{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# The Specific Factors or Ricardo-Viner Model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Background\n", "\n", "The SF model is a workhorse model in trade, growth, political economy and development. We will see variants of the model used to describe rural to urban migration, the Lewis model and other dual sector models of sectoral misallocation, models such as the Harris-Todaro model that explain migration and the urban informal sector. The specific factors model predicts that, in the absence of political redistribution mechanisms, specific factors in declining sectors will organize strong opposition to policies that might otherwise raise growth. The initial distribution of factor endowments may therefore make a big difference in terms of what types of political coalitions mobilize for and against different policies. This is the basic driving force in Moav-Galor's (2006) growth model on why some regions made public investments in human capital which sped the transition from agriculture to manufacturing and enhanced growth, whereas similar policies were delayed in other regions where political/economic resistance was stronger, for instance where landlords had stronger voice in political decisions. \n", "\n", "These are just a few of the applications. The model is relatively easy to analyze -- it can be described compactly in terms of diagrams and yet is very rich in predictions. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Specific Factors (SF) or Ricardo-Viner model is a close relative of the Hecksher-Ohlin-Samuelson (HOS) neoclassical trade model. The 2x2 HOS model assumes production in each of two sectors takes place by firms using constant returns to scale technologies with capital and labor as inputs and that both capital and labor are mobile across sectors. In the SF model only labor is inter-sectorally mobile and the fixed amounts of capital become 'specific' to the sector they are trapped within. \n", "\n", "In effect the SF model therefore consists of three factors of production: mobile labor and two types of capital, one specific to each sector. Let's label the two sectors are Agriculture and Manufacturing. In agriculture competitive firms bid to hire land and labor. In manufacturing competitive firms bid to hire capital and labor. Each factor of production will be competitively priced in equilibrium but only labor is priced on a national labor market. \n", "\n", "The SF model is often described as a short-run version of the HOS model. For example suppose we start with a HOS model equilibrium where labor wage and rental rate of capital have equalized across sectors (which also implies marginal products are equalized across sectors -- no productivity differences across sectors). Now suppose that the relative price of manufacturing products suddenly rises (due to a change of world price, or government trade protection or other policies that favor manufacturing). The higher relative product price should lead firms in the booming manufacturing sector to demand both more capital and labor. Correspondingly, demand for land and labor decline in the agricultural sector. In the short run however only labor can be move from agriculture to manufacturing. Agricultural workers can become factory workers but agricultural capital (say 'land' or 'tractors') cannot be easily converted to manufacturing capital (say 'weaving machines'). So labor moves from manufacturing to the agriculture, lowering the capital labor ratio in manufacturing and raising the land to labor ratio in agriculture. The model thus predicts a surge in the real return to capital in the expanding sector and a real decline in the real return to capital in agriculture (land). Hence the measured average and marginal product of capital will now diverge across sectors. What happens to the real wage is more ambiguous: it rises measured in terms of purchasing power over agricultural goods but falls in terms of purchasing power over manufacturing goods. Whether workers are better off or worse off following this price/policy change therefore comes down to how important agricultural and manufacturing goods are in their consumption basket. This result is labeled the neo-classical ambiguity. \n", "\n", "Over the longer-term weaving machines cannot be transformed into tractors but over time new capital accumulation will build tractors and old weaving machines can be sold overseas or as scrap metal. Hence over time more capital will arrive into the manufacturing sector and leave the agricultural sector, whcih in turn will lead to even more movement of labor to manufacturing. If this process continues capital has, in effect become mobile over time, and we end up getting closer to the predictions of the HOS model." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Technology and Endowments\n", "There are two sectors Agriculture and Manufacturing. Production in each sector takes place with a linear homogenous (constant returns to scale) production functions. Agricultural production requires land which is non-mobile or specific to the sector and mobile labor.\n", "\n", "$$Q_a = F(\\bar T, L_a)$$\n", "\n", "Manufacturing production requires specific capital $K$ and mobile labor. \n", "\n", "$$Q_m = G(\\bar K, L_m)$$\n", "\n", "The quantity of land in the agricultural sector and the quantity of capital in the manufacturing sector are in fixed supply during the period of analysis. That means that firms within the agricultural (manufacturing) sector may compete with one another for the limited supply of the factor, but no new land (capital) can be supplied in the short-run period of analysis. This of course means that the price of the factor will rise (or fall) quickly in response to swings in factor demand compared to the wage of labor whose supply is more elastic.\n", "\n", "The market for mobile labor is competitive and the market clears at a wage where the sum of labor demands from each sector equals total labor supply. While the total labor supply in the economy is inelastic, the supply of labor to each sector will be elastic, since a rise in the wage in one sector will attract workers from the other sector. \n", "\n", "$$L_a + L_m = \\bar{L}$$\n", "\n", "Notice that we can invert the two production function to get minimum labor requirement functions $L_a(Q_a)$ and $L_m(Q_m)$ which tell us the minimum amount of labor $L_i$ required in sector $i$ to produce quantity $Q_i$. If we take these expressions and substitute them into the labor resource constraint we get an expression for the **production possibility frontier (PPF)** which summarizes the tradeoffs between sectors. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Assumptions and parameters for visualizations\n", "\n", "Let's get concrete and assume each sector employs a CRS Cobb-Douglas production function:\n", "\n", "$$F(\\bar T, L_a)=\\bar T^{1-\\alpha} \\cdot L_a^\\alpha$$\n", "\n", "$$G(\\bar K, L_m)=\\bar K^{1-\\beta} \\cdot L_m^\\beta$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If $\\alpha = \\beta = \\frac{1}{2}$ and $\\bar T= \\bar K = 100$. Then\n", "\n", "$$Q_a = \\sqrt{\\bar T} \\sqrt{L_a} $$\n", "\n", "$$Q_m = \\sqrt{\\bar K} \\sqrt{L_m}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Substituting these into the labor resource constraint yields:\n", "\n", "$$\\frac{Q_a^2}{\\bar T}+\\frac{Q_m^2}{\\bar K} = \\bar L$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "or \n", "\n", "$$Q_m = \\sqrt{\\bar K \\bar L - \\frac{\\bar K Q_a^2}{\\bar T} } $$\n", "\n", "If we make the further assumption that $\\bar K = \\bar L = 100$ and $\\bar L = 400$ then the PPF would look like this:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**NOTE:** If you are running this as a live jupyter notebook please first go to the [code section](#codesection) below and execute all the code cells there. Then return and run the code cells that follow sequentially." ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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uT7HjhUnLGPnJbJZv3snx++byr+P3Zdn0iWq3COk9F5nKtJuZlStRJXTXn5l1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\nYh1KuShRiYjUMqnJSZzUsxnvz1jNzt3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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ppf(Tbar=100, Kbar=100, Lbar=400)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Labor market equilibrium" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Profit maximizing firms in each sector will hire labor up to the point where the marginal value product of labor (MVPL) equals the market wage. Since labor is mobile across sectors in equilibrium workers must be paid the same nominal wage $w$ in either sector:\n", "\n", "$$ P_a \\cdot MPL_a(\\bar T, L_a) = w = P_m \\cdot MPL_m(\\bar K, L_m) $$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It will be useful to express the wage in real terms. Divide each expression above by $P_m$ to get\n", "\n", "$$ p \\cdot MPL_a = \\frac{w}{p_m} = MPL_m $$\n", "\n", "$$\\text{ where } p = \\frac{P_a}{P_m}$$\n", "\n", "In the plots below we will place the real wage measured in terms of manufactured goods on the vertical axis of the labor demand and supply diagrams." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Labor allocation across sectors \n", "\n", "In a competitive market firms take the market prices of goods $p$ and wages $w$ as given. Since in equilibrium the labor market clears we can write $L_m = \\bar L - L_a$ and substitute into the equilibrium condition above to get:\n", "\n", "$$p \\cdot MPL_a(L_A) = w = MPL_m(\\bar L-L_A) $$\n", "\n", "The left hand side $p \\cdot MPL_a(L_A)=w$ can be solved to give us demand for labor in the agricultural sector as a function of the wage $L_a(w/p)$ and is plotted below. The right hand side $w = MPL_m(\\bar L-L_a)$ gives us demand for labor in the manufacturing sector $L_m$ as a function of the real wage but this in turn also gives us the supply of labor to the agricultural sector $L_a^s = \\bar L - L_m(w/p)$ since firms in the agricultural sector can only attract workers to their sector by paying those workers just a bit above what they would be paid for the jobs they have to leave in the manufacturing sector. \n", "\n", "The diagram below can therefore be interpreted as showing labor demand and supply in the agricultural sector and their intersection gives us the equilibrium real wage (measured on the vertical in terms of purchasing power over manufactured goods)." ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(La, Lm) = (200, 200) (w/Pm, w/Pa) =(0.35, 0.35)\n", "(v/Pa, v/Pm) = (0.7, 0.7) (r/Pa, r/Pm) = (0.7, 0.7)\n" ] }, { "data": { "image/png": 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OnTrV/1Zjl+oafFdT9IvAhgPoAu0b0hillH8VjvMYtIVk2+PGekOzlFKJ1Rct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\n/zDfe3kXZfXNHc4tnZjMzy+ZxuljEoNUnYgMBVvLC/jmxn+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14FcDUKuIDKC02ChuXJDD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\nC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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sfmplot(p=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can solve for the equilibrium labor allocation $L_a$ as a function of the relative price $p$, and this in turn also gives us the equilibrium real wage. When $\\alpha=\\beta = \\frac{1}{2}$ the equilibrium condition $p \\cdot MPL_a(L_a) = MPL_m(\\bar L-L_a)$ becomes:\n", "\n", "$$p \\cdot \\frac{\\sqrt{\\bar T}}{\\sqrt{L_a}} = \\frac{\\sqrt{\\bar K}}{\\sqrt{\\bar L - L_a}}$$\n", "\n", "which we solve to find:\n", "\n", "$$L_a^e = \\frac{p^2 \\bar T \\bar L}{\\bar K - p^2 \\bar T}$$\n", "\n", "For cases where $\\alpha \\ne \\beta$ we find the optimal $L_a$ that solves this equilibrium condition numerically. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Autarky prices\n", "\n", "Thus far we have a pretty complete model of how production allocations and real wages would be determined in a small open economy where producers face world price ratio $p$. we explore comparative statics in this economy in more detail below. \n", "\n", "If however the economy is inititally in autarky or closed to the world then we must also consider the role of domestic consumer preferences in the determination of domestic equilibrium product prices. \n", "\n", "With Cobb-Douglas preferences $u(x,y) = \\gamma \\ln(x) + (1-\\gamma) \\ln(y)$ consumers demands can be written as a function of relative price $p=\\frac{P_a}{P_m}$. Setting $P_m=1$ to make manufacturing the numeraire good, this can be written:\n", "\n", "$$\\begin{align}\n", "C_a(p) =& \\gamma \\cdot \\frac{I(p)}{p} \\\\\n", "C_m(p) =& (1-\\gamma) \\cdot I(p)\n", "\\end{align}$$\n", "\n", "Income $I$ in the expressions is given by the value of national production or GDP at these prices. Measured in manufactured goods:\n", "\n", "$$I(p) = p \\cdot F(\\bar T, L_a(p)) + G(\\bar K, \\bar L - L_a(p)$$\n", "\n", "By Walras' law we only need to find the relative price at which output equals demand in one of the two product markets so in the the code below we solve for equilibrium domestic prices from the condition $Q_a(p)=C_a(p)$. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For parameters $\\alpha=\\beta=\\gamma = \\frac{1}{2}$, $\\bar T = \\bar K =100$ and $\\bar L=400$ the domestic equilibrium prices are unitary:" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.0" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "p_autarky(Lbar, Tbar, Kbar)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And this in turn leads to an equilibrium autarky allocation with $L_a = L_m = 200$ and a real wage $\\frac{w}{p}=0.35$." ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(200.0, 0.35355339059327373)" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eqn(p_autarky())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The plot below shows the autarky production and consumption point (marked by an 'X') as well as the new production point (marked by a circle) and consumption point (marked by a square) if the country opened to trade with a world relative price $p=\\frac{7}{4}$. \n", "\n", "Opening to trade leads the country to expand agricultural production by re-allocating labor from manufacturing to agriculture. We confirm the expected **neoclassical ambiguity** result which is that an increase in the relative price of agricultural goods will lead to an *increase* in the real wage measured in terms of manufactured goods $\\frac{w}{p_m}$ ($=w$ since we have $P_m=1$) but a *decrease* in real wage measured in terms of agricultural goods or $\\frac{w}{P_a} = \\frac{w}{p}$ in our notation (since $\\frac{w}{P_a} = \\frac{w}{p_m} \\cdot \\frac{P_m}{P_a}$).\n", "\n", "Diagrammatically\n", "\n", "$$p \\uparrow \\rightarrow \\frac{w}{p_m} \\uparrow , \\frac{w}{p_a} \\downarrow$$" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(301.53846153846149, 0.50389110926865943, 0.28793777672494825)" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pw = 7/4\n", "Lao, wo = eqn(p=pw)\n", "Lao, wo, wo/pw" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "image/png": 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O4+Li6NmzJ59++qlH13fHdbjoooto2rQpr776Krt373aTy83N9eiqXlkwNaRy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\nnfj6tGvJSE7hlPee5Kkfvqo2vnIZuLeUYZNoe+m/ObjiI7u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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sfmtrade(p=7/4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Effects of a price change on the income distribution" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "More explanations to be placed here..." ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "image/png": 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8hZGLc1FBXf9M1e88yO6H3qPsg+24OhwmRimE8EcHa/7m3d7aksmomFwTo/Ff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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sfmplot2(2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "## Code Section\n", "\n", "Make sure you run the cells below FIRST. Then run the cells above" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Python simulation and plots" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "from scipy.optimize import fsolve\n", "np.seterr(divide='ignore', invalid='ignore')\n", "import matplotlib.pyplot as plt\n", "from ipywidgets import interact, fixed\n", "import seaborn\n", "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "plt.style.use('seaborn-colorblind')\n", "plt.rcParams[\"figure.figsize\"] = [7,7]\n", "plt.rcParams[\"axes.spines.right\"] = True\n", "plt.rcParams[\"axes.spines.top\"] = False\n", "plt.rcParams[\"font.size\"] = 18\n", "plt.rcParams['figure.figsize'] = (10, 6)\n", "plt.rcParams['axes.grid']=True" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "Tbar = 100 # Fixed specific land in ag. \n", "Kbar = 100 # Fixed specific capital in manuf\n", "Lbar = 400 # Total number of mobile workers\n", "LbarMax = 400 # Lbar will be on slider, max value.\n", "\n", "p = 1.00 # initial rel price of ag goods, p = Pa/Pm\n", "alpha, beta = 0.5, 0.5 # labor share in ag, manuf" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For the plots we want to plot over $L_a$ and $L_m = \\bar L -l_a$:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "La = np.linspace(1, LbarMax-1,LbarMax)\n", "Lm = Lbar - La" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The production functions in each sector:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "def F(La, Tbar = Tbar):\n", " return (Tbar**(1-alpha) * La**alpha)\n", "\n", "def G(Lm, Kbar =Kbar):\n", " return (Kbar**(1-beta) * Lm**beta) " ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "def MPLa(La):\n", " return alpha*Tbar**(1-alpha) * La**(alpha-1)\n", "\n", "def MPLm(Lm):\n", " return beta*Kbar**(1-beta) * Lm**(beta-1)\n", "\n", "def MPT(La, Tbar=Tbar):\n", " return (1-alpha)*Tbar**(-alpha) * La**alpha\n", "\n", "def MPK(Lm, Kbar=Kbar):\n", " return (1-beta)*Kbar**(-beta) * Lm**beta" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "We have enough to plot a production possibility Frontier (and how it varies with factor supplies):" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "def ppf(Tbar=Tbar, Kbar=Kbar, Lbar=Lbar):\n", " Qa = F(La, Tbar) * (La" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ppf(Tbar=100, Kbar=100, Lbar=400)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Labor demand in each sector as a function of $p=\\frac{P_a}{P_m}$:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "LDa = p * MPLa(La) *(La" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sfmtrade(p=7/4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Simple example with $\\bar L$ at $\\bar L^{max}$" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "La = np.arange(0, LbarMax) # this is always over the LbarMax range\n", "\n", "def sfmplot(p, Lbar=LbarMax, show=True):\n", " Lm = Lbar - La\n", " Qa = (Tbar**(1-alpha) * La**alpha) * (La" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sfmplot(p=2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Suppose that by opening to trade the relative price of agricultural goods $p$ doubles from $p=1$ to $p=2$. This greatly shifts the demand for agricultural workers:" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "def sfmplot2(p):\n", " sfmplot(1, show=False)\n", " sfmplot(p, show=False)\n", " plt.grid(False)\n", " if p == 1:\n", " plt.title('SF Model');\n", " else:\n", " La0, w0 = eqn(1)\n", " plt.scatter(La0,w0*p, s=100, color='black') #where wage would rise to without labor movement \n", " if p>1:\n", " plt.title(r'$\\frac{P_a}{P_m} \\uparrow \\rightarrow \\frac{w}{P_m} \\uparrow, \\frac{w}{P_a} \\downarrow $' );\n", " elif p<1:\n", " plt.title(r'$\\frac{P_a}{P_m} \\downarrow \\rightarrow \\frac{w}{P_m} \\downarrow, \\frac{w}{P_a} \\uparrow $' );\n", " plt.show();\n", " " ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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8hZGLc1FBXf9M1e88yO6H3qPsg+24OhwmRimE8EcHa/7m3d7aksmomFwTo/Ff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Failed to display Jupyter Widget of type interactive.

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\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 Jupyter\n", " Widgets Documentation for setup instructions.\n", "

\n", "

\n", " If you're reading this message in another frontend (for example, a static\n", " rendering on GitHub or NBViewer),\n", " it may mean that your frontend doesn't currently support widgets.\n", "

\n" ], "text/plain": [ "interactive(children=(FloatSlider(value=1.0, description='p', max=2.0, min=0.1), Output()), _dom_classes=('widget-interact',))" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "interact(sfmplot2, p=(0.1, 2,0.1));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Before and after plots" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The trick here is to define a new plotting function that first plots a static plot and then allows an interaction. " ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "dcae3d0069114e129e8f1ba90c1a461a", "version_major": 2, "version_minor": 0 }, "text/html": [ "

Failed to display Jupyter Widget of type interactive.

\n", "

\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 Jupyter\n", " Widgets Documentation for setup instructions.\n", "

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\n", " If you're reading this message in another frontend (for example, a static\n", " rendering on GitHub or NBViewer),\n", " it may mean that your frontend doesn't currently support widgets.\n", "

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