 1;\n",
                "gamma = 0.5;\n",
                "k = 0.2;\n",
                "\n",
                "n = 13;\n",
                "smin = 6;\n",
                "smax = 9;\n",
                "fspace = fundefn('spli', n, smin, smax);\n",
                "snodes = funnode(fspace);\n",
                "\n",
                "model.func = 'public_resource';\n",
                "model.discount = delta;\n",
                "model.params = {alpha beta gamma k};\n",
                "\n",
                "sstar = (alpha^2-1/delta^2)/(2*beta);\n",
                "xstar = sstar - (delta*alpha-1)/(delta*beta);\n",
                "pstar = xstar^(-gamma) - k;\n",
                "\n",
                "[vlq,xlq] = lqapprox(model, snodes, sstar, xstar,pstar);"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 109,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "Warning: You are using the m-file version of a function that is coded as a C Mex file.\n",
                        "  Running this M file version may be significantly slower and more memory intensive.\n",
                        "  Use MEXALL to create the executable (MEX or DLL) and make sure it is on the MATLAB path.\n",
                        "   1    4.5e-02\n",
                        "   2    4.1e-04\n",
                        "   3    7.8e-09\n",
                        "Elapsed Time =    0.34 Seconds\n",
                        "\n"
                    ]
                }
            ],
            "source": [
                "[c,s,v,x] = dpsolve(model, fspace, snodes, vlq,xlq);"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 110,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "\n"
                    ]
                },
                {
                    "data": {
                        "image/png": 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\n",
                        "text/plain": [
                            "<IPython.core.display.Image object>"
                        ]
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "plot(s,x,s,xlq,sstar,xstar,'*')\n",
                "title('Optimal harvesting policy');\n",
                "xlabel('Stock')\n",
                "ylabel('Harvest amount')"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 107,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "\n"
                    ]
                },
                {
                    "data": {
                        "image/png": 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\n",
                        "text/plain": [
                            "<IPython.core.display.Image object>"
                        ]
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "nyrs = 20;\n",
                "sinit = 3;\n",
                "[spath, xpath] = dpsimul(model, sinit, nyrs, s,x);\n",
                "plot(linspace(0,nyrs, nyrs+1), spath)\n",
                "title('Stock in time')\n",
                "xlabel('Years')\n",
                "ylabel('Stock')"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "### Private Nonrenewable Resource\n",
                "Each period begins with a predetermined stock of ore $s$, of which $x$ is extracted at a total cost $c(s)$ and sold at market price $p$. What is the optimal extraction policy?\n",
                "\n",
                "Infinite horizon. State variable: $s$. Choice variable: $x\\in [0,s]$. Current profit: $f(s,x) = px - c(x)$. Value function: $$V(s) = \\max_{0\\leq x\\leq s}[px - c(x)+\\delta V(s-x)]$$\n",
                "\n",
                "Since the constraints might be binding, the Euler conditions take the form of a complementarity condition. The shadow price of the resource $\\lambda(s)$ is characterized by \n",
                "\n",
                "$$\n",
                "p - c'(x) - \\delta \\lambda(s-x) = \\mu\n",
                "$$\n",
                "$$\n",
                "\\lambda(s) = \\delta \\lambda(s-x) + \\max(\\mu,0)\n",
                "$$\n",
                "where $x$ and long run marginal profit of extraction $\\mu$ must satisfy complementarity conditions $0\\leq x\\leq s, x>0\\Rightarrow \\mu >0, x<s \\Rightarrow \\mu \\leq 0$\n",
                "Ore is extracted until the long-run marginal profit is driven to 0 or $x=s$, which ever comes first. \n",
                "\n",
                "Suppose $p = a_1 -a_2 x/2, c(x) = b_1x-b_2x\\frac{2s-x}{2}$, and state transition is $s_{t+1} = s_t - x_t$"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 111,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "Created file 'C:\\Users\\barry\\Documents\\Academics\\Quantecon-Notes\\functions\\nonrenewable_ore.m'.\n"
                    ]
                }
            ],
            "source": [
                "%%file functions\\nonrenewable_ore.m\n",
                "function [out1, out2, out3] = nonrenewable_ore(flag, s,x,e,a,b)\n",
                "switch flag\n",
                "case 'b'\n",
                "out1 = zeros(size(s));\n",
                "out2 = s;\n",
                "case 'f';\n",
                "out1 = (a(1)-a(2).*x).*x/2 - b(1).*x+b(2).*x.*(2*s-x)/2;\n",
                "out2 = a(1)-a(2).*x - b(1)+b(2)*s-b(2).*x;\n",
                "out3 = (-a(2)-b(2))*ones(size(s));\n",
                "case 'g';\n",
                "out1 = s-x;\n",
                "out2 = -ones(size(s));\n",
                "out3 = zeros(size(s));\n",
                "end"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 119,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "Warning: You are using the m-file version of a function that is coded as a C Mex file.\n",
                        "  Running this M file version may be significantly slower and more memory intensive.\n",
                        "  Use MEXALL to create the executable (MEX or DLL) and make sure it is on the MATLAB path.\n",
                        "   1    1.6e+01\n",
                        "   2    2.7e+02\n",
                        "   3    3.5e+03\n",
                        "   4    3.3e+04\n",
                        "   5    2.8e+05\n",
                        "   6    1.9e+06\n",
                        "   7    1.7e+06\n",
                        "   8    1.3e+03\n",
                        "   9    1.3e+03\n",
                        "  10    1.3e+03\n",
                        "  11    1.3e+03\n",
                        "  12    1.3e+03\n",
                        "  13    1.3e+03\n",
                        "  14    1.3e+03\n",
                        "  15    1.3e+03\n",
                        "  16    1.3e+03\n",
                        "  17    1.3e+03\n",
                        "  18    1.2e+02\n",
                        "  19    2.8e-14\n",
                        "Elapsed Time =    1.24 Seconds\n",
                        "\n"
                    ]
                }
            ],
            "source": [
                "clear all\n",
                "a = [10 0.8];\n",
                "b = [12 1.0];\n",
                "delta = 0.9;\n",
                "\n",
                "model.func = 'nonrenewable_ore';\n",
                "model.discount = delta;\n",
                "model.params = {a b};\n",
                "\n",
                "n = 100;\n",
                "smin = 0;\n",
                "smax = 10;\n",
                "fspace = fundefn('spli',n,smin, smax);\n",
                "snodes = funnode(fspace);\n",
                "\n",
                "xinit = zeros(size(snodes));\n",
                "vinit = zeros(size(snodes));\n",
                "\n",
                "[c,s,v,x] = dpsolve(model, fspace, snodes, vinit, xinit);"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 123,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "\n"
                    ]
                },
                {
                    "data": {
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\n",
                        "text/plain": [
                            "<IPython.core.display.Image object>"
                        ]
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "plot(s,x,s,s,':')\n",
                "title('Optimal harvesting policy')\n",
                "xlabel('Available Stock');\n",
                "ylabel('Harvest')"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 124,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "\n"
                    ]
                },
                {
                    "data": {
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\n",
                        "text/plain": [
                            "<IPython.core.display.Image object>"
                        ]
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "plot(s,v)\n",
                "title('Value function')\n",
                "xlabel('Available stock')"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 125,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "\n"
                    ]
                },
                {
                    "data": {
                        "image/png": 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\n",
                        "text/plain": [
                            "<IPython.core.display.Image object>"
                        ]
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "p = funeval(c,fspace, s,1);\n",
                "plot(s,p);\n",
                "title('Shadow price function')"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "### Optimal Monetary Policy\n",
                "\n",
                "The central bank wishes to control nominal interest rate $x$ in order to minimize the volatility of the inflation rate $s_1$ and the output gap $s_2$. Specifically, it minimizes the expected discounted stream of weightes squared deviations from zero targets: $L(s) = \\frac{1}{2}(s-s^*)^T\\Omega (s-s^*)$, where s = [inflation; output gap] and $\\Omega$ is 2x2 positive definite weight matrix. The inflation rate and the output gap are jointly controlled linear Markov process $s_{t+1} = \\alpha+\\beta s_t + \\gamma x +\\epsilon$. The nominal rate cannot be negative. What is the optimal monetary policy?\n",
                "\n",
                "Infinite horizon. State variable: s = [inflation; output gap]. Choice variable: $x \\in [0,\\infty)$. Current reward: $f(s) = -L(s)$. Value function:\n",
                "\n",
                "$$\n",
                "V(s) = \\max_{0\\leq x}[-L(s) + \\delta EV(g(s,x,\\epsilon))]\n",
                "$$\n",
                "\n"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "Suppose $\\epsilon \\sim N(0, \\Sigma)$"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 3,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "Created file 'C:\\Users\\barry\\Documents\\Academics\\Quantecon-Notes\\functions\\monetary_policy.m'.\n"
                    ]
                }
            ],
            "source": [
                "%%file functions\\monetary_policy.m\n",
                "function [out1, out2, out3] = monetary_policy(flag, s, x, e, alpha, beta, gamma, omega,starget);\n",
                "[n ds] = size(s);\n",
                "switch flag\n",
                "case 'b'\n",
                "out1 = zeros(n,1);\n",
                "out2 = inf*ones(n,1);\n",
                "case 'f'\n",
                "starget = starget(ones(n,1),:);\n",
                "out1 = -0.5*((s-starget).^2)*omega';\n",
                "out2 = zeros(n,1);\n",
                "out3 = zeros(n,1);\n",
                "case 'g'\n",
                "out1 = alpha(ones(n,1),:)+s*beta'+x*gamma+e;\n",
                "out2 = gamma(ones(n,1),:);\n",
                "out3 = zeros(n,ds);\n",
                "end"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 44,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "Warning: You are using the m-file version of a function that is coded as a C Mex file.\n",
                        "  Running this M file version may be significantly slower and more memory intensive.\n",
                        "  Use MEXALL to create the executable (MEX or DLL) and make sure it is on the MATLAB path.\n",
                        "   1    8.2e+01\n",
                        "   2    5.5e-03\n",
                        "   3    1.4e-06\n",
                        "   4    3.7e-13\n",
                        "Elapsed Time =    1.08 Seconds\n",
                        "\n"
                    ]
                }
            ],
            "source": [
                "clear all\n",
                "alpha = [0.8 0.2];\n",
                "beta = [0.8 0.2;0.13 0.5];\n",
                "gamma = [-0.8 0];\n",
                "omega = [0.3 1];\n",
                "starget = [0 1];\n",
                "sigma = 0.04*eye(2);\n",
                "delta = 0.9;\n",
                "\n",
                "m = [5 5];\n",
                "mu = [0 0];\n",
                "[e,w] = qnwnorm(m,mu,sigma);\n",
                "\n",
                "model.func = 'monetary_policy';\n",
                "model.discount = delta;\n",
                "model.e = e;\n",
                "model.w = w;\n",
                "model.params = {alpha beta gamma omega starget};\n",
                "\n",
                "n = [20 20];\n",
                "nn = prod(n);\n",
                "smin = [-15 -10];\n",
                "smax = [15 10];\n",
                "fspace = fundefn('spli',n, smin, smax);\n",
                "scoord = funnode(fspace);\n",
                "snodes = gridmake(scoord);\n",
                "\n",
                "estar = mu;\n",
                "sstar = starget;\n",
                "xstar = (sstar(1)-alpha(1)-beta(1,:)*sstar')/gamma(1);\n",
                "pstar = [0 0];\n",
                "\n",
                "[vlq,xlq,plq,ss,xx,pp] = lqapprox(model,snodes,sstar,xstar,pstar);\n",
                "\n",
                "optset('dpsolve','nres',4);\n",
                "[c,s,v,x] = dpsolve(model, fspace, snodes,vlq, xlq);"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 5,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "\n"
                    ]
                },
                {
                    "data": {
                        "image/png": 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\n",
                        "text/plain": [
                            "<IPython.core.display.Image object>"
                        ]
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "figure(1)\n",
                "hh = surf(s{1},s{2},x');\n",
                "title('Optimal Monetary Policy');\n",
                "xlabel('GDP Gap');\n",
                "ylabel('Inflation Rate');\n",
                "zlabel('Norminal Interest Rate');"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 11,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "\n"
                    ]
                },
                {
                    "data": {
                        "image/png": 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\n",
                        "text/plain": [
                            "<IPython.core.display.Image object>"
                        ]
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "figure(2)\n",
                "contour(s{1},s{2},x',25);\n",
                "title('Optimal Monetary Policy');\n",
                "xlabel('GDP Gap');\n",
                "ylabel('Inflation Rate');\n",
                "zlabel('Norminal Interest Rate');\n",
                "rotate3d"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 45,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "\n"
                    ]
                },
                {
                    "data": {
                        "image/png": 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\n",
                        "text/plain": [
                            "<IPython.core.display.Image object>"
                        ]
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "nyrs = 20;\n",
                "nrep = 5000;\n",
                "sinit = smax(ones(nrep,1),:)-1;\n",
                "[spath,xpath] = dpsimul(model, sinit, nyrs, s,x);\n",
                "s1path = squeeze(spath(:,1,:));\n",
                "s2path = squeeze(spath(:,2,:));\n",
                "\n",
                "figure(3);\n",
                "plot(0:nyrs,mean(s1path));\n",
                "title('Expected State Path');\n",
                "xlabel('Year');\n",
                "ylabel('GDP Gap');"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 9,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "\n"
                    ]
                },
                {
                    "data": {
                        "image/png": 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\n",
                        "text/plain": [
                            "<IPython.core.display.Image object>"
                        ]
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "figure(4);\n",
                "plot(0:nyrs,mean(s2path));\n",
                "title('Expected State Path');\n",
                "xlabel('Year');\n",
                "ylabel('Inflation');"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "### Production Inventory model\n",
                "\n",
                "A competitive price taking firm wishes to manage production and inventories so as to maximize long-term profit. Each period begins with a predetermined stock of inventory $s$ and decides how much to produce $q$ and how much to store $x$, buying or selling the resulting difference $s+q-x$ with price $p$. The firm's production and storage costs are given by $c(q)$ and $k(x)$, and market price follows $p_{t+1} = g(s_t, \\epsilon_{t+1})$. \n",
                "\n",
                "State variable: $p$ and $s$. Choice variables: $q\\geq 0$ and $x\\geq 0$. Current profit: $f(p,s,q,x) = p(s+q-x)-c(q)-k(x)$. Bellman equation:\n",
                "$$\n",
                "V(p,s) = \\max_{x,q}[p(s+q-x)-c(q)-k(x)+\\delta EV(g(p,\\epsilon),x)]\n",
                "$$\n",
                "\n"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "If increasing marginal cost of production and $c'(0)$ is very small, then the production will be positive and the $q=0$ will never bind. Therefore, the Euler equation will satisfy \n",
                "$$\n",
                "p = c'(q)\n",
                "$$\n",
                "$$\n",
                "\\delta E\\lambda(g(p,\\epsilon),x) - p - k'(x) = \\mu\n",
                "$$\n",
                "$$\n",
                "\\lambda(p,s) = p\n",
                "$$\n",
                "$$x\\geq 0, \\mu \\leq 0, x>0\\Rightarrow \\mu = 0$$\n",
                "\n",
                "State transition: $s_{t+1} = x_t$, $p_{t+1} = \\bar{p} + \\rho(p-\\bar{p})+\\epsilon$, $c = c_1q+\\frac{1}{2}c_2q^2$, $k = k_1x+\\frac{1}{2}k_2x^2$"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 2,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "Created file 'C:\\Users\\barry\\Documents\\Academics\\Quantecon-Notes\\functions\\production_inventory.m'.\n"
                    ]
                }
            ],
            "source": [
                "%%file functions\\production_inventory.m\n",
                "function [out1, out2, out3] = production_inventory(flag,s,x,e,c,k,pbar,rho)\n",
                "n = size(s,1);\n",
                "ds = 2;\n",
                "dx = 2;\n",
                "switch flag\n",
                "case 'b'\n",
                "out1 = zeros(size(s));\n",
                "out2 = inf*ones(size(s));\n",
                "case 'f'\n",
                "out1 = zeros(n,1);\n",
                "out2 = zeros(n,dx);\n",
                "out3 = zeros(n,dx,dx);\n",
                "out1 = s(:,2).*(s(:,1)+x(:,1)-x(:,2))...\n",
                "        -(c(1)+0.5*c(2)*x(:,1)).*x(:,1)...\n",
                "        - (k(1)+0.5*k(2)*x(:,2)).*x(:,2);\n",
                "out2(:,1) = s(:,2) - (c(1)+c(2)*x(:,1));\n",
                "out2(:,2) = -s(:,2) - (k(1)+k(2))*x(:,2);\n",
                "out3(:,1,1) = -c(2)*ones(n,1);\n",
                "out3(:,2,2) = -k(2)*ones(n,1);\n",
                "case 'g'\n",
                "out1 = zeros(n,ds);\n",
                "out2 = zeros(n,ds,dx);\n",
                "out3 = zeros(n,ds,dx,dx);\n",
                "out1 = [x(:,2) pbar+rho*(s(:,2)-pbar)+e];\n",
                "out2(:,1,2) = ones(n,1);\n",
                "end"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 6,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "Possible Error in Derivatives\n",
                        "Discrepancies in derivatives = \n",
                        "    0.1000    0.1000         0         0\n",
                        "\n",
                        "\n"
                    ]
                }
            ],
            "source": [
                "clear all\n",
                "c = [0.5 0.1];\n",
                "k = [0.1 0.1];\n",
                "pbar = 1.0;\n",
                "rho = 0.5;\n",
                "sigma = 0.2;\n",
                "delta = 0.9;\n",
                "\n",
                "m = 2;\n",
                "[e,w] = qnwnorm(m,0,sigma^2);\n",
                "\n",
                "model.func = 'production_inventory';\n",
                "model.discount = delta;\n",
                "model.e = e;\n",
                "model.w = w;\n",
                "model.params = {c k pbar rho};\n",
                "\n",
                "estar = 0;\n",
                "sstar = [0 pbar];\n",
                "xstar = [(pbar-c(1))/c(2) 0];\n",
                "pstar = [pbar xstar(1)/(1-delta*rho)];\n",
                "\n",
                "n = [4 20];\n",
                "smin = [0 pbar + min(e)/(1-rho)];\n",
                "smax = [2 pbar + max(e)/(1-rho)];\n",
                "fspace = fundefn('spli',n,smin,smax);\n",
                "scoord = funnode(fspace);\n",
                "snodes = gridmake(scoord);\n",
                "\n",
                "dpcheck(model, sstar, xstar, estar);\n",
                "\n",
                "[vlq, xlq, plq, ss,xx,pp] = lqapprox(model, snodes, sstar, xstar, pstar);\n",
                "\n"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 7,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "Warning: You are using the m-file version of a function that is coded as a C Mex file.\n",
                        "  Running this M file version may be significantly slower and more memory intensive.\n",
                        "  Use MEXALL to create the executable (MEX or DLL) and make sure it is on the MATLAB path.\n",
                        "   1    2.3e+00\n",
                        "   2    5.5e-14\n",
                        "Elapsed Time =    2.00 Seconds\n",
                        "\n"
                    ]
                }
            ],
            "source": [
                "[c,s,v,x] = dpsolve(model, fspace, snodes, vlq, xlq);"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 8,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "\n"
                    ]
                },
                {
                    "data": {
                        "image/png": 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\n",
                        "text/plain": [
                            "<IPython.core.display.Image object>"
                        ]
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "figure(1)\n",
                "hh = surf(s{1},s{2},x(:,:,1)');\n",
                "title('Optimal production policy')\n",
                "xlabel('Beginning inventories');\n",
                "ylabel('Prices');\n",
                "zlabel('Production amount')"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 9,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "\n"
                    ]
                },
                {
                    "data": {
                        "image/png": 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\n",
                        "text/plain": [
                            "<IPython.core.display.Image object>"
                        ]
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "figure(2)\n",
                "surf(s{1},s{2},x(:,:,2)');\n",
                "title('Optimal Inventory Policy');\n",
                "xlabel('Beginning Inventory');\n",
                "ylabel('Price');\n",
                "zlabel('Storage')"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 10,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "\n"
                    ]
                },
                {
                    "data": {
                        "image/png": 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\n",
                        "text/plain": [
                            "<IPython.core.display.Image object>"
                        ]
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "figure(3)\n",
                "surf(s{1},s{2},v');\n",
                "title('Value function');\n",
                "xlabel('Beginning Inventory');\n",
                "ylabel('Price');"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 20,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "\n"
                    ]
                }
            ],
            "source": [
                "nyrs = 20;\n",
                "nrep = 1000;\n",
                "sinit = smin(ones(nrep,1),:);\n",
                "[spath,xpath] = dpsimul(model, sinit, nyrs, s,x);"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 19,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "\n"
                    ]
                },
                {
                    "data": {
                        "image/png": 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\n",
                        "text/plain": [
                            "<IPython.core.display.Image object>"
                        ]
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "s1path = squeeze(spath(:,1,:));\n",
                "s2path = squeeze(spath(:,2,:));\n",
                "xpath = squeeze(xpath(:,1,:));\n",
                "\n",
                "figure(4)\n",
                "plot(0:nyrs, mean(s1path));\n",
                "title('Expected State Path');\n",
                "xlabel('Year');\n",
                "ylabel('Inventory')"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 15,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "\n"
                    ]
                },
                {
                    "data": {
                        "image/png": 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\n",
                        "text/plain": [
                            "<IPython.core.display.Image object>"
                        ]
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "figure(5)\n",
                "plot(0:nyrs, mean(s2path));\n",
                "title('Expected State Path');\n",
                "xlabel('Year');\n",
                "ylabel('Price')"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 17,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "\n"
                    ]
                },
                {
                    "data": {
                        "image/png": 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\n",
                        "text/plain": [
                            "<IPython.core.display.Image object>"
                        ]
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "figure(6)\n",
                "plot(0:nyrs, mean(xpath));\n",
                "title('Expected Choice Path');\n",
                "xlabel('Year');\n",
                "ylabel('Production')"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": null,
            "metadata": {},
            "outputs": [],
            "source": []
        }
    ],
    "metadata": {
        "kernelspec": {
            "display_name": "Matlab",
            "language": "matlab",
            "name": "matlab"
        },
        "language_info": {
            "codemirror_mode": "octave",
            "file_extension": ".m",
            "help_links": [
                {
                    "text": "MetaKernel Magics",
                    "url": "https://metakernel.readthedocs.io/en/latest/source/README.html"
                }
            ],
            "mimetype": "text/x-octave",
            "name": "matlab",
            "version": "0.16.7"
        }
    },
    "nbformat": 4,
    "nbformat_minor": 2
}