From e9cbefcbe850721414fe879390efdb97225ca3ef Mon Sep 17 00:00:00 2001 From: John Stachurski Date: Thu, 6 Sep 2018 21:48:31 -0400 Subject: [PATCH] misc --- .../supply_and_demand-checkpoint.ipynb | 308 ++++++++++++++++++ ...ply_and_demand_solution_1-checkpoint.ipynb | 199 +++++++++++ ...ply_and_demand_solution_2-checkpoint.ipynb | 230 +++++++++++++ sept_7_seminar/supply_and_demand.ipynb | 308 ++++++++++++++++++ .../supply_and_demand_solution_1.ipynb | 199 +++++++++++ .../supply_and_demand_solution_2.ipynb | 230 +++++++++++++ 6 files changed, 1474 insertions(+) create mode 100644 sept_7_seminar/.ipynb_checkpoints/supply_and_demand-checkpoint.ipynb create mode 100644 sept_7_seminar/.ipynb_checkpoints/supply_and_demand_solution_1-checkpoint.ipynb create mode 100644 sept_7_seminar/.ipynb_checkpoints/supply_and_demand_solution_2-checkpoint.ipynb create mode 100644 sept_7_seminar/supply_and_demand.ipynb create mode 100644 sept_7_seminar/supply_and_demand_solution_1.ipynb create mode 100644 sept_7_seminar/supply_and_demand_solution_2.ipynb diff --git a/sept_7_seminar/.ipynb_checkpoints/supply_and_demand-checkpoint.ipynb b/sept_7_seminar/.ipynb_checkpoints/supply_and_demand-checkpoint.ipynb new file mode 100644 index 0000000..baddb38 --- /dev/null +++ b/sept_7_seminar/.ipynb_checkpoints/supply_and_demand-checkpoint.ipynb @@ -0,0 +1,308 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Writing Clean Code" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### John Stachurski" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here is some code that needs improving. It involves a basic supply and demand problem. \n", + "\n", + "First let's do some standard imports and set up commands" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from scipy.optimize import bisect" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### A Market " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now consider a market where supply is given by\n", + "\n", + "$$ q_s(p) = \\exp(\\alpha p) - \\beta. $$\n", + "\n", + "The demand curve is\n", + "\n", + "$$ q_d(p) = \\gamma p^{-\\delta}. $$\n", + "\n", + "The values $\\alpha$, $\\beta$, $\\gamma$ and $\\delta$ are parameters.\n", + "\n", + "The equilibrium $p^*$ is the price such that $q_d(p) = q_s(p)$.\n", + "\n", + "We can solve for this equilibrium using a root finding algorithm. Specifically, we will find the $p$ such that $h(p) = 0$, where\n", + "\n", + "$$ h(p) := q_d(p) - q_s(p) $$\n", + "\n", + "This yields the equilibrium price $p^*$. From this we get the equilibrium price by $q^* = q_s(p^*)$\n", + "\n", + "Then we'll plot our results. The parameter values will be\n", + "\n", + "* $\\alpha = 0.1$\n", + "* $\\beta = 1$\n", + "* $\\gamma = 1$\n", + "* $\\delta = 1$" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Equilibrium price is 2.93\n", + "Equilibrium quantity is 0.34\n" + ] + } + ], + "source": [ + "# Compute equilibrium\n", + "def h(p):\n", + " return p**(-1) - (np.exp(0.1 * p) - 1)\n", + "\n", + "p_star = bisect(h, 2, 4)\n", + "q_star = np.exp(0.1 * p_star) - 1\n", + "\n", + "print(f'Equilibrium price is {p_star: .2f}')\n", + "print(f'Equilibrium quantity is {q_star: .2f}')" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Now plot\n", + "grid = np.linspace(2, 4, 100)\n", + "fig, ax = plt.subplots(figsize=(8, 6))\n", + "\n", + "qs = np.exp(0.1 * grid) - 1\n", + "qd = grid**(-1)\n", + "\n", + "ax.plot(grid, qd, 'b-', lw=2, label='demand')\n", + "ax.plot(grid, qs, 'g-', lw=2, label='supply')\n", + "\n", + "ax.set_xlabel('price', fontsize=14)\n", + "ax.set_ylabel('quantity', fontsize=14)\n", + "ax.legend(loc='upper center')\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "### Demand Shift\n", + "\n", + "What happens when demand shifts up, with $\\gamma$ increasing to $1.25$?" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Equilibrium price is 3.25\n", + "Equilibrium quantity is 0.38\n" + ] + } + ], + "source": [ + "# Compute equilibrium\n", + "def h(p):\n", + " return 1.25 * p**(-1) - (np.exp(0.1 * p) - 1)\n", + "\n", + "p_star = bisect(h, 2, 4)\n", + "q_star = np.exp(0.1 * p_star) - 1\n", + "\n", + "print(f'Equilibrium price is {p_star: .2f}')\n", + "print(f'Equilibrium quantity is {q_star: .2f}')" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Now plot\n", + "p_grid = np.linspace(2, 4, 100)\n", + "fig, ax = plt.subplots(figsize=(8, 6))\n", + "\n", + "qs = np.exp(0.1 * p_grid) - 1\n", + "qd = 1.25 * p_grid**(-1)\n", + "\n", + "\n", + "ax.plot(grid, qd, 'b-', lw=2, label='demand')\n", + "ax.plot(grid, qs, 'g-', lw=2, label='supply')\n", + "\n", + "ax.set_xlabel('price', fontsize=14)\n", + "ax.set_ylabel('quantity', fontsize=14)\n", + "ax.legend(loc='upper center')\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "### Supply Shift\n", + "\n", + "Now let's take $\\gamma$ back to 1 but increase $\\alpha$ to 0.12" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Equilibrium price is 2.66\n", + "Equilibrium quantity is 0.38\n" + ] + } + ], + "source": [ + "# Compute equilibrium\n", + "def h(p):\n", + " return p**(-1) - (np.exp(0.12 * p) - 1)\n", + "\n", + "p_star = bisect(h, 2, 4)\n", + "q_star = np.exp(0.12 * p_star) - 1\n", + "\n", + "print(f'Equilibrium price is {p_star: .2f}')\n", + "print(f'Equilibrium quantity is {q_star: .2f}')" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Now plot\n", + "p_grid = np.linspace(2, 4, 100)\n", + "fig, ax = plt.subplots(figsize=(8, 6))\n", + "\n", + "qs = np.exp(0.12 * p_grid) - 1\n", + "qd = p_grid**(-1)\n", + "\n", + "\n", + "ax.plot(grid, qd, 'b-', lw=2, label='demand')\n", + "ax.plot(grid, qs, 'g-', lw=2, label='supply')\n", + "\n", + "ax.set_xlabel('price', fontsize=14)\n", + "ax.set_ylabel('quantity', fontsize=14)\n", + "ax.legend(loc='upper center')\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.4" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/sept_7_seminar/.ipynb_checkpoints/supply_and_demand_solution_1-checkpoint.ipynb b/sept_7_seminar/.ipynb_checkpoints/supply_and_demand_solution_1-checkpoint.ipynb new file mode 100644 index 0000000..47e4adc --- /dev/null +++ b/sept_7_seminar/.ipynb_checkpoints/supply_and_demand_solution_1-checkpoint.ipynb @@ -0,0 +1,199 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Writing Clean Code: Solution with Functions" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### John Stachurski" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from scipy.optimize import bisect" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "First let's define supply and demand functions" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "def qs(p, α, β):\n", + " return np.exp(α * p) - β\n", + "\n", + "def qd(p, γ, δ):\n", + " return γ * p**(-δ)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's a function to compute the equilibrium:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "def compute_equilibrium(α=0.1, β=1, γ=1, δ=1):\n", + " # Define excess demand function\n", + " def h(p):\n", + " return qd(p, γ, δ) - qs(p, α, β)\n", + " \n", + " p_star = bisect(h, 2, 4)\n", + " q_star = qs(p_star, α, β)\n", + " \n", + " print(f'Equilibrium price is {p_star: .2f}')\n", + " print(f'Equilibrium quantity is {q_star: .2f}')" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Equilibrium price is 2.93\n", + "Equilibrium quantity is 0.34\n" + ] + } + ], + "source": [ + "compute_equilibrium()" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "def plot_equilibrium(α=0.1, β=1, γ=1, δ=1):\n", + " grid = np.linspace(2, 4, 100)\n", + " fig, ax = plt.subplots(figsize=(8, 6))\n", + "\n", + " ax.plot(grid, qd(grid, γ, δ), 'b-', lw=2, label='demand')\n", + " ax.plot(grid, qs(grid, α, β), 'g-', lw=2, label='supply')\n", + "\n", + " ax.set_xlabel('price', fontsize=14)\n", + " ax.set_ylabel('quantity', fontsize=14)\n", + " ax.legend(loc='upper center')\n", + "\n", + " plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_equilibrium(α=0.12)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.4" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/sept_7_seminar/.ipynb_checkpoints/supply_and_demand_solution_2-checkpoint.ipynb b/sept_7_seminar/.ipynb_checkpoints/supply_and_demand_solution_2-checkpoint.ipynb new file mode 100644 index 0000000..da89eb1 --- /dev/null +++ b/sept_7_seminar/.ipynb_checkpoints/supply_and_demand_solution_2-checkpoint.ipynb @@ -0,0 +1,230 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Writing Clean Code: Solution with Classes" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### John Stachurski" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from scipy.optimize import bisect" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "First let's define a \"Market\" as a class. It contains parameters and a supply and demand curve" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "class Market:\n", + " \n", + " def __init__(self, α=0.1, β=1, γ=1, δ=1):\n", + " self.α, self.β, self.γ, self.δ = α, β, γ, δ\n", + "\n", + " def qs(self, p):\n", + " return np.exp(self.α * p) - self.β\n", + " \n", + " def qd(self, p):\n", + " return self.γ * p**(-self.δ)\n", + " " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's a function to compute the equilibrium:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "def compute_equilibrium(mkt):\n", + " # Define excess demand function\n", + " def h(p):\n", + " return mkt.qd(p) - mkt.qs(p)\n", + " # Find zero of h\n", + " p_star = bisect(h, 2, 4)\n", + " q_star = mkt.qs(p_star)\n", + " \n", + " print(f'Equilibrium price is {p_star: .2f}')\n", + " print(f'Equilibrium quantity is {q_star: .2f}')" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "mkt = Market()" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Equilibrium price is 2.93\n", + "Equilibrium quantity is 0.34\n" + ] + } + ], + "source": [ + "compute_equilibrium(mkt)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's a function for plotting." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "def plot_equilibrium(mkt):\n", + " grid = np.linspace(2, 4, 100)\n", + " fig, ax = plt.subplots(figsize=(8, 6))\n", + "\n", + " ax.plot(grid, mkt.qd(grid), 'b-', lw=2, label='demand')\n", + " ax.plot(grid, mkt.qs(grid), 'g-', lw=2, label='supply')\n", + "\n", + " ax.set_xlabel('price', fontsize=14)\n", + " ax.set_ylabel('quantity', fontsize=14)\n", + " ax.legend(loc='upper center')\n", + "\n", + " plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_equilibrium(mkt)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "mkt.α = 0.12" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Equilibrium price is 2.66\n", + "Equilibrium quantity is 0.38\n" + ] + } + ], + "source": [ + "compute_equilibrium(mkt)" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_equilibrium(mkt)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.4" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/sept_7_seminar/supply_and_demand.ipynb b/sept_7_seminar/supply_and_demand.ipynb new file mode 100644 index 0000000..baddb38 --- /dev/null +++ b/sept_7_seminar/supply_and_demand.ipynb @@ -0,0 +1,308 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Writing Clean Code" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### John Stachurski" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here is some code that needs improving. It involves a basic supply and demand problem. \n", + "\n", + "First let's do some standard imports and set up commands" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from scipy.optimize import bisect" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### A Market " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now consider a market where supply is given by\n", + "\n", + "$$ q_s(p) = \\exp(\\alpha p) - \\beta. $$\n", + "\n", + "The demand curve is\n", + "\n", + "$$ q_d(p) = \\gamma p^{-\\delta}. $$\n", + "\n", + "The values $\\alpha$, $\\beta$, $\\gamma$ and $\\delta$ are parameters.\n", + "\n", + "The equilibrium $p^*$ is the price such that $q_d(p) = q_s(p)$.\n", + "\n", + "We can solve for this equilibrium using a root finding algorithm. Specifically, we will find the $p$ such that $h(p) = 0$, where\n", + "\n", + "$$ h(p) := q_d(p) - q_s(p) $$\n", + "\n", + "This yields the equilibrium price $p^*$. From this we get the equilibrium price by $q^* = q_s(p^*)$\n", + "\n", + "Then we'll plot our results. The parameter values will be\n", + "\n", + "* $\\alpha = 0.1$\n", + "* $\\beta = 1$\n", + "* $\\gamma = 1$\n", + "* $\\delta = 1$" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Equilibrium price is 2.93\n", + "Equilibrium quantity is 0.34\n" + ] + } + ], + "source": [ + "# Compute equilibrium\n", + "def h(p):\n", + " return p**(-1) - (np.exp(0.1 * p) - 1)\n", + "\n", + "p_star = bisect(h, 2, 4)\n", + "q_star = np.exp(0.1 * p_star) - 1\n", + "\n", + "print(f'Equilibrium price is {p_star: .2f}')\n", + "print(f'Equilibrium quantity is {q_star: .2f}')" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Now plot\n", + "grid = np.linspace(2, 4, 100)\n", + "fig, ax = plt.subplots(figsize=(8, 6))\n", + "\n", + "qs = np.exp(0.1 * grid) - 1\n", + "qd = grid**(-1)\n", + "\n", + "ax.plot(grid, qd, 'b-', lw=2, label='demand')\n", + "ax.plot(grid, qs, 'g-', lw=2, label='supply')\n", + "\n", + "ax.set_xlabel('price', fontsize=14)\n", + "ax.set_ylabel('quantity', fontsize=14)\n", + "ax.legend(loc='upper center')\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "### Demand Shift\n", + "\n", + "What happens when demand shifts up, with $\\gamma$ increasing to $1.25$?" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Equilibrium price is 3.25\n", + "Equilibrium quantity is 0.38\n" + ] + } + ], + "source": [ + "# Compute equilibrium\n", + "def h(p):\n", + " return 1.25 * p**(-1) - (np.exp(0.1 * p) - 1)\n", + "\n", + "p_star = bisect(h, 2, 4)\n", + "q_star = np.exp(0.1 * p_star) - 1\n", + "\n", + "print(f'Equilibrium price is {p_star: .2f}')\n", + "print(f'Equilibrium quantity is {q_star: .2f}')" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Now plot\n", + "p_grid = np.linspace(2, 4, 100)\n", + "fig, ax = plt.subplots(figsize=(8, 6))\n", + "\n", + "qs = np.exp(0.1 * p_grid) - 1\n", + "qd = 1.25 * p_grid**(-1)\n", + "\n", + "\n", + "ax.plot(grid, qd, 'b-', lw=2, label='demand')\n", + "ax.plot(grid, qs, 'g-', lw=2, label='supply')\n", + "\n", + "ax.set_xlabel('price', fontsize=14)\n", + "ax.set_ylabel('quantity', fontsize=14)\n", + "ax.legend(loc='upper center')\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "### Supply Shift\n", + "\n", + "Now let's take $\\gamma$ back to 1 but increase $\\alpha$ to 0.12" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Equilibrium price is 2.66\n", + "Equilibrium quantity is 0.38\n" + ] + } + ], + "source": [ + "# Compute equilibrium\n", + "def h(p):\n", + " return p**(-1) - (np.exp(0.12 * p) - 1)\n", + "\n", + "p_star = bisect(h, 2, 4)\n", + "q_star = np.exp(0.12 * p_star) - 1\n", + "\n", + "print(f'Equilibrium price is {p_star: .2f}')\n", + "print(f'Equilibrium quantity is {q_star: .2f}')" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Now plot\n", + "p_grid = np.linspace(2, 4, 100)\n", + "fig, ax = plt.subplots(figsize=(8, 6))\n", + "\n", + "qs = np.exp(0.12 * p_grid) - 1\n", + "qd = p_grid**(-1)\n", + "\n", + "\n", + "ax.plot(grid, qd, 'b-', lw=2, label='demand')\n", + "ax.plot(grid, qs, 'g-', lw=2, label='supply')\n", + "\n", + "ax.set_xlabel('price', fontsize=14)\n", + "ax.set_ylabel('quantity', fontsize=14)\n", + "ax.legend(loc='upper center')\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.4" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/sept_7_seminar/supply_and_demand_solution_1.ipynb b/sept_7_seminar/supply_and_demand_solution_1.ipynb new file mode 100644 index 0000000..47e4adc --- /dev/null +++ b/sept_7_seminar/supply_and_demand_solution_1.ipynb @@ -0,0 +1,199 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Writing Clean Code: Solution with Functions" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### John Stachurski" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from scipy.optimize import bisect" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "First let's define supply and demand functions" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "def qs(p, α, β):\n", + " return np.exp(α * p) - β\n", + "\n", + "def qd(p, γ, δ):\n", + " return γ * p**(-δ)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's a function to compute the equilibrium:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "def compute_equilibrium(α=0.1, β=1, γ=1, δ=1):\n", + " # Define excess demand function\n", + " def h(p):\n", + " return qd(p, γ, δ) - qs(p, α, β)\n", + " \n", + " p_star = bisect(h, 2, 4)\n", + " q_star = qs(p_star, α, β)\n", + " \n", + " print(f'Equilibrium price is {p_star: .2f}')\n", + " print(f'Equilibrium quantity is {q_star: .2f}')" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Equilibrium price is 2.93\n", + "Equilibrium quantity is 0.34\n" + ] + } + ], + "source": [ + "compute_equilibrium()" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "def plot_equilibrium(α=0.1, β=1, γ=1, δ=1):\n", + " grid = np.linspace(2, 4, 100)\n", + " fig, ax = plt.subplots(figsize=(8, 6))\n", + "\n", + " ax.plot(grid, qd(grid, γ, δ), 'b-', lw=2, label='demand')\n", + " ax.plot(grid, qs(grid, α, β), 'g-', lw=2, label='supply')\n", + "\n", + " ax.set_xlabel('price', fontsize=14)\n", + " ax.set_ylabel('quantity', fontsize=14)\n", + " ax.legend(loc='upper center')\n", + "\n", + " plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_equilibrium(α=0.12)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.4" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/sept_7_seminar/supply_and_demand_solution_2.ipynb b/sept_7_seminar/supply_and_demand_solution_2.ipynb new file mode 100644 index 0000000..da89eb1 --- /dev/null +++ b/sept_7_seminar/supply_and_demand_solution_2.ipynb @@ -0,0 +1,230 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Writing Clean Code: Solution with Classes" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### John Stachurski" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from scipy.optimize import bisect" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "First let's define a \"Market\" as a class. It contains parameters and a supply and demand curve" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "class Market:\n", + " \n", + " def __init__(self, α=0.1, β=1, γ=1, δ=1):\n", + " self.α, self.β, self.γ, self.δ = α, β, γ, δ\n", + "\n", + " def qs(self, p):\n", + " return np.exp(self.α * p) - self.β\n", + " \n", + " def qd(self, p):\n", + " return self.γ * p**(-self.δ)\n", + " " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's a function to compute the equilibrium:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "def compute_equilibrium(mkt):\n", + " # Define excess demand function\n", + " def h(p):\n", + " return mkt.qd(p) - mkt.qs(p)\n", + " # Find zero of h\n", + " p_star = bisect(h, 2, 4)\n", + " q_star = mkt.qs(p_star)\n", + " \n", + " print(f'Equilibrium price is {p_star: .2f}')\n", + " print(f'Equilibrium quantity is {q_star: .2f}')" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "mkt = Market()" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Equilibrium price is 2.93\n", + "Equilibrium quantity is 0.34\n" + ] + } + ], + "source": [ + "compute_equilibrium(mkt)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's a function for plotting." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "def plot_equilibrium(mkt):\n", + " grid = np.linspace(2, 4, 100)\n", + " fig, ax = plt.subplots(figsize=(8, 6))\n", + "\n", + " ax.plot(grid, mkt.qd(grid), 'b-', lw=2, label='demand')\n", + " ax.plot(grid, mkt.qs(grid), 'g-', lw=2, label='supply')\n", + "\n", + " ax.set_xlabel('price', fontsize=14)\n", + " ax.set_ylabel('quantity', fontsize=14)\n", + " ax.legend(loc='upper center')\n", + "\n", + " plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_equilibrium(mkt)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "mkt.α = 0.12" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Equilibrium price is 2.66\n", + "Equilibrium quantity is 0.38\n" + ] + } + ], + "source": [ + "compute_equilibrium(mkt)" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", 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