{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Edgeworth Box: Efficiency in production allocation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Efficiency in production"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consider a small-open economy with two production sectors -- agriculture and manufacturing -- with production in each sector taking place with constant returns to scale production functions.  Producers in the agricultural sector maximize profits\n",
    "\n",
    "$$\\max_{K_A,L_A} p_A F(K_A,L_A) - w L_A - r K_A$$\n",
    "\n",
    "And producers in manufacturing similarly maximize\n",
    "\n",
    "$$\\max_{K_M,L_M} p_M G(K_M,L_M) - w L_M - r K_M$$\n",
    "\n",
    "In equilibrium total factor demands must equal total supplies:\n",
    "\n",
    "$$K_A + K_M = \\bar K$$\n",
    "\n",
    "$$L_A + L_M = \\bar L$$ \n",
    "\n",
    "The first order necessary conditions for an interior optimum in each sector lead to an equilibrium where the following condition must hold:\n",
    "\n",
    "$$\\frac{F_L(K_A,L_A)}{F_K(K_A,L_A)} = \\frac{w}{r} \n",
    "       =\\frac{G_L(\\bar K-K_A,\\bar L- L_A)}{F_K(\\bar K-K_A,\\bar L- L_A)} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Efficiency requires that the marginal rates of technical substitutions (MRTS) be equalized across sectors (and across firms within a sector which is being assumed here). In an Edgeworth box, isoquants from each sector will be tanget to a common wage-rental ratio line.  \n",
    "\n",
    "If we assume Cobb-Douglas forms $F(K,L) = K^\\alpha L^{1-\\alpha}$ and $G(K,L) = K^\\beta L^{1-\\beta}$ the efficiency condition can be used to find a closed form solution for $K_A$ in terms of $L_A$:\n",
    "\n",
    "$$\\frac{(1-\\alpha)}{\\alpha}\\frac{K_A}{L_A} =\\frac{w}{r} =\\frac{(1-\\beta)}{\\beta}\\frac{\\bar K-K_A}{\\bar L-L_A}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Rearranging the expression above we can get a closed-form expression for the efficiency locus $K_A (L_A)$:\n",
    "\n",
    "$$K_A(L_A) = \\frac{L_A \\cdot \\bar K}\n",
    "{ \\frac{\\beta(1-\\alpha)}{\\alpha (1-\\beta)} (\\bar L -L_A)+L_A}$$\n",
    "\n",
    "With this we can now plot the *efficiency locus* curve in an Edgeworth box."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Edgeworth Box plots"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is and Edgeworth Box depicting the situation where $L_A = 50$ units of labor are allocated to the agricultural sector and all other allocations are efficient (along the efficiency locus)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(LA,KA)=(50.0, 69.2)  (QA, QM)=(60.8, 41.2)  RTS= 2.1\n"
     ]
    },
    {
     "data": {
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LKYdSlHYonfCVpzQl7UuSMZ2MPjTK92sDmbXrIr909KBhqbxGlyPSgNDQUHx8fJg+fTrR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\n7U8U3KAhwCzn3NfOuf0EWss1Q51dREQkK8KmpXuCmTUiUEwbAnkJjNh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      "text/plain": [
       "<matplotlib.figure.Figure at 0x27f7142db00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "edgeplot(50)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you're reading this using a jupyter server you can interact with the following plot, changing the technology parameters and position of the isoquant. If you are not this may appear blank or static."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "ab38fbcc9f134259b02965dca73b08fb",
       "version_major": 2,
       "version_minor": 0
      },
      "text/html": [
       "<p>Failed to display Jupyter Widget of type <code>interactive</code>.</p>\n",
       "<p>\n",
       "  If you're reading this message in the Jupyter Notebook or JupyterLab Notebook, it may mean\n",
       "  that the widgets JavaScript is still loading. If this message persists, it\n",
       "  likely means that the widgets JavaScript library is either not installed or\n",
       "  not enabled. See the <a href=\"https://ipywidgets.readthedocs.io/en/stable/user_install.html\">Jupyter\n",
       "  Widgets Documentation</a> for setup instructions.\n",
       "</p>\n",
       "<p>\n",
       "  If you're reading this message in another frontend (for example, a static\n",
       "  rendering on GitHub or <a href=\"https://nbviewer.jupyter.org/\">NBViewer</a>),\n",
       "  it may mean that your frontend doesn't currently support widgets.\n",
       "</p>\n"
      ],
      "text/plain": [
       "interactive(children=(IntSlider(value=50, description='LA', max=90, min=10), FloatSlider(value=0.6, description='alpha', max=0.9, min=0.1), FloatSlider(value=0.4, description='beta', max=0.9, min=0.1), Output()), _dom_classes=('widget-interact',))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "LA = 50\n",
    "interact(edgeplot, LA=(10, LBAR-10,1), \n",
    "         Kbar=fixed(KBAR), Lbar=fixed(LBAR),z\n",
    "         alpha=(0.1,0.9,0.1),beta=(0.1,0.9,0.1));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Production Possiblity Frontier\n",
    "\n",
    "The **efficiency locus** also allows us to trace out the production possibility frontier: by varying $L_A$ from 0 to $\\bar L$ and, for every $L_A$, calculating $K_A(L_A)$ and with that efficient production $(q_A,q_B)$ where $q_A=F(K_A(L_A), L_A)$ and $q_B=F(\\bar K - K_A(L_A), \\bar L - L_A)$. \n",
    "\n",
    "For Cobb-Douglas technologies the PPF will be quite straight unless $\\beta$ and $\\alpha$ are very different from each other."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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2bet1LElnSdmFOw9oaGalkri8X1WeIhLsMmTIwJw5c6hduzbt27fnzTff9DqS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\nRUREkkEFKiIikgwqUBERkWT4P0QTfW+WODq8AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x27f6feecf28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(7,6))\n",
    "ppf(30,alpha =0.8, beta=0.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Efficient resource allocation and comparative advantage in a small open economy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have a production possibility frontier which also tells us the opportunity cost of producing different amounts of good $A$ in terms of how much of good B (via its slope or the Rate of Product Transformation (RPT) $\\frac{MC_A}{MC_B}$). This is given by the slope of the PPF. The bowed out shape of the PPF tells us that the opportunity cost of producing either good is rising in its quantity. \n",
    "\n",
    "How much of each good will the economy produce?   If this is a competitive small open economy then product prices will be given by world prices. Each firm maximizes profits which leads every firm in the A sector to increase output until $MC_X(q_a) = P_A$ and similarly in the B sector so that in equlibrium we must have \n",
    "\n",
    "$$\\frac{MC_A}{MC_B} = \\frac{P_A}{P_B}$$\n",
    "\n",
    "and the economy will produce where the slope of the PPF exactly equals the world relative price.  This is where national income valued at world prices is maximized, and the country is producing according to comparative advantage.\n",
    "\n",
    "Consumers take this income as given and maximize utility.  If we make heroic assumptions about preferences (preferences are identical and homothetic) then we can represent consumer preferences on the same diagram and we would have consumers choosing a consumption basket somewhere along the *consumption possibliity frontier* given by the world price line passing thorugh the production point. \n",
    "\n",
    "If the economy is instead assumed to be closed then product prices must be calculated alongside the resource allocation. The PPF itself becomes the economy's budget constraint and we find an optimum (and equlibrium autarky domestic prices) where the community indifference curve is tangent to the PPF."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As previously noted, given our linear homogenous production technology, profit maximization in agriculture will lead firms to choose inputs to satisfy $\\frac{(1-\\alpha)}{\\alpha}\\frac{K_A}{L_A} =\\frac{w}{r}$. This implies a relationship between the optimal production technique or capital-labor intensity $\\frac{K_A}{L_A}$ in agriculture and the factor price ratio $\\frac{w}{r}$:\n",
    "\n",
    "$$  \\frac{K_A}{L_A} = \\frac{\\alpha}{1-\\alpha} \\frac{w}{r} $$\n",
    "\n",
    "and similarly in manufacturing\n",
    "\n",
    "$$  \\frac{K_M}{L_M} = \\frac{\\beta}{1-\\beta} \\frac{w}{r} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the first order conditions we also have:\n",
    "\n",
    "$$P_A F_L(K_A,L_A) = w = P_M G_L(K_M,L_M) $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note this condition states that competition has driven firms to price at marginal cost in each industry or $P_A = MC_A = w\\frac{1}{F_L}$ and $P_M = MC_M = w\\frac{1}{G_L}$ which in turn implies that at a market equilibrium optimum \n",
    "\n",
    "$$\\frac{P_A}{P_M} = \\frac{G_L(K_M,L_M)}{F_L(K_A,L_A)}$$\n",
    "\n",
    "This states that the world price line with slope (negative) $\\frac{P_A}{P_M}$ will be tangent to the production possibility frontier which as a slope (negative) $\\frac{MC_A}{MC_M}= \\frac{P_A}{P_M}$ which can also be written as $\\frac{G_L}{F_L}$ or equivalently $\\frac{G_K}{F_K}$. The competitive market leads producers to move resources across sectors to maximize the value of GDP at world prices. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With the Cobb Douglas technology we can write:\n",
    "\n",
    "$$F_L = (1-\\alpha) \\left [ \\frac{K_A}{L_A} \\right]^\\alpha$$\n",
    "\n",
    "$$G_L = (1-\\beta) \\left [ \\frac{K_M}{L_M} \\right]^\\beta$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using these expressions and the earlier expression relating $\\frac{K_A}{L_A}$ and $\\frac{K_M}{L_M}$ to $\\frac{w}{r}$ we have:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\frac{P_A}{P_M} \n",
    "=\\frac{1-\\alpha}{1-\\beta} \n",
    "    \\frac{\\left [ \\frac{ (1-\\beta)}{\\beta} \\frac{w}{r} \\right]^\\beta} \n",
    "    { \\left [ \\frac{ (1-\\alpha)}{\\alpha} \\frac{w}{r} \\right]^\\alpha}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "or \n",
    "\n",
    "$$\\frac{P_A}{P_M} = \\Gamma \\left [ \\frac{w}{r}  \\right]^{\\beta - \\alpha}\n",
    "$$\n",
    "where"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\Gamma =\n",
    "\\frac{1-\\alpha}{1-\\beta} \n",
    "\\left ( \\frac{\\alpha}{1-\\alpha} \\right )^\\alpha \n",
    "\\left ( \\frac{1-\\beta}{\\beta} \\right )^\\beta \n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Solving for $\\frac{w}{r}$ as a function of the world prices we find an expression for the 'Stolper-Samuelson' (SS) line:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\frac{w}{r} = \\frac{1}{\\Gamma} \\left [  \\frac{P_A}{P_M}   \\right ]^\\frac{1}{\\beta-\\alpha} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Stolper Samuelson Theorem\n",
    "\n",
    "The Stolper Samuelson theorem tells us how changes in the world relative price of products translates into changes in the relative price of factors and therefore in the distribution of income in society.\n",
    "\n",
    "The theorem states that an increase in the relative price of a good will lead to an increase in both the relative and the real price of the factor used intensively in the production of that good (and conversely to a decline in both the real and the relative price of the other factor)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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O7tEi6FhxR0UhIqH0waJN3Dx5Lut25HH1UV34/Wk9Sayju6wg6KcuIqGyPaeAO6fOZ9LX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\nFCIiUi4VhYiIlEtFISIi5fo/TmJ6iu3i6KYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x27f7016e1d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ssline(a=0.6, b=0.3);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This relationship can be seen from the formula.  If agriculture were more labor intensive than manufacturing, so $\\alpha < \\beta$, then an increase in the relative price of agricultural goods creates an incipient excess demand for labor and an excess supply of capital (as firms try to expand production in the now more profitable labor-intensive agricultural sector and cut back production in the now relatively less profitable and capital-intensive manufacturing sector). Equilibrium will only be restored if the equilibrium wage-rental ratio falls which in turn leads firms in both sectors to adopt more capital-intensive techniques.  With more capital per worker in each sector output per worker and hence real wages per worker $\\frac{w}{P_a}$ and $\\frac{w}{P_m}$ increase.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### To be completed\n",
    "\n",
    " * Code to solve for unique HOS equilibrium as a function of world relative price $\\frac{P_A}{P_M}$\n",
    " * Interactive plot with $\\frac{P_A}{P_M}$ slider that plots equilibrium in Edgeworth box and PPF\n",
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Code section\n",
    "To keep the presentation tidy I've put the code that is used in the notebook above at the end of the notebook. \n",
    "Run all code below this cell first.  Then return and run all code above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from ipywidgets import interact, fixed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "ALPHA = 0.6   # capital share in agriculture\n",
    "BETA = 0.4   # \n",
    "\n",
    "KBAR = 100\n",
    "LBAR = 100\n",
    "\n",
    "p = 1      # =Pa/Pm  relative price of ag goods\n",
    "\n",
    "def F(K,L,alpha=ALPHA):\n",
    "    \"\"\"Agriculture Production function\"\"\"\n",
    "    return (K**alpha)*(L**(1-alpha))\n",
    "\n",
    "def G(K,L,beta=BETA):\n",
    "    \"\"\"Manufacturing Production function\"\"\"\n",
    "    return (K**beta)*(L**(1-beta))\n",
    "\n",
    "def budgetc(c1, p1, p2, I):\n",
    "    return (I/p2)-(p1/p2)*c1\n",
    "\n",
    "def isoq(L, Q, mu):\n",
    "    return (Q/(L**(1-mu)))**(1/mu)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def edgeworth(L, Kbar=KBAR, Lbar=LBAR,alpha=ALPHA, beta=BETA):\n",
    "    \"\"\"efficiency locus: \"\"\"\n",
    "    a = (1-alpha)/alpha\n",
    "    b = (1-beta)/beta\n",
    "    return b*L*Kbar/(a*(Lbar-L)+b*L)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def edgeplot(LA, Kbar=KBAR, Lbar=LBAR,alpha=ALPHA,beta=BETA):\n",
    "    \"\"\"Draw an edgeworth box\n",
    "    \n",
    "    arguments:\n",
    "    LA -- labor allocated to ag, from which calculate QA(Ka(La),La) \n",
    "    \"\"\"\n",
    "    KA = edgeworth(LA, Kbar, Lbar,alpha, beta)\n",
    "    RTS = (alpha/(1-alpha))*(KA/LA)\n",
    "    QA = F(KA,LA,alpha)\n",
    "    QM = G(Kbar-KA,Lbar-LA,beta)\n",
    "    print(\"(LA,KA)=({:4.1f}, {:4.1f})  (QA, QM)=({:4.1f}, {:4.1f})  RTS={:4.1f}\"\n",
    "          .format(LA,KA,QA,QM,RTS))\n",
    "    La = np.arange(1,Lbar)\n",
    "    fig, ax = plt.subplots(figsize=(7,6))\n",
    "    ax.set_xlim(0, Lbar)\n",
    "    ax.set_ylim(0, Kbar)\n",
    "    ax.plot(La, edgeworth(La,Kbar,Lbar,alpha,beta),'k-')\n",
    "    #ax.plot(La, La,'k--')\n",
    "    ax.plot(La, isoq(La, QA, alpha))\n",
    "    ax.plot(La, Kbar-isoq(Lbar-La, QM, beta),'g-')\n",
    "    ax.plot(LA, KA,'ob')\n",
    "    ax.vlines(LA,0,KA, linestyles=\"dashed\")\n",
    "    ax.hlines(KA,0,LA, linestyles=\"dashed\")\n",
    "    ax.text(-6,-6,r'$O_A$',fontsize=16)\n",
    "    ax.text(Lbar,Kbar,r'$O_M$',fontsize=16)\n",
    "    ax.set_xlabel(r'$L_A -- Labor$', fontsize=16)\n",
    "    ax.set_ylabel('$K_A - Capital$', fontsize=16)\n",
    "    #plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ppf(LA,Kbar=KBAR, Lbar=LBAR,alpha=ALPHA,beta=BETA):\n",
    "    \"\"\"Draw a production possibility frontier\n",
    "    \n",
    "    arguments:\n",
    "    LA -- labor allocated to ag, from which calculate QA(Ka(La),La) \n",
    "    \"\"\"\n",
    "    KA = edgeworth(LA, Kbar, Lbar,alpha, beta)\n",
    "    RTS = (alpha/(1-alpha))*(KA/LA)\n",
    "    QA = F( KA,LA,alpha)\n",
    "    QM = G(Kbar-KA,Lbar-LA,beta)\n",
    "    ax.scatter(QA,QM)\n",
    "    La = np.arange(0,Lbar)\n",
    "    Ka = edgeworth(La, Kbar, Lbar,alpha, beta)\n",
    "    Qa = F(Ka,La,alpha)\n",
    "    Qm = G(Kbar-Ka,Lbar-La,beta)\n",
    "    ax.set_xlim(0, Lbar)\n",
    "    ax.set_ylim(0, Kbar)\n",
    "    ax.plot(Qa, Qm,'k-')\n",
    "    ax.set_xlabel(r'$Q_A$',fontsize=18)\n",
    "    ax.set_ylabel(r'$Q_B$',fontsize=18)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It's interesting to note that for Cobb-Douglas technologies you really need quite a difference in capital-intensities between the two technologies in order to get much curvature to the production function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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rLCyMWbNmcfbsWTp16kT69Olp1aqV17EkhcVnqL15wINmVjKey/td5SkiwS5N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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x18d15365c18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(7,6))\n",
    "ppf(20,alpha =0.8, beta=0.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Code for Stolper Samuelson line"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def wreq(p,a=ALPHA, b=BETA):\n",
    "    B = ((1-a)/(1-b))*(a/(1-a))**a  * ((1-b)/b)**b\n",
    "    return B*p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ssline(a=ALPHA, b=BETA):\n",
    "    p = np.linspace(0.1,10,100)\n",
    "    plt.title('The Stolper-Samuelson line')\n",
    "    plt.xlabel(r'$p = \\frac{P_a}{P_m}$', fontsize=18)\n",
    "    plt.ylabel(r'$ \\frac{w}{r}$', fontsize=18)\n",
    "    plt.plot(p,wreq(p, a, b));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x18d15758518>"
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     "metadata": {},
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    "lenName": 16,
    "lenType": 16,
    "lenVar": 40
   },
   "kernels_config": {
    "python": {
     "delete_cmd_postfix": "",
     "delete_cmd_prefix": "del ",
     "library": "var_list.py",
     "varRefreshCmd": "print(var_dic_list())"
    },
    "r": {
     "delete_cmd_postfix": ") ",
     "delete_cmd_prefix": "rm(",
     "library": "var_list.r",
     "varRefreshCmd": "cat(var_dic_list()) "
    }
   },
   "types_to_exclude": [
    "module",
    "function",
    "builtin_function_or_method",
    "instance",
    "_Feature"
   ],
   "window_display": true
  },
  "widgets": {
   "application/vnd.jupyter.widget-state+json": {
    "state": {
     "0109b96b7f7c42c28714108af0c000e4": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "1.0.0",
      "model_name": "IntSliderModel",
      "state": {
       "description": "LA",
       "layout": "IPY_MODEL_d117f71d82bb4ca1893c1d8dab6380cd",
       "max": 90,
       "min": 10,
       "style": "IPY_MODEL_8c803a4670e24cffb5f2fddb8fe6a037",
       "value": 38
      }
     },
     "059b8be418ec4f20b5dfd003c5e573ce": {
      "model_module": "jupyter-js-widgets",
      "model_module_version": "~2.1.4",
      "model_name": "LayoutModel",
      "state": {
       "_model_module_version": "~2.1.4",
       "_view_module_version": "~2.1.4"
      }
     },
     "0b1c55bd5201414fb735c34e9b4055d1": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "1.0.0",
      "model_name": "FloatSliderModel",
      "state": {
       "description": "beta",
       "layout": "IPY_MODEL_77c712d7d5d745b2aabcf3b1b47587c9",
       "max": 0.9,
       "min": 0.1,
       "step": 0.1,
       "style": "IPY_MODEL_b108c04b01ac408c9a3caf2d183a24ab",
       "value": 0.7
      }
     },
     "0c787ba61c03410292c5886a9304714f": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.0.0",
      "model_name": "LayoutModel",
      "state": {}
     },
     "20da10bc0e594cc8ad1b8fbb0a23ff49": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "1.0.0",
      "model_name": "SliderStyleModel",
      "state": {
       "description_width": ""
      }
     },
     "23714c6c310f4197a2a10bfd5d6cf657": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "1.0.0",
      "model_name": "IntSliderModel",
      "state": {
       "description": "LA",
       "layout": "IPY_MODEL_3795e7fe42f443d6844138ed1830cfdf",
       "max": 90,
       "min": 10,
       "style": "IPY_MODEL_3c067e088de5442785d609a47ef8c98c",
       "value": 50
      }
     },
     "283c1323c23f4915b6041b60c1a57ab1": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "1.0.0",
      "model_name": "FloatSliderModel",
      "state": {
       "description": "alpha",
       "layout": "IPY_MODEL_6bb65799036441ebb4eecbe1476cfa35",
       "max": 0.9,
       "min": 0.1,
       "step": 0.1,
       "style": "IPY_MODEL_f215aaa189d443bd8241291461096f3d",
       "value": 0.4
      }
     },
     "302df58d877846e99412ccfb2548352f": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "layout": "IPY_MODEL_c18ed217ec1a44699f4b271cfe0690b8",
       "outputs": [
        {
         "name": "stdout",
         "output_type": "stream",
         "text": "(LA,KA)=(50.0, 22.2)  (QA, QM)=(36.1, 68.1)  RTS= 0.3\n"
        },
        {
         "data": {
          "image/png": 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+XSFEmn355Ze4ubnx7rvvGh0l00npilTxyOZEqbyeMoNZCJEmoaGhzJs3j7fffht7XKZX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\nP5oHuEtTdC0ioWsmErqiMgoKCoiKiuKDDz5g796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       "outputs": [
        {
         "name": "stdout",
         "output_type": "stream",
         "text": "(LA,KA)=(38.0, 68.2)  (QA, QM)=(57.2, 47.5)  RTS= 4.2\n"
        },
        {
         "data": {
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NmoSnpydt27Zl//79jBw5knPnzrFmzRpat24tgSuynbR0xVPxLVeY3i958NvuczSr6EK9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\nQuT/A+WVdFjEBYH0AAAAAElFTkSuQmCC\n",
          "text/plain": "<matplotlib.figure.Figure at 0x27f6fe7fa90>"
         },
         "metadata": {},
         "output_type": "display_data"
        }
       ]
      }
     },
     "a0bdfed1fb604861afd20ce65d23c0bf": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "1.0.0",
      "model_name": "FloatSliderModel",
      "state": {
       "description": "beta",
       "layout": "IPY_MODEL_5695595285e842d693e5a73d13738d3f",
       "max": 0.9,
       "min": 0.1,
       "step": 0.1,
       "style": "IPY_MODEL_435e876b6655494a824f786a69e89613",
       "value": 0.4
      }
     },
     "ab38fbcc9f134259b02965dca73b08fb": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "1.0.0",
      "model_name": "VBoxModel",
      "state": {
       "_dom_classes": [
        "widget-interact"
       ],
       "children": [
        "IPY_MODEL_fc90bad4f0f84f2cba370fa2cbb6c35a",
        "IPY_MODEL_b994175f22a94ccaa70d00a0d1d3c2c7",
        "IPY_MODEL_a0bdfed1fb604861afd20ce65d23c0bf",
        "IPY_MODEL_abbf5273b4294d24a367c446790d020d"
       ],
       "layout": "IPY_MODEL_bdd4da44dfea4f38818517c6e6162fbb"
      }
     },
     "abbf5273b4294d24a367c446790d020d": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "layout": "IPY_MODEL_6f37a9b27d9b418d9e81329edf9b3cfc",
       "outputs": [
        {
         "name": "stdout",
         "output_type": "stream",
         "text": "(LA,KA)=(50.0, 69.2)  (QA, QM)=(60.8, 41.2)  RTS= 2.1\n"
        },
        {
         "data": {
          "image/png": 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LKYdSlHYonfCVpzQl7UuSMZ2MPjTK92sDmbXrIr909KBhqbxGlyPSgNDQUHx8fJg+fTrR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\nsWTp9qXUf7E+UztOpesVXX3HkZNoRqoo9+ijj7JmzRpeeOE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