firm theory - 1.1 production function and isoquant curves - CD production function.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Import necessary packages."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import all functions from python labrary: sympy\n",
    "from sympy import *\n",
    "# import python library: matplotlib (for nice plots)\n",
    "import matplotlib\n",
    "# set sympy output to print pretty math expressions\n",
    "init_printing()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Declare variables we are going to use as 'symbols'. We will add more along the way."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "L, K, w, r = symbols('L K w r')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1.1. Cobb-Douglas (CD) Production Function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Define a production function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define a CD production function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle K^{\\beta} L^{\\alpha}$"
      ],
      "text/plain": [
       " β  α\n",
       "K ⋅L "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alpha, beta = symbols('alpha beta')\n",
    "# Note: in sympy syntax: use double star ** for power\n",
    "q = L**(alpha) * K**(beta)\n",
    "# show the defined function\n",
    "q"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate marginal product of labor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/latex": [
       "$\\displaystyle K^{\\beta} L^{\\alpha - 1} \\alpha$"
      ],
      "text/plain": [
       " β  α - 1  \n",
       "K ⋅L     ⋅α"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Note: in sympy \n",
    "mpl = q.diff(L)\n",
    "mpl.simplify()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/latex": [
       "$\\displaystyle K^{\\beta - 1} L^{\\alpha} \\beta$"
      ],
      "text/plain": [
       " β - 1  α  \n",
       "K     ⋅L ⋅β"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mpk = q.diff(K)\n",
    "mpk.simplify()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle - \\frac{K \\alpha}{L \\beta}$"
      ],
      "text/plain": [
       "-K⋅α \n",
       "─────\n",
       " L⋅β "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mrts = simplify(-mpl / mpk)\n",
    "mrts"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualize the production function in 3D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import plot3d function from sympy\n",
    "from sympy.plotting import plot3d\n",
    "# enable package matplotlib, and its notebook model to display the plot in a plot window \n",
    "# (allowing rotation of the 3d plot) \n",
    "%matplotlib notebook\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle K^{0.5} L^{0.5}$"
      ],
      "text/plain": [
       " 0.5  0.5\n",
       "K   ⋅L   "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# set production parameters for plotting\n",
    "qplot = q.subs([(alpha, 1/2), (beta, 1/2)])\n",
    "qplot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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       "        alert('Your browser does not have WebSocket support. ' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
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       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
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       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option);\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width / mpl.ratio, fig.canvas.height / mpl.ratio);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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\" width=\"639.9999861283738\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x7fb9a891d990>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot3d(qplot, (L,0,10), (K,0,10))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the isoquant curve that has output level of 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x7fb9c9475250>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# set matplotlib to inline model for faster display (don't need the interactive window for 2d plots)\n",
    "%matplotlib inline\n",
    "# plot an implicit function of K in terms of L defined by: q(L,K) = 5\n",
    "# note: this function becomes very slow if alpha != 1/2\n",
    "plot_implicit(Eq(qplot, 5), (L,0,10), (K,0,10), xlim=(0,10), ylim=(0,10))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Derive the expression for the isoquant curve"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[ \\left(L^{- \\alpha} \\bar{q}\\right)^{\\frac{1}{\\beta}}\\right]$"
      ],
      "text/plain": [
       "⎡     ________⎤\n",
       "⎢beta╱  -α    ⎥\n",
       "⎣  ╲╱  L  ⋅q̅ ⎦"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# define a new symbol ubar\n",
    "qbar = symbols('qbar')\n",
    "# explicitly solve for the isoquant curve: K as a function of qbar and L\n",
    "isoquant_sol = solve(Eq(q, qbar), K)\n",
    "# show the expression of the isoquant curve\n",
    "isoquant_sol"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nice! Now we call this element (the solution we want): isoquant"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left(L^{- \\alpha} \\bar{q}\\right)^{\\frac{1}{\\beta}}$"
      ],
      "text/plain": [
       "     ________\n",
       "beta╱  -α    \n",
       "  ╲╱  L  ⋅q̅ "
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "isoquant = isoquant_sol[0]\n",
    "isoquant"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle - \\frac{\\alpha \\left(L^{- \\alpha} \\bar{q}\\right)^{\\frac{1}{\\beta}}}{L \\beta}$"
      ],
      "text/plain": [
       "        ________ \n",
       "   beta╱  -α     \n",
       "-α⋅  ╲╱  L  ⋅q̅  \n",
       "─────────────────\n",
       "       L⋅β       "
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "isoquant.diff(L).simplify()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot isoquant curves"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's plot multiple isoquant curves"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left(\\frac{\\bar{q}}{L^{0.5}}\\right)^{2.0}$"
      ],
      "text/plain": [
       "          2.0\n",
       "⎛ -0.5   ⎞   \n",
       "⎝L    ⋅q̅⎠   "
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# set production function parameters for plotting\n",
    "isoquant_plot = isoquant.subs([(alpha,0.5), (beta,0.5)])\n",
    "isoquant_plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "isoquant_plot1 = plot(isoquant_plot.subs(qbar, 1), xlim=[0,10], ylim=[0,10], xlabel=\"$L$\", ylabel=\"$K$\", show=False)\n",
    "isoquant_plot2 = plot(isoquant_plot.subs(qbar, 2), xlim=[0,10], ylim=[0,10], xlabel=\"$L$\", ylabel=\"$K$\", show=False)\n",
    "isoquant_plot3 = plot(isoquant_plot.subs(qbar, 3), xlim=[0,10], ylim=[0,10], xlabel=\"$L$\", ylabel=\"$K$\", show=False)\n",
    "isoquant_plot4 = plot(isoquant_plot.subs(qbar, 4), xlim=[0,10], ylim=[0,10], xlabel=\"$L$\", ylabel=\"$K$\", show=False)\n",
    "isoquant_plot5 = plot(isoquant_plot.subs(qbar, 5), xlim=[0,10], ylim=[0,10], xlabel=\"$L$\", ylabel=\"$K$\", show=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, let's plot all 5 indifference curves in one graph!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "isoquant_plot_combo = isoquant_plot1\n",
    "isoquant_plot_combo.extend(isoquant_plot2)\n",
    "isoquant_plot_combo.extend(isoquant_plot3)\n",
    "isoquant_plot_combo.extend(isoquant_plot4)\n",
    "isoquant_plot_combo.extend(isoquant_plot5)\n",
    "isoquant_plot_combo.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also change color of a particular curve with the 'line_color' method. \n",
    "\n",
    "For some choices of colors, see: https://www.w3schools.com/cssref/css_colors.asp\n",
    "\n",
    "Be creative, have fun!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "isoquant_plot_combo[0].line_color='salmon'\n",
    "isoquant_plot_combo[1].line_color='tomato'\n",
    "isoquant_plot_combo[2].line_color='orchid'\n",
    "isoquant_plot_combo[3].line_color='navy'\n",
    "isoquant_plot_combo[4].line_color='black'\n",
    "isoquant_plot_combo.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Questions and challenges"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Q1. Given a CD production function $ q = L^{\\alpha} K^{\\beta} $, calculate average product of labor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle K^{\\beta} L^{\\alpha - 1}$"
      ],
      "text/plain": [
       " β  α - 1\n",
       "K ⋅L     "
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "apl = (q/L).simplify()\n",
    "apl"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Q2. Impose values $\\alpha = 0.5, \\beta = 0.5, K=5$, then plot on the same graph:\n",
    "1. total product of labor\n",
    "2. average product of labor\n",
    "3. marginal product of labor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle 2.23606797749979 L^{0.5}$"
      ],
      "text/plain": [
       "                  0.5\n",
       "2.23606797749979⋅L   "
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q.subs([(alpha,0.5),(beta,0.5),(K,5)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "# impose specific values for plotting\n",
    "tpl_SR_plot = q.subs([(alpha,0.5),(beta,0.5),(K,5)])\n",
    "# calculate MP of labor\n",
    "mpl_SR_plot = tpl_SR_plot.diff(L)\n",
    "# calculate AP of labor\n",
    "apl_SR_plot = tpl_SR_plot/L"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# create plots\n",
    "tpl_plot = plot((tpl_SR_plot, (L,0.1,10)), xlim=[0,10], ylim=[0,10], xlabel=\"$L$\", ylabel=\"$q$\", show=False, line_color='salmon')\n",
    "mpl_plot = plot((mpl_SR_plot, (L,0.1,10)), xlim=[0,10], ylim=[0,10], xlabel=\"$L$\", ylabel=\"$q$\", show=False, line_color='orchid')\n",
    "apl_plot = plot((apl_SR_plot, (L,0.1,10)), xlim=[0,10], ylim=[0,10], xlabel=\"$L$\", ylabel=\"$q$\", show=False, line_color='navy')\n",
    "\n",
    "# combine plots and show\n",
    "product_plot_combo = tpl_plot\n",
    "product_plot_combo.extend(mpl_plot)\n",
    "product_plot_combo.extend(apl_plot)\n",
    "\n",
    "product_plot_combo.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Q3. Choose different $\\alpha$ values, repeat the plot, and compare against the plot in Q2 to investigate how the plot changes as $\\alpha$ changes. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Q4. Fixing $\\alpha=0.5$, and choose different $\\beta$ values, and compare against the plot in Q2 to investigate how the plot changes as $\\beta$ changes. \n",
    "\n",
    "Is $MP_L$ affected by $\\beta$? What's the intuition?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "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": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}