├── environment.yml ├── .gitignore ├── LICENSE ├── index.ipynb ├── notebooks ├── cobweb.py └── cobweb-models.ipynb └── README.md /environment.yml: -------------------------------------------------------------------------------- 1 | name: sfi-complexity-economics 2 | 3 | dependencies: 4 | - python=3.5 5 | - ipywidgets 6 | - numpy 7 | - matplotlib 8 | - seaborn 9 | - scipy -------------------------------------------------------------------------------- /.gitignore: -------------------------------------------------------------------------------- 1 | # Byte-compiled / optimized / DLL files 2 | __pycache__/ 3 | *.py[cod] 4 | 5 | # C extensions 6 | *.so 7 | 8 | # Distribution / packaging 9 | .Python 10 | env/ 11 | build/ 12 | develop-eggs/ 13 | dist/ 14 | downloads/ 15 | eggs/ 16 | .eggs/ 17 | lib/ 18 | lib64/ 19 | parts/ 20 | sdist/ 21 | var/ 22 | *.egg-info/ 23 | .installed.cfg 24 | *.egg 25 | 26 | # PyInstaller 27 | # Usually these files are written by a python script from a template 28 | # before PyInstaller builds the exe, so as to inject date/other infos into it. 29 | *.manifest 30 | *.spec 31 | 32 | # Installer logs 33 | pip-log.txt 34 | pip-delete-this-directory.txt 35 | 36 | # Unit test / coverage reports 37 | htmlcov/ 38 | .tox/ 39 | .coverage 40 | .coverage.* 41 | .cache 42 | nosetests.xml 43 | coverage.xml 44 | *,cover 45 | 46 | # Translations 47 | *.mo 48 | *.pot 49 | 50 | # Django stuff: 51 | *.log 52 | 53 | # Sphinx documentation 54 | docs/_build/ 55 | 56 | # PyBuilder 57 | target/ 58 | 59 | # IPython checkpoints 60 | .ipynb_checkpoints/ 61 | notebooks/.ipynb_checkpoints/ 62 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | The MIT License (MIT) 2 | 3 | Copyright (c) 2015 David R. Pugh 4 | 5 | Permission is hereby granted, free of charge, to any person obtaining a copy 6 | of this software and associated documentation files (the "Software"), to deal 7 | in the Software without restriction, including without limitation the rights 8 | to use, copy, modify, merge, publish, distribute, sublicense, and/or sell 9 | copies of the Software, and to permit persons to whom the Software is 10 | furnished to do so, subject to the following conditions: 11 | 12 | The above copyright notice and this permission notice shall be included in all 13 | copies or substantial portions of the Software. 14 | 15 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 16 | IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 17 | FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE 18 | AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER 19 | LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, 20 | OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE 21 | SOFTWARE. 22 | 23 | -------------------------------------------------------------------------------- /index.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "markdown", 5 | "metadata": {}, 6 | "source": [ 7 | "

SFI Complexity Economics MOOC

\n", 8 | "\n", 9 | "

Prof. J. Doyne Farmer and Dr. David R. Pugh

\n", 10 | "\n", 11 | "Here are links to the current list of lectures...\n", 12 | "\n", 13 | "" 16 | ] 17 | }, 18 | { 19 | "cell_type": "code", 20 | "execution_count": null, 21 | "metadata": { 22 | "collapsed": true 23 | }, 24 | "outputs": [], 25 | "source": [] 26 | } 27 | ], 28 | "metadata": { 29 | "kernelspec": { 30 | "display_name": "Python 3", 31 | "language": "python", 32 | "name": "python3" 33 | }, 34 | "language_info": { 35 | "codemirror_mode": { 36 | "name": "ipython", 37 | "version": 3 38 | }, 39 | "file_extension": ".py", 40 | "mimetype": "text/x-python", 41 | "name": "python", 42 | "nbconvert_exporter": "python", 43 | "pygments_lexer": "ipython3", 44 | "version": "3.4.4" 45 | } 46 | }, 47 | "nbformat": 4, 48 | "nbformat_minor": 0 49 | } 50 | -------------------------------------------------------------------------------- /notebooks/cobweb.py: -------------------------------------------------------------------------------- 1 | import ipywidgets 2 | import matplotlib.pyplot as plt 3 | import numpy as np 4 | from scipy import optimize 5 | 6 | 7 | EPSILON = 0.01 8 | a_float_slider = ipywidgets.FloatSlider(value=3.0, 9 | min=0.0, 10 | max=10.0, 11 | step=EPSILON, 12 | description=r"$a$") 13 | 14 | b_float_slider = ipywidgets.FloatSlider(value=0.25, 15 | min=0.0, 16 | max=1.0, 17 | step=EPSILON, 18 | description=r"$b$") 19 | 20 | w_float_slider = ipywidgets.FloatSlider(value=0.3, 21 | min=0.0, 22 | max=1.0, 23 | step=EPSILON, 24 | description=r"$w$") 25 | 26 | gamma_float_slider = ipywidgets.FloatSlider(value=3.6, 27 | min=0.0, 28 | max=10.0, 29 | step=EPSILON, 30 | description=r"$\gamma$") 31 | 32 | p_bar_float_slider = ipywidgets.FloatSlider(value=5.0, 33 | min=0.0, 34 | max=10.0, 35 | step=EPSILON, 36 | description=r"$\bar{p}$") 37 | 38 | initial_expected_price_slider = ipywidgets.FloatSlider(value=5.0, 39 | min=0.0, 40 | max=10.0, 41 | step=EPSILON, 42 | description=r"$p_0^e$") 43 | 44 | T_int_slider = ipywidgets.IntSlider(value=50, 45 | min=1, 46 | max=500, 47 | step=EPSILON, 48 | description=r"$T$") 49 | 50 | 51 | def _excess_demand(price, D, S, a, b, gamma, p_bar): 52 | """Excess demand function.""" 53 | return D(price, a, b) - S(price, gamma, p_bar) 54 | 55 | 56 | def _forecast_error(D_inverse, S, expected_price, **params): 57 | """Difference between observed price and expected price.""" 58 | return observed_price(D_inverse, S, expected_price, **params) - expected_price 59 | 60 | 61 | def _simulate(X0, F, T, **params): 62 | """Simulate a map F for T periods starting from X0.""" 63 | X = np.empty(T + 1) 64 | X[0] = X0 65 | for t in range(T): 66 | X[t+1] = F(X[t], **params) 67 | return X 68 | 69 | 70 | 71 | def quantity_demand_plot(D, a, b): 72 | """Plot quantity of goods demanded as a function of the observed price.""" 73 | prices = np.linspace(0, 10, 1000) 74 | plt.plot(prices, D(prices, a, b), label=r"$D(p_t)$") 75 | plt.xlabel("Prices", fontsize=15) 76 | plt.ylabel("Quantities", fontsize=15) 77 | plt.ylim(0, 1.05 * a) 78 | plt.title("Goods demand function", fontsize=25) 79 | plt.legend() 80 | 81 | 82 | def quantity_supply_plot(S, gamma, p_bar): 83 | """Plot quantity of goods supplied as a function of the expected price.""" 84 | expected_prices = np.linspace(0, 2 * p_bar, 1000) 85 | plt.plot(expected_prices, S(expected_prices, gamma, p_bar), 86 | label=r"$S(p_t^e)$") 87 | plt.xlabel("Prices", fontsize=15) 88 | plt.ylabel("Quantities", fontsize=15) 89 | plt.xlim(0, 2 * p_bar) 90 | plt.ylim(0, 3.5) 91 | plt.title("Goods supply function", fontsize=25) 92 | plt.legend() 93 | 94 | 95 | def supply_demand_plot(D, S, a, b, gamma, p_bar): 96 | """Plot demand and supply curves to find the market clearing equilibrium.""" 97 | equilibrium_price = optimize.bisect(_excess_demand, 0, 100 * p_bar, 98 | args=(D, S, a, b, gamma, p_bar)) 99 | 100 | prices = np.linspace(0, 2 * equilibrium_price, 1000) 101 | plt.plot(prices, S(prices, gamma, p_bar), label=r"$S_{\gamma}(p_t^e)$") 102 | plt.plot(prices, D(prices, a, b), label=r"$D(p_t)$") 103 | plt.plot(equilibrium_price, D(equilibrium_price, a, b), linestyle='none', 104 | marker='o', color='k', label=r"$p^*={}$".format(equilibrium_price)) 105 | plt.xlabel("Prices", fontsize=15) 106 | plt.ylabel("Quantities", fontsize=15) 107 | plt.xlim(0, prices[-1]) 108 | plt.ylim(0, 1.05 * a) 109 | plt.title("Market clearing equilibrium", fontsize=25) 110 | plt.legend() 111 | 112 | 113 | def time_series_plot(F, X0, T, **params): 114 | """Plot time series of some map F.""" 115 | delta = 1e-6 116 | traj1 = _simulate(X0, F, T, **params) 117 | traj2 = _simulate((1 + delta) * X0, F, T, **params) 118 | 119 | fig, ax = plt.subplots(1, 2, sharex=True) 120 | ax[0].plot(traj1) 121 | ax[0].set_xlabel('Time', fontsize=15) 122 | ax[0].set_ylabel('$p_t^e$', fontsize=15, rotation='horizontal') 123 | 124 | ax[1].plot(np.abs(traj1 - traj2)) 125 | ax[0].set_xlabel('Time', fontsize=15) 126 | ax[1].set_yscale('log') 127 | ax[1].set_title("Dependence on initial conditions?", fontsize=15) 128 | fig.tight_layout() 129 | 130 | 131 | def forecast_error_plot(D_inverse, S, F, X0, T, **params): 132 | """Plot forecast errors.""" 133 | trajectory = _simulate(X0, F, T, **params) 134 | errors = _forecast_error(D_inverse, S, trajectory , **params) 135 | 136 | fig, ax = plt.subplots(1, 2) 137 | ax[0].plot(errors) 138 | ax[0].set_xlabel('Time') 139 | 140 | ax[1].hist(errors, bins=20) 141 | fig.suptitle('Forecast errors', fontsize=25) 142 | ax[1].set_xlabel('Errors') 143 | fig.tight_layout() 144 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | [![Binder](http://mybinder.org/badge.svg)](http://mybinder.org/repo/davidrpugh/sfi-complexity-mooc) 2 | 3 | # SFI Complexity Economics MOOC 4 | 5 | Instructors: Prof. J. Doyne Farmer and Dr. David R. Pugh (and co-conspirators!) 6 | 7 | From one of Gabby’s previous emails… 8 | 9 | > On average an SFI MOOC is 10 weeks long, with 1 unit per week. Each unit is made up of roughly six-ten subunits. Most of the subunits consists of 1 to 3 video segments (ideally less than 10 minutes long), exercises (if appropriate) a quiz, and quiz solutions (in text or video form). The last subunits may not have video, instead having a homework assignment and homework solution, and an end of unit test. As an example of how a course is structured see the outline for the Introduction to Complexity MOOC. 10 | 11 | # Course Outline 12 | 13 | ## Lecture 1: Introduction to Complexity Economics 14 | We want to highlight the frontier research (hopefully in a way the will make it digestible to second year undergraduates). 15 | 16 | Might make sense to have the following sub-units: 17 | Introductory video providing clear explanation of what complexity economics is (and what it isn’t). We will want to define key themes that will run throughout the course as well as terms and definitions (i.e., what is equilibrium, etc). A constructive critique of the mainstream approach to economics. 18 | 19 | * Video on the scientific method and how it differs in physics and economics. 20 | * Discussion of pre-requisites with pointers to other relevant SFI MOOCS as well as third-party materials. 21 | * Primer on use of Jupyter notebooks in the cloud (include pointers to instructions for installing software including on where to go to learn more about [best-practices for scientific computing](http://journals.plos.org/plosbiology/article?id=10.1371/journal.pbio.1001745); no support for software install will be given!). 22 | 23 | Also we will need to leave time to cover usual course logistics. 24 | 25 | ## Lecture 2: Cobweb Models and Expectations 26 | **Key ideas: Illustrate the important role of expectations in economic models. Distinguish between extreme forms of expectations (i.e., naive vs rational) and stress that real expectations formation rules fall somewhere in between.** 27 | 28 | ### YouTube length segments... 29 | 30 | 1. Discuss the basic idea behind the cobweb model. Explain the basic building blocks of the classic Brock and Hommes' [Rational Route to Randomness](http://www.ssc.wisc.edu/~wbrock/rp457a.pdf). This model provides a nice framework that can be easily extended to incorporate some of the ingredients of Car's more recent work. 31 | 2. Describe different rules for forming expectations in the cobweb model. Expectation formations rules are predictor functions that take a time series of prices and return a predicted value for a future price. Contrast various expectations formation rules with rational expectations. 32 | 3. Simulate the Brock and Hommes model with homogenous beliefs (i.e., all agents use the same expectation formation rule)! Under what conditions does one get limit cycles? Chaotic dynamics? Equilibria? Brock and Hommes model with homogenous beliefs is *very* close to the earlier Hommes model in [Dynamics of the cobweb model with adaptive expectations and non-linear supply and demand](http://www.parisschoolofeconomics.eu/docs/guesnerie-roger/hommes94.pdf). 33 | 4. Simulate the Brock and Hommes model with heterogenous beliefs (i.e., agents use different expectation formation rules!). Under what conditions does one get limit cycles? Chaotic dynamics? Equilibria? 34 | 5. Short quiz. 35 | 6. **Cars Hommes contribution: Lecture on experimental evidence on how real market participants form expectations. Need to discuss this with Cars ASAP!** 36 | 7. Explicitly make the link between simulation and computation and experimental work by use simulations to replicate some of the experimental evidence that Cars discusses in his lecture. 37 | 8. Short quiz. 38 | 39 | ## Lecture 3: Networks 40 | **Summary: Majority of economic interactions typically involves a very small minority of the population. The tendency to focus our attention on a few individuals or activities is an attribute of the real-world that is typically omitted from the standard characterization of markets in economics. In standard models of markets, agents interact impersonally and efficiently with 41 | countless other faceless agents. This lecture looks into the consequences of including explicit connections between agents in economic decision making. Agents are assumed to occupy the nodes of a network and to interact exclusively with agents to whom they are directly linked. As motivating examples we will look at both the evolution of game strategies and the effectiveness of exchange as the topology of the underlying network is altered. Conclusion: networks matter, in particular, changes in a network’s structure can alter both the steady-state attributes of an economy as well as its dynamics.** 42 | 43 | Lecture draws heavily from Allen Wilhite's [Economic Activity on Fixed Networks](http://www.sciencedirect.com/science/article/pii/S1574002105020204) (Chapter 20 of the Handbook of Computational Economics, Vol 2). 44 | 45 | ### YouTube length segments... 46 | 47 | 1. Some notable networks: Provide basic concepts and terminology (i.e., graph, node/vertex, edge, directed vs. undirected, weighted vs. unweighted, etc). Discuss the following classes of networks that show up repeatedly in the literature: 48 | * The complete network 49 | * The star 50 | * The ring 51 | * The grid 52 | * The tree 53 | * Small-worlds 54 | * Power networks 55 | Again, this lesson should summarize relevant bits of the network literature and point interested students at the SFI MOOC on networks for more details. 56 | 2. Short quiz. 57 | 3. Coordination and Cooperation on Networks: In this section we describe a few canonical games (i.e., coordination games and the prisoner's dilemma) that agents might play on some network. Using these rules, we simulate agent-based computational models in which agents play games on each of the seven networks of interest. We show how to use Monte Carlo experiments (for each network and updating routine) to derive "typical" outcomes for each model. 58 | 3. Homework assignment. 59 | 4. Exchange on Networks: This section considers exchange when it is shaped 60 | by a network. The pure exchange economy created here differs from 61 | the games played above because agents do not alter their behavior based on a neighbor’s behavior. Agents simply exchange if they find it beneficial, and prices are set by an exogenous formula known by all. Thus the economic problem is one of matching voluntary traders. Our primary interest is how the topology of a network affects the efficiency of exchange. 62 | 5. Homework assignment. 63 | 6. Conclusions: Summary of key ideas and pointers to additional (more advanced material). In particular, further applications of networks in complexity economics can be found on Prof. Leigh Tesfatsion's [website](http://www2.econ.iastate.edu/tesfatsi/anetwork.htm). Other resources include Matt Jackson's book and Sanjeev Goyal's book. For recent applications of networks in mainstream macroeconomics see Acemoglu et al's [Network Origins of Aggregate Fluctuations](http://economics.mit.edu/files/8135) and [Networks, Shocks, and Systemic Risk](http://economics.mit.edu/files/10423). 64 | 7. End of unit test. 65 | 66 | ## Lecture 3: Business Cycles 67 | Key idea: business cycles are fundamentally endogenous phenomena and are not driven by exogenous shocks as is typically (but not always!) assumed in mainstream approaches. Models of "Predator-prey" dynamics. 68 | 69 | ## Lectures 4 and 5: Growth and Innovation 70 | Will use the Solow growth model as point of departure for lecture 4 Will need to explain the basic idea behind the model to non-economics audience. Solow model can be used to motivate the importance of explicitly modeling the process of technological innovation. 71 | 72 | Evolutionary view of technological progress. See W. Brian Arthur’s Nature of Technology. We should ask Brian if he would be interested in giving some parts of lectures 4 and 5. 73 | 74 | ## Lectures 6 and 7: Financial Markets 75 | This lecture will motivate the use of ABMs by covering two different ABMs of financial markets: SFI stock market (old) and Farmer, et al Leverage Causes Fat Tails and Clustered Volatility model (new). 76 | 77 | ## Lecture 8: Game Theory 78 | Obvious ties with the mainstream literature. Motivated by recent (and ongoing) work of Farmer & Galla. Key idea: learning and convergence to “equilibrium”. When and under what circumstances do learning rules lead to a convergence to Nash-like equilibrium in games. 79 | 80 | Iterated Prisoner's dilemma tournament using code from Alan Isaac's [Simulating Evolutionary Games: A Python-Based Introduction(http://jasss.soc.surrey.ac.uk/11/3/8.html). Perhaps could make use of Luzius's code to run the tournament. Each student would submit a simple Python agent with a particular strategy and then we would run face them off against one another. 81 | 82 | ## Lectures 9: Inequality 83 | Sugarscape-esque simulations to demonstrate conditions for skewed distributions of wealth. Can be tied to Edgeworth Box diagrams. Contrast the robustness of the first welfare theorem, with the fragility of the second welfare theorem. 84 | 85 | ## 10: Overflow! 86 | I expect that this lecturers will fill out once we start filling in lecturers 1-8… 87 | 88 | Topics that don’t seem to fit anywhere yet: 89 | 90 | Rob’s model of firms… 91 | Brian’s work on increasing returns to scale and path dependence. 92 | Need to figure out a way to incorporate ScalABM to some extent. Possibly have some web application running interesting model on AWS that students can interact. Fabulous opportunity to build user community… 93 | However, ScalABM is cutting edge research tool. Pedagogically better to teach simulation and computation using Python a la Software Carpentry. 94 | 95 | ## Additional teaching resources 96 | Leigh Tesfatsion’s [excellent website](http://www2.econ.iastate.edu/tesfatsi/ace.htm). We need to find a way to include more of her work into the course!!!! 97 | -------------------------------------------------------------------------------- /notebooks/cobweb-models.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "markdown", 5 | "metadata": {}, 6 | "source": [ 7 | "

The Cobweb Model

\n", 8 | "\n", 9 | "Presentation follows Hommes, JEBO 1994. Let $p_t$ denote the observed price of goods and $p_t^e$ the expected price of goods in period $t$. Similarly, let $q_t^d$ denote the quantity demanded of all goods in period $t$ and $q_t^s$ the quantity supplied of all goods in period $t$.\n", 10 | "\n", 11 | "\\begin{align}\n", 12 | " q_t^d =& D(p_t) \\tag{1} \\\\\n", 13 | " q_t^s =& S(p_t^e) \\tag{2} \\\\\n", 14 | " q_t^d =& q_t^s \\tag{3} \\\\\n", 15 | " p_t^e =& p_{t-1}^e + w\\big(p_{t-1} - p_{t-1}^e\\big) = (1 - w)p_{t-1}^e + w p_{t-1} \\tag{4}\n", 16 | "\\end{align}\n", 17 | "\n", 18 | "Equation 1 says that the quantity demanded of goods in period $t$ is some function of the observed price in period $t$. Equation 2, meanwhile, states that the quantity of goods supplied in period $t$ is a function of the expected price in period $t$. Equation 3 is a market clearing equilibrium condition. Finally, equation 4 is an adaptive expectation formation rule that specifies how goods producers form their expectations about the price of goods in period $t$ as a function of past prices.\n", 19 | "\n", 20 | "Combine the equations as follows. Note that equation 3 implies that...\n", 21 | "\n", 22 | "$$ D(p_t) = q_t^d = q_t^s = S(p_t^e) $$\n", 23 | "\n", 24 | "...and therefore, assuming the demand function $D$ is invertible, we can write the observed price of goods in period $t$ as...\n", 25 | "\n", 26 | "$$ p_t = D^{-1}\\big(S(p_t^e)\\big). \\tag{5}$$\n", 27 | "\n", 28 | "Substituting equation 5 into equation 4 we arrive at the following difference equation\n", 29 | "\n", 30 | "$$ p_{t+1}^e = w D^{-1}\\big(S(p_t^e)\\big) + (1 - w)p_t^e. \\tag{7}$$" 31 | ] 32 | }, 33 | { 34 | "cell_type": "code", 35 | "execution_count": 1, 36 | "metadata": { 37 | "collapsed": true 38 | }, 39 | "outputs": [], 40 | "source": [ 41 | "%matplotlib inline" 42 | ] 43 | }, 44 | { 45 | "cell_type": "code", 46 | "execution_count": 2, 47 | "metadata": { 48 | "collapsed": true 49 | }, 50 | "outputs": [], 51 | "source": [ 52 | "%load_ext autoreload" 53 | ] 54 | }, 55 | { 56 | "cell_type": "code", 57 | "execution_count": 3, 58 | "metadata": { 59 | "collapsed": true 60 | }, 61 | "outputs": [], 62 | "source": [ 63 | "%autoreload 2" 64 | ] 65 | }, 66 | { 67 | "cell_type": "code", 68 | "execution_count": 4, 69 | "metadata": { 70 | "collapsed": false 71 | }, 72 | "outputs": [], 73 | "source": [ 74 | "import functools\n", 75 | "\n", 76 | "import ipywidgets\n", 77 | "import matplotlib.pyplot as plt\n", 78 | "import numpy as np\n", 79 | "from scipy import optimize\n", 80 | "import seaborn as sns\n", 81 | "\n", 82 | "import cobweb" 83 | ] 84 | }, 85 | { 86 | "cell_type": "code", 87 | "execution_count": 5, 88 | "metadata": { 89 | "collapsed": true 90 | }, 91 | "outputs": [], 92 | "source": [ 93 | "def observed_price(D_inverse, S, expected_price, **params):\n", 94 | " \"\"\"The observed price of goods in a particular period.\"\"\"\n", 95 | " actual_price = D_inverse(S(expected_price, **params), **params)\n", 96 | " return actual_price\n", 97 | "\n", 98 | "\n", 99 | "def adaptive_expectations(D_inverse, S, expected_price, w, **params):\n", 100 | " \"\"\"An adaptive expectations price forecasting rule.\"\"\"\n", 101 | " actual_price = observed_price(D_inverse, S, expected_price, **params)\n", 102 | " price_forecast = w * actual_price + (1 - w) * expected_price\n", 103 | " return price_forecast\n" 104 | ] 105 | }, 106 | { 107 | "cell_type": "markdown", 108 | "metadata": {}, 109 | "source": [ 110 | "

Non-linear supply functions

\n", 111 | "\n", 112 | "When thinking about supply it helps to start with the following considerations...\n", 113 | "
    \n", 114 | "
  1. ...when prices are low, the quantity supplied increases slowly because of fixed costs of production (think startup costs, etc).\n", 115 | "
  2. ...when prices are high, supply also increases slowly because of capacity constraints.\n", 116 | "
\n", 117 | "\n", 118 | "These considerations motivate our focus on \"S-shaped\" supply functions...\n", 119 | "\n", 120 | "$$ S_{\\gamma}(p_t^e) = -tan^{-1}(-\\gamma \\bar{p}) + tan^{-1}(\\gamma (p_t^e - \\bar{p})). \\tag{10}$$\n", 121 | "\n", 122 | "The parameter $0 < \\gamma < \\infty$ controls the \"steepness\" of the supply function." 123 | ] 124 | }, 125 | { 126 | "cell_type": "code", 127 | "execution_count": 6, 128 | "metadata": { 129 | "collapsed": true 130 | }, 131 | "outputs": [], 132 | "source": [ 133 | "def quantity_supply(expected_price, gamma, p_bar, **params):\n", 134 | " \"\"\"The quantity of goods supplied in period t given the epxected price.\"\"\"\n", 135 | " return -np.arctan(-gamma * p_bar) + np.arctan(gamma * (expected_price - p_bar))" 136 | ] 137 | }, 138 | { 139 | "cell_type": "markdown", 140 | "metadata": {}, 141 | "source": [ 142 | "

Exploring supply shocks

\n", 143 | "\n", 144 | "Interactively change the value of $\\gamma$ to see the impact on the shape of the supply function." 145 | ] 146 | }, 147 | { 148 | "cell_type": "code", 149 | "execution_count": 7, 150 | "metadata": { 151 | "collapsed": true 152 | }, 153 | "outputs": [], 154 | "source": [ 155 | "ipywidgets.interact?" 156 | ] 157 | }, 158 | { 159 | "cell_type": "code", 160 | "execution_count": 8, 161 | "metadata": { 162 | "collapsed": false 163 | }, 164 | "outputs": [ 165 | { 166 | "data": { 167 | "image/png": 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3rMO1Wi18fX2tj318fFBSUuLo8oiIqA4Wi4hSg6niVlaO0jJTxc1ggq7ysSgI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\nQ1J59koicn8MeiICULE2DwDtI2y7oBQ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168 | "text/plain": [ 169 | "" 170 | ] 171 | }, 172 | "metadata": {}, 173 | "output_type": "display_data" 174 | } 175 | ], 176 | "source": [ 177 | "interactive_quantity_supply_plot = ipywidgets.interact(cobweb.quantity_supply_plot,\n", 178 | " S=ipywidgets.fixed(quantity_supply),\n", 179 | " gamma=cobweb.gamma_float_slider,\n", 180 | " p_bar=cobweb.p_bar_float_slider)\n" 181 | ] 182 | }, 183 | { 184 | "cell_type": "markdown", 185 | "metadata": {}, 186 | "source": [ 187 | "

Special case: Linear demand functions

\n", 188 | "\n", 189 | "Suppose the the quantity demanded of goods is a simple, decresing linear function of the observed price.\n", 190 | "\n", 191 | "$$ q_t^d = D(p_t) = a - b p_t \\implies p_t = D^{-1}(q_t^d) = \\frac{a}{b} - \\frac{1}{b}q_t^d \\tag{11} $$\n", 192 | "\n", 193 | "...where $-\\infty < a < \\infty$ and $0 < b < \\infty$. " 194 | ] 195 | }, 196 | { 197 | "cell_type": "code", 198 | "execution_count": 9, 199 | "metadata": { 200 | "collapsed": true 201 | }, 202 | "outputs": [], 203 | "source": [ 204 | "def quantity_demand(observed_price, a, b):\n", 205 | " \"\"\"The quantity demand of goods in period t given the price.\"\"\"\n", 206 | " quantity = a - b * observed_price\n", 207 | " return quantity\n", 208 | "\n", 209 | "\n", 210 | "def inverse_demand(quantity_demand, a, b, **params):\n", 211 | " \"\"\"The price of goods in period t given the quantity demanded.\"\"\"\n", 212 | " price = (a / b) - (1 / b) * quantity_demand\n", 213 | " return price" 214 | ] 215 | }, 216 | { 217 | "cell_type": "markdown", 218 | "metadata": {}, 219 | "source": [ 220 | "

Exploring demand shocks

\n", 221 | "\n", 222 | "Interactively change the values of $a$ and $b$ to get a feel for how they impact demand. Shocks to $a$ shift the entire demand curve; shocks to $b$ change the slope of the demand curve (higher $b$ implies greater sensitivity to price; lower $b$ implies less sensitivity to price)." 223 | ] 224 | }, 225 | { 226 | "cell_type": "code", 227 | "execution_count": 10, 228 | "metadata": { 229 | "collapsed": false 230 | }, 231 | "outputs": [ 232 | { 233 | "data": { 234 | "image/png": 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QJyIindFoO5qBvh76dLbHkun+GNHLGfdKHmDdnot4/5dTiLmYyzn0iYhIJzS6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\npSHh4eEYMGAAiouL631gRES6ytzUEK/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235 | "text/plain": [ 236 | "" 237 | ] 238 | }, 239 | "metadata": {}, 240 | "output_type": "display_data" 241 | } 242 | ], 243 | "source": [ 244 | "interactive_quantity_demand_plot = ipywidgets.interact(cobweb.quantity_demand_plot,\n", 245 | " D=ipywidgets.fixed(quantity_demand),\n", 246 | " a=cobweb.a_float_slider,\n", 247 | " b=cobweb.b_float_slider)\n" 248 | ] 249 | }, 250 | { 251 | "cell_type": "markdown", 252 | "metadata": {}, 253 | "source": [ 254 | "

Supply and demand

\n", 255 | "\n", 256 | "Market clearing equilibrium price, $p^*$, satisfies...\n", 257 | "\n", 258 | "$$ D(p_t) = S(p_t^e). $$\n", 259 | "\n", 260 | "Really this is also an equilibrium in beliefs because we also require that $p_t = p_t^e$!" 261 | ] 262 | }, 263 | { 264 | "cell_type": "code", 265 | "execution_count": 13, 266 | "metadata": { 267 | "collapsed": false 268 | }, 269 | "outputs": [ 270 | { 271 | "data": { 272 | "image/png": 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HMHHi8/zww7cAxMXdJCUlmVq1nO57HA8PT06cOE5WVlZ5hyxKqMYmbMhfbMXH\nuYWh2MpxKbYihKgizp49ja9vS8NzFxcXwsIuAbBp03q6d+9p9LE6dnyA3bt3lHWIooxUy/uwTeVs\n7cRLbSeyN/IAay9t4vfTi+hcrz3DvQZjY2Fz/wMIIWqs1Rc3FviQr1YpaLNLfomtnVtrnvAcaNS2\nZ8+eYezYCfmW3bmTM1KYkJBg+H7s06dPsm/fHjw8WmBlZcnt27cZPHhovv08PDzZsGGNfK1mJVWj\ne9h5qRQVPd278F7H12js0JCD0UeZcXAW5xMumjs0IYQo0qVLl/DwaGF4Hhp6Fg8PLwAyMtINy3U6\nHVqtliZNmtKjRy927NgGQEjI6YoNWJSY9LDvUc/Ojbfav8yW8J1su7KL74//Si/3bgxu3g+NWr7B\nRgiR3xOeAwv0hivq+51v3bqFo6MjKlVu3+vvv3cyZMgTAPmuR7du7c/8+XPx9vYhMTHRsO7Agf34\n+bUybJeaKmWcKyvpYRdCX2zlzfYv4mabU2xlphRbEUJUMjnXr/0Mzy9dukhCQjwPP/wIAGq12rAu\nMzMTRcl5vH//Xvr2HcCBA/tRFIXk5DuG7VSq3H1E5SIJuxhNHRvzfsfX6N7wIaKTY/jqyGwptiKE\nqBROnz7JqlXLuXXrFhs3rmPlykAOHAji7benGraxtrY2PA4NDUGj0RAUtJebN2/y+ONPcPv2LQYM\nGIS1tU2h+4jKRYbE78NSbclT3kNo7eLLn2eXs+HyVk7fPMt4v6dws3Uxd3hCiBqqVas2/N///VDs\nNq6udUlKSsLBwYFTp04yfPgoAgI60LVrdyCn1x0bG4OLiysA165F4uHhWe6xi5KRHraR9MVW2rv5\nG4qt7JNiK0KISmzQoCHs2rWda9ci2bFjK7GxMQXWt2nTFguLnL7bP/8EyQzxSkx62Caw09jybKsx\ntIn2I/D8WgLPrebUzRDG+AyjlpWjucMTQoh87O3tadq0ORYWFvzxx+Jit712LRJPzxZYWVlVUHTC\nVIqukncRK2KmZUkkpN3iz7MrCE24gJ3GllHeT9LOrbVZY6qomanVhbSX8aStTFMV2yszMxONxjx3\nwlTF9iovrq4ORa6TIfES0hdbGd7icTK0Gfx+ehELQgJJzZJbIoQQVY+5krUwngyJl4K+2IpP7RYs\nCAnkUPQxLiRcZpzvCLxry8QNIYQQZUd62GUgp9jKSwxo+gi3MxL5IfhXVl5YT4Y209yhCSGEqCYk\nYZcRtUp9/8B1AAAgAElEQVTNY3mKreyOCOJLKbYihBCijEjCLmOFF1vZKcVWhBBClIok7HKgL7by\nsv8kHDT2bLi8jVnHfiE25aa5QxNCCFFFScIuR751vJjW+Y3cYiuHZkmxFSGEECUiCbuc6YutPOM3\nCrXKgsBzq/n55DxupyeaOzQhhBBViCTsCtKhXjumdXodH+cWnIkLZcahbzkWe9LcYQkhqqmwsMul\nPsalSxeBnCpoGRkZBdZnZ2fz119b2LNnF2vWrCxyWWZmJlu3bmLPnl18/vl/SUtLy7fdkiVLDMfU\n6XTMnv2t4XlExFVWr16R76tCC1tWVLwHDx5g5cpAVq1aTnp6GgDz5/9OUNAeFi78w6Tz6iUlJTFn\nTk4d96ysLFatWs7SpX/y228/G9pg4cI/2L59K+vXrym+kU0gCbsCGYqteD1OhjaTuaf/ZP6ZQFIy\npdiKENXZmjUr6dHjQerXd6ZHjwcNiay8XLhwnqNHD7Fnz+5SHeeVV57n8cf7sXfv31haWhZYf/Dg\nPzRv7kmPHr2oXbs258+HFlh24cI5zp49w+HDB+nRoxcpKckcPXo433YuLi5cuHCOxMREli9fQnDw\nccM5YmNjmD37WwYOfITHH+/LO++8VuiywuJNTLzN1q2bGDZsJLduJXDlSjhHjhwCoGvXHmRlZXHi\nRLDR59Xbvn0rt24lALB79w769OnHqFFjuXIlnJCQ0+zYsY26devRp08/IiMjiImJLtXroCeFUyqY\nSlHRs1EXfJ1bsCBkGYdjjnHxlhRbEaK6WrNmJc8//6zh+dmzZwzPhw4dVi7n1OmyiY+Px8GhdN9x\n8Nprb/Poo0V/GYitrR1z5/7CRx99xs2bN2jfvhOpqakFltnb29O8ec7ft1u3buHr60dExFXDdrGx\nsbRo0Rp7e3ueemoM+/fvM5wjLS2NnTv3o1KpOH36JE5Ozly5El5gWWHx7ty5HT+/VgA8/fRELCws\nmDfvN7y8fADw8vLm2LHD+Pu3Neq8kNPzrl+/PqGhIQBcvXqF5OQ7DBkyjAYNGnLjRiwnT56gV6+c\n7ySvV68+J04EF9uOxqrwHvYTTzzB+PHjGT9+PFOnTr3/DtVUXTs33mz/ohRbEaKa++67bwpd/v33\n3xa63FinT5/k559n89dfW9mzZ1e+oVcvLx/69OlH374DSnWOc+dCOHAgiKVL/yx0vb9/OxwcHBk3\nbgQ2NrbY29sXugxyho4DA/9kwIBB1K5dJ992tra5292rS5duqFQqUlJSiIqKolEj90KXFRbv5cuX\nuHEjhgMHgggMzFmWkBCPjU3O93/b2NgSFxdn9Hkh51JDs2Yehu3GjXuG/v0HAjlD8n5+rbC1tUWr\nzbmVV6fTcfNmrPGNXowK7WHrryksXLiwIk9baemLrbR08WFBSCC7I4I4G3+Bp/2eorFDI3OHJ4Qo\nA+fPh5q03Fg6nQ6tVkuTJk3x9vbh1VdfYPDgoYb1zZo1L3S/sLDLHD58EEVRCqzr339gvsT58suv\noygKUVFRHDr0L506PZBv+7i4m7Rp44+/fzt+//0XOnbsjEqlKrDM1dUNJycnRo4cywcfvEPDhu40\natTIsN0PP/yAj48/rq5uRf6+y5cv4amnxhS7TB/v9evXOXjwADpdNnZ29jz4YFfCwsI4cCCI7Gwd\nKlVOXzU7W4taXXy/Ne85Tp06QevW/oZr4YDhUsGJE8G0b98BV1c3Hn20PydPBtOxY2cuXbqAu3uT\nYs9hrApN2KGhoaSkpDBx4kS0Wi2vv/46/v7+FRlCpaQvtrL20mb2RP7D10d+5LFmfejTuCdqldrc\n4QkhSsHLy4ezZ88Uurw0Wrf2Z/78uXh7+5CYmFjo5KjCNGvWvMhkntfmzRvIztYycOAQrKysuHjx\nQoGEvWHDWsaNewa1Wk39+g3YseMv0tPT8i3bufMvRo4ca9inceOmbN++FRcXF8N2vr6e7NjxF6NG\njb03DINjx44wYcKkIpfljdfS0pJLly7g4uKKi4srAI6Ojly+fIk6deqQmpozbyg5Odkw1G3Mea9e\nvUJkZAS3bt3i2rVITp8+RatWrUlKSuLkyWDGjZsAgKdnCxITb3PgwH5cXd1o3tyjmDMYr0ITtrW1\nNRMnTmT48OGEh4fz3HPPsW3bNsOnnZrMUm3JCK8htK7jx6Kzy9lweRunb55lvN9I3GxdzB2eEKKE\nXnvtzXzXsPX+8583SnXczMxM9J3k/fv3Gj38re9h30tRFPr1ewwHh5yvd6xVywk/v5YAREdfp127\n9obH9erVzxeHWq3Gw8OThIR4IiKuFli2aNF8MjMzePbZySQkxOPh4cmdO3cM23l5eREWFmk45r21\nKq5evUJmZmaxywqLV6PRcOzYEQASExPx9PTCwsKCs2fP8OCDXQgJOUOHDp2MPu9jjw02HD8s7BKt\nWuV8pfLOndsYM2Y8WVlZBAcfIzs7m9jYGAYOfJyDBw/Qvn3Hol8QE1Rowm7atClNmjQxPHZycuLG\njRvUrVu3yH2K+27Q6sjVtT0BzXz4/Vgg/1w9wszD3zGu7ZP08ehW6BBWwf1rVnuVlrSX8aStTKNv\nr8mTn8HR0YYvvviCkJAQ/Pz8eP/99xk5cmSpjn/s2DHs7Gw4deowaWlJTJ482ci4/OnU6f4jm48/\n3p9FixbdnTDWmH79epGYmMiMGR8RGBgIwPPPT2T58uW4ubmhKAojRz55d8Z1/mWRkZEEBwezd+9f\nODk58MILk0hKSiqwXUpKCsuXLycy8iqbNq3iqaeewsbGhvh4DY0bN8r3Hrx3WWHxAoSGnmTv3r+o\nVcuWgQMfRafTceLEYY4e3Y+dnRWPPdbHpPOmp6fzxx9ruHAhlPDwUMLCwvj11znMnfs/dDodf/75\nJ9bW1uzaFcX27Rt44onB1K9ffC/eWIquAstuLV26lPPnz/Pxxx8TExPDM888w8aNG4vtYdfkLzU/\nEhNM4Lk1pGal4lfHm7E+w6llVfSsT/kSeNNIexlP2so0FdFeS5YswsfHl4CADuV6noog769cxX0w\nrtCx6GHDhpGUlMTo0aN58803+fzzz2U4vBgd6rblg85v4Fvbi5C4c8w4KMVWhBA5hUF27NhKbGyM\nuUMRFahCe9glIZ+6cq6r7L12gDUXN5GZnUnHugGM8HocW41Nvu3kU6pppL2MJ21lGmkv00h75Squ\nhy2FU6oARVHo0eghfJw9pdiKEELUUDIeXYUYiq006yPFVoQQooaRhF3FqFVqHmvWh7fav0RdW1d2\nRwTx5eHvuZoUef+dhRBCVFmSsKuoJo7uvNfxP/Ro9BDRKbF8feRHVp3ZjDZba+7QhBBClANJ2FWY\nvtjKy20n4WjpwLLTG5h17GdiU26YOzQhhBBlTBJ2NeBb24tpnV6nS+MOhCVe5YtD37Hv2oECVXuE\nEEJUXZKwqwlbjS3/eXAiz7QcjVplQeC5Ncw5+Qe30xPNHZoQQogyIAm7mpFiK0IIUT1Jwq6GnKxq\n8ZL/REZ4DSEjO5O5p/9k/pmlpGSmmjs0IYQQJSSFU6qpgsVWjnPhbrEVn9otzB2eEEIIE0kPu5rL\nW2wlMSOJ2cG/sfK8FFsRQoiqRhJ2DVCg2Erk3WIriVJsRQghqgpJ2DVIbrGVLjnFVo7+yJawnVJs\nRQghqgBJ2DVMTrGVxw3FVjaGbZNiK0IIUQVIwq6h9MVWOtRtayi2sjdSiq0IIURlJQm7BrPV2PJM\ny9E823I0FioLlp1fw5wTf3Ar/ba5QxNCCHEPSdiC9nXbMk1fbCX+HJ8fnCXFVoQQopKRhC2A3GIr\nT0mxFSGEqJSkcIowUBSF7o0ewtvZkwVnpdiKEEJUJtLDFgXUtXPjzYAXeSxPsZUV59dJsRUhhDAj\nSdiiUGqVmgGGYitu/B25n5lSbEUIIcxGErYolr7YSs9GXYgxFFvZIcVWhBCigknCFvdlqdYwPF+x\nlb/49tjPxEixFSGEqDCSsIXR8hZbCU+8ykwptiKEEBVGErYwiRRbEUII85CELUqksGIrR2NOmDss\nIYSotiRhixK7t9jKH2cWM+/MElIyU8wdmhBCVDtSOEWUiqHYSu0WLAgJ5EhMMBdvhUmxFSGEKGPS\nwxZloq6tK28GvMjAZo9KsRUhhCgHkrBFmVGr1PRv9kiBYitXEiPMHZoQQlR5krBFmbu32Mr/Hf1J\niq0IIUQpScIW5UJfbOWVts9JsRUhhCgDkrBFufKp3SJfsZUvDn3H3sh/pNiKEEKYSBK2KHe5xVbG\noFFZsOz8Wn46MVeKrQghhAkkYYsK076uv6HYytn488w4+K0UWxFCCCNJwhYVKrfYylCysrOk2IoQ\nQhhJCqeICpdTbOVBvGt7SrEVIYQwkvSwhdkUVmxl+fl1ZGgzzB2aEEJUOpKwhVndW2xlT+R+Zh7+\nQYqtCCHEPSRhi0qhsGIrm8O2S7EVIYS4SxK2qDTuLbayKWw73xybI8VWhBACMyTsuLg4evbsSVhY\nWEWfWlQROcVW3qBj3XZcSYyQYitCCEEFJ+ysrCw+/vhjrK2tK/K0ogqy1dgwoeUoJrYai6VKI8VW\nhBA1XoUm7C+//JJRo0bh5uZWkacVVViAWxumdn79nmIrweYOSwghKlyFJezVq1dTp04dunTpIkOb\nwiQFi60skWIrQogaR9FVUPYcO3YsiqIAEBoaSrNmzfj555+pU6dOsfvduJFUEeFVC66uDtW+vWJT\nbrAgZBnhiVdxsqpVqmIrNaG9yoq0lWmkvUwj7ZXL1dWhyHUVlrDzGjduHJ988gnNmjWr6FOLakCb\nrWXt2W2sPLMJrS6bfi16MqbNUKwsLM0dmhBClBuzlCbV97SNIZ+6jFeTPqV2d+tGU+tmzA8JZOuF\nvzl+7QxP+42kiaO70ceoSe1VWtJWppH2Mo20V65K18M2hbyIxquJb/oMbSbrL21hd2QQKkVFv6a9\n6dekF2qV+r771sT2KilpK9NIe5lG2itXcQlbCqeIKs1SrWGY12BDsZXNUmxFCFFNScIW1UJusZUA\nQ7GVPVJsRQhRjUjCFtVGTrGVkYZiK8ul2IoQohqRhC2qHX2xFb/a3lJsRQhRbUjCFtWSk1UtXvR/\nlpHeUmxFCFE9mOW2LiEqgqIodGv4IN7OniwIWcaRmGAu3gpjrO9wfGt7mTs8IYQwifSwRbXnZuvK\nGwFTGNisL4kZSfwY/DvLz68lPSvD3KEJIYTRpIctagS1Sk3/Zr1pWcebBSGB7In8hwu3LzHWe4RJ\nxVaEEMJcpIctapTGjo14t+N/eNi9K1FJMfzf0Z/YFLYdbbbW3KEJIUSxJGGLGsdSrWFYi8F82PM/\nucVWjs4hJjnW3KEJIUSRjE7YOp2OdevWER0dDcBPP/3EwIEDmTZtGikpMvNWVD2t6/rkFltJiuCL\nw99LsRUhRKVldML+8ccfmT59OtHR0Rw+fJjZs2fTsWNHjh8/ztdff12eMQpRbqTYihCiqjA6Ya9Z\ns4avv/6atm3bsnXrVgICAvj444+ZMWMG27dvL88YhSh3AW5tmNb5Dfzq5BZbOSLFVoQQlYjRCfvG\njRu0atUKgKCgILp16waAq6srd+7cKZ/ohKhAtawcebFNbrGVeWeW8MfpxSRLsRUhRCVg9G1d7u7u\nnD59mvj4eK5cuUL37t0B2L17N+7ucluMqB7yFltZGLKMo7EnuHgrjHF+I6TYihDCrIzuYU+aNInX\nX3+dUaNG0bFjR1q2bMmcOXOYOXMmkyZNKs8YhahwbrauvB4whUHN+5KUecdQbCVDK8VWhBDmoehM\nmBIbGhpKZGQk3bp1w8rKin/++QeNRkPHjh3LLUD5UnPjyZfAm8bY9rqaFMmCkGVEJ8dQ19aVp/1G\n1rhiK/LeMo20l2mkvXK5ujoUuc6k+7B9fHxo27YtwcHBpKWl4e3tXa7JWojKoLFDI97t8CoPu3cl\nJuVGTrGVy39JsRUhRIUyOmFnZGQwdepUunbtyjPPPMONGzf46KOPePrpp0lKkk9GonrTF1t5te1k\nalk6sjl8hxRbEUJUKJPuwz516hRLlizBysoKyLmuHR0dLfdhixrDu7YnUzu9nq/Yyt+R+8nWZZs7\nNCFENWd0wt6yZQsffPABAQEBhmXt2rXj008/ZdeuXeUSnBCV0b3FVlacX8dPwVJsRQhRvoxO2LGx\nsTRo0KDAchcXFxkSFzVS3mIroQkX+EyKrQghypHRCdvX15edO3cWWL58+XJ8fHzKNCghqorcYitP\noJViK0KIcmR04ZS33nqLSZMmERwcTFZWFr/99huXLl3ixIkT/Prrr+UZoxCVWk6xlQcKFlvxHYFv\nHSm2IoQoG0b3sDt06MDSpUvRaDQ0adKEU6dO0aBBA1avXs1DDz1UnjEKUSW42brwesALDGreL6fY\nyonfWXZOiq0IIcqGSYVTzEFupjeeFB8wTXm2V95iK262LkzwG1Wli63Ie8s00l6mkfbKVVzhlGKH\nxD/88EPee+897Ozs+PDDD4s9yaefflqy6ISohvTFVjZc3squiH3839Gf6NekF/2a9katUps7PCFE\nFVRswg4PD0er1RoeCyGMZ6nW8GSLQbSq48uis8vZHL6D03GhPO03knp2buYOTwhRxZTJkHhcXBx1\n6tQpi3gKkGES48mwkmkqsr1SMlNZcWEdh6KPoVFZMMTzMbo3fBCVYlJ1YLOR95ZppL1MI+2Vq0xq\nifv6+hIfH19geVRUFI888kjJIhOihrDV2PC030gmtRqHpdpSiq0IIUxW7JD45s2b2bdvHwA6nY7P\nPvvMUJZULzIyEjs7u/KLUIhqpJ1ba5rXasLi0JWciQvls4PfMtJrCB3qtTN3aEKISq7YHnZAQAAx\nMTFER0cDOdXOoqOjDf9iYmJwcnKSWuJCmKCWlSNT2jzDKH2xlZClUmxFCHFfxfaw69Wrxx9//AHA\n+++/z7Rp07C3t6+QwISozhRFoWvDB/C6p9jKWN/h+NXxNnd4QohKqNhJZzExMdStW9fwuDj67cqa\nTEQwnkzcME1laS9ttpbtV/ewKewvsnXZdG/4EEM9B2CptjR3aAaVpa2qCmkv00h75Srxfdg9e/Yk\nKCiIOnXq0KNHDxRFKbCNTqdDURTOnj1b+kiFqIHUKjX9mvbCr44XC0KWsffaP4QmnOdpv5E0dWxs\n7vCEEJVEsQl7wYIF1KpVC4CFCxdWSEBC1FSNHRrxXodXWX+32Mo3R+fQt0kv+kuxFSEE90nYnTp1\nMjw+dOgQEydOxMbGJt82d+7cYfbs2fm2FUKUjOZusZXWLr4sDFnOlvAdnJFiK0II7jNLPD4+nqio\nKKKiovjpp5+4fPmy4bn+37///svSpUsrKl4hagQvZ0+mdX6dzvXaczUpkpmHv+PviP1k67LNHZoQ\nwkyK7WHv3buX9957z3DtetiwYYVu16dPn7KPTIgazsbChvF+T9HaxY+l51ax4sI6Tt0MYazvcJyt\nncwdnhCighWbsIcMGULjxo3Jzs5m7NixzJkzx3BNG3JuTbGzs8PT07PcAxWipsopttKUxaErOBMX\nyoxDs6TYihA1kNG1xK9du0aDBg0KnSlenmSqv/Hk1gjTVLX20ul07I86yKqLG8nQZtDezZ+nvIdi\np7Et93NXtbYyN2kv00h75SrxbV151a9fn40bNxIcHExmZib35nn5ek0hypcUWxGiZjM6Yc+YMYOl\nS5fi7e1doNqZsb3u7OxsPvjgA8LCwlCpVPz3v/+V4XQhTORm68LrAS8Yiq38dGIu3Rs+yBDPx7Cq\nRMVWhBBly+iEvXHjRmbOnMngwYNLfLJdu3ahKApLly7l0KFDfPvtt8yZM6fExxOiptIXW2lZx5v5\nIYHsvXaA0PgLjPcbSbNaUmxFmE+2Tkd2ds4/bbYOnS7nZ3a2jmwdaLOz8zzOWZ6YriUuPjl3u2wd\nWp0OXXbefQs+1uU5hv58hvPrctZnZ+vQoSM7O+eyUr7lOu4+v7ufDnR3Y8vZJ+82+n3uri9wrPzL\n8x0r7zLdvcfNXa7TwdLPBhTZtkYn7KysLNq1K90kl0ceeYRevXoBOdfE805gE0KYzt2hoaHYyu6I\nIL49JsVWqhN9ssvMyiZLm33Pz5zlmXmW69dps3VotTnbaLN1aLP1j7PRanW5j7N1Oc/vLtdm68jS\n5u6f8zx32yxt7nLDOfIkzJzkWDMp5Iw2q1R3fyoKikLuT5Vyd3nuerVKQaVSGZar7jNabXTC7t27\nN5s3b+b5558v1S+lUql477332LFjBz/88EOpjiWEyFtsxY+FIcuk2Eo5y9bpSM/QkpGVTXqmloxM\nLRmZ2Tk/s7SkZ2ZjFZ5AXHwy6ZnZd5fl3Sb77v7aPAlYR6Y2m6y7CTjvT3MmQAVQq1Wo1QoWKiXn\nsSon0Vhp1KjViuG5SqWgVnJ+Gv4puevufazS76co2NlbkpGWhaLCsCzv+vseL9/zu0lSv2+eBKnc\nXXe/ZJq7Trm7jgLHujcxV8SEbKNniX/77bfMnz8fX19fmjZtiqVl/mtlpk46i4uLY/jw4WzevBlr\na2uT9hVCFC4lI5U/ji9jb/hBNGoNY9oMoV+LnqiUYmsk1Qg6nY70TC13UjJJSsngTkomd1IzSU3P\nJCUti9T0rDw/8yxLzyI1LYvU9ExS07NITdeWWUyKAhq1Co2FCo1GjcZChaWFCo1FzuOc52os8jzO\n2fae53f3sdSosFDn/NPoE22enwUeqxQ0FirUKhUW6pyEbGHYJ2e9qDyM7mEfP34cf39/AKKiokp0\nsnXr1hETE8PkyZOxsrJCpVKhUhX/h0Sm+htPbo0wTXVtr6eaP4mXvRdLz61i/vEV/BseXOpiK5Wx\nrTKzsklMziAxJYPbyRk5j5MzuJOaSfLdhJucmklyWhZ30jJJTs0iS2t6pThLCxXWlmqsrSxwc7LF\n2lKNlaUaK01Ogsz5qcbSIvdxHWdbMtIzsbybRO9db6XJSbAWaqXCb5UtIDsbsrPJyoIsIN0MIVTG\n95e5FHdbl9E97LKQmprK+++/z82bN8nKyuL555/n4YcfLnYfeRGNJ29601T39rqdnmQotmJjYcNT\nXkPoULdtiRJERbZVtk5HYnIGcYlpJCSmE5eYRnxiOgl30km8k87tlEwSkzNITc+677EUwNbaAjtr\nDXY2+p8a7O4us7W2wMbKAmtLde5PSwusrdRYW+Y8t1CbPjpR3d9bZU3aK1eZJez4+HjCwsLIzs75\nlKrT6cjIyODUqVNMmTKl9JEWQl5E48mb3jQ1ob3uLbYS4NaGkd5PmFxspazbKjU9i9iEVGJvpRIT\nn0JMQgo3bqURn5hGQlI62uzC/ywpgL2tBkc7SxxtLallZ5nz+O5zRztLHGzvJmQbDTZWFvedyFMe\nasJ7qyxJe+Uqk8Ipa9eu5aOPPiIjIwNFUQzfgw3QuHHjckvYQoiS0xdb8XZuwcKzgRyLPcmlW2GM\n9R1RIcVWUtOzuHYjmYgbd4i8cYdrsXeISUjldnJGwViBWvaWNK3ngLOjNbUdrKjtaE0dx5yfzg5W\nONhqUN/nMpoQ1ZXRCfuXX35hyJAhPPfccwwbNox58+YRFxfHxx9/XOqZ40KI8uVqW4fXA6aw/crf\nbArbXi7FVtIysgi7nsTlqNtcjkokIvYON2+n5dtGUaCOozUtm9WmrrMNbs621HW2oW5tW1xqWZdo\n+FmImsLohB0ZGcnPP/+Mu7s7Pj4+xMbG0rNnT6ZNm8bs2bN54oknyjNOIUQpqRQVfZv2wq+ODwtC\nlpa62Mqd1ExCryRw9koCFyJvc+3mHfJeYHO01eDX1JlGrvY0crXH3c2e+nVssdTI/eFClITRCdvG\nxsYwo7tJkyacP3+enj174uvry5UrV8otQCFE2XJ3aMC7HV5lw+Vt7IrYd7fYysP0b/pIscVWsnU6\nLl9LJPjiTULC47kSnWS4R9jSQkWLhrVo3rAWzes70ryBI7Ud5XZNIcqS0Qm7Xbt2zJ07l2nTpuHn\n58e6deuYPHkyJ06cwM7OrjxjFEKUMY1awxMtBtLKxfdusZWdnIkLxe2SPfN//p3z50Px8vLhP/95\nA9+A3qzce5n9J6O4fSfn2rNapeDl7oRfU2f8mtamST0HGc4WopwZPUs8NDSUiRMn8swzzzBy5EgG\nDRpESkoKycnJjB8/nnfeeadcApSZg8aTmZamkfbKkZqVyorz61mxehkHf9hRYH27AW/S0Kcb9jYa\n2rZwIcDLFd/GzlhZytB2UeS9ZRppr1xldltXamoqqamp1K5dm9jYWDZu3Ej9+vXp379/mQRaGHkR\njSdvetNIe+XXuUs7wi5cKrC8vrsnW3b+Q11HS5mhbSR5b5lG2itXmdzWBTnXsW1sbABwc3Pj2Wef\nLV1kQgizy9bpOHbuBuGXwgpdf+N6OP4tXOUPqhBmZnTCbtmyZbEVkk6fPl0mAQkhKs65qwks332R\nsOtJ2Nd2J+lmwQmkLo3rcic92QzRCSHyMjphf/rpp/kSdlZWFuHh4axdu7bcrl8LIcrH7TvpLN5+\nniPnbgDQydeNru+9x3tvFSyA1GSgL29u/ZRR3sNoWQHFVoQQhTM6YRd1n3XLli1ZuXIljz/+eJkF\nJYQoHzqdjn9ORxO48wLJaVl4NHRkZO8WeDSoBbTC2cGK77//1jBL/NVXX8c+wIWN4X8x58RcujV8\nkKFlWGxFCGG8Un/5x7Vr1xgwYAAnTpwoq5jyketmxpOJG6apae2Vmp7FvM1nOXLuBlYaNcMf9qBn\nu4ZG1dpOtrjFrP1zuZ4cg5uNS4mLrdQUNe29VVrSXrmKm3RWqimf6enpLFmyBBcXl9IcRghRzq7d\nTObTBUc4cu4GXu5OfDqxE70CGhn9xRhNnd15t8Or9Hbvzo3UOL49NoeNl7ehzS6774YWQhSvVJPO\ntFotiqLw3//+t8wDE0KUjfMRt/h+5UlS07Po16kxT/ZsXqLbs4oqtvK030jq2dUth8iFEHkZPSS+\nZu3BSoAAACAASURBVM2aAss0Gg3+/v64u7uXeWB6MkxiPBlWMk1NaK/jF27wy7ozZGfrePYxXx5s\nWa9Ex7m3rfTFVg5GH0WjsuBxjwH0aPQQKkXu04aa8d4qS9JeuUp9H/bVq1e5dOkSx48fJz4+HkdH\nR9q0acPo0aNxd3fniy++wN3dnbFjx5ZZ0EKI0gm+cJOfVp/GwkLh1WFtaN28Tpkd28bChvF+T9HG\ntSVLQ1ex8sJ6Tt0MYZzvCJytncrsPEKIXPf9OLxmzRoGDRpEYGAgNjY2tGzZklq1arF+/XoGDRrE\nrFmzWLFiBd26dauIeIUQRgi9ksCctaexUCu8MaJtmSbrvNq6tmJqpzdoVceXcwkXmXHoWw5FH6OU\nc1mFEIUotocdHBzMhx9+yHPPPceUKVOwtMy9lSMjI4PffvuNH3/8kbFjx9KkSZNyD1YIcX8x8SnM\nXn0KnU7Hy0+2wcu9fHu8tawceKHNBP65foiVFzawICSQkzdDGOk9FHuNfDGQEGWl2IQ9d+5chg4d\nyn/+858C6ywtLbG3t0etVhMREVFuAQohjJeansUPq3ImmE18zJdW5dSzvpeiKHRp0BkvJ08Wng3k\neOxJLt8KY4zvCCm2IkQZKXZI/Pjx4zz11FNFrl+0aBFvvfUWJ0+eLPPAhBCm0el0LNgayvW4FPp0\ncKdL6/oVHoOrbR1eD5jC4837cyczhTkn5hJ4bg3p2owKj0WI6qbYhJ2cnEzt2rWLXL9mzRr69OlD\nampqmQcmhDDNwZAYDp2NxbNhLUb08jBbHCpFxaNNH+btDq9Q364u+64dYOah7wi7XbBOuRDCeMUm\n7EaNGhX7pR4ODg6cOnWKRo0alXlgQgjjxSemseiv81hp1Ewa6FspvgbT3aFBvmIr3xydwwYptiJE\niRX7v7p///7MmjWLpKTC74+7desW33//PYMGDSqX4IQQxlm68wKp6Vk81dsTN2dbc4djoC+28p92\nk3G2dmJr+E6+Pvoj0ckx5g5NiCqn2IT97LPPotFoePzxx1m8eDEhISFERERw+vRpFixYwNChQ7G3\nt2fChAkVFK4Q4l5nwuM5eu4Gng1r0d2/gbnDKVQLZw+mdnqdB+p1ICLpGjMPf8/uiCCyddnmDk2I\nKqPYWeLW1tYsXryYzz//nJkzZ5KVlWVYp0/k7777br7bvYQQFSdLm82S7edRgDF9vIyuDW4ONhbW\njPMbQWtXPym2IkQJGF2aNCkpiVOnTpGQkICzszOtW7fGwaHoEmplRcrVGU/K+5mmOrTX3hNRzN8S\nSs+2DRjfz6fczlPWbZWYkcSS0JWcunkWGwtrRngNoWPddgW+r6Cqqg7vrYok7ZWr1KVJIWeC2UMP\nPVQmAQkhSi9Lm83Gf8KxUKsY1KWZucMxiaOlA8+3lmIrQpjC6IQthKhc/jkdzc3baTzSvhHODlbm\nDsdk+YutLMtTbGU4LeuU32iBEFWV+e/9EEKYTJud07vWWKgY8GDVLgucU2zlhTzFVv5g6bnVUmxF\niHtIwhaiCgq+EMfN22l0bV0fJ/uq17u+V95iKw3s6hF07V++ODRLiq0IkYckbCGqoJ1Hc+r392pf\nvYoWuTs04J0Or9C7cXdupsZLsRUh8pCELUQVE3njDqFXb+HbxJmGLtVvgpZGreEJz4LFVq5LsRVR\nw0nCFqKK2XXsGgC9q1nv+l6GYiv1c4ut7IrYJ8VWRI0lCVuIKiQzS8vBkBicHaxo6+li7nDKnY2F\nNeN8RzC59Xis1VasurCB2cG/E5+WYO7QhKhwkrCFqEJOXIwjNT2LB/zqolJVjyIjxvB3bcW0zm/Q\n2sWX8wkX+fzQLA5FH8PIuk9CVAuSsIWoQg6ciQbggZb1zBxJxdMXWxnt8yTZumwWhAQy9/Sf3MlM\nNndoQlQIKZwiRBVxJzWTU5fjaORqh7ubvbnDMQt9sRVvZ08WhCzj+I1TXLodzlgptiJqAOlhC1FF\nHDkXS5ZWVyN71/dysblbbMWjP8lSbEXUEJKwhagijp27AUAnXzczR1I5qBQVj/5/e3ce1dSBtw/8\nSUgCgbAEAgqIKIsC1VpUqtXX1traVlvrWB03BHu6TKeeGan6Vk9nnNa2b8uxy7Sj4tRlfq+K/oZq\na6116OY42tbWtW4oLgRRNsu+L1lu3j8CCC4oFnLvTZ7POZyEkJhvrsDDvbn3ueEPYjHLVshFMLCJ\nZKCx2YLsS5XoG6SDwVcr9jiS0sc7BIsT5uPhvg9cLVsxfgWLYLn1g4lkhIFNJAOnL1bAKthwT7Tz\nH8p1J9RKFaZEPY6U+BfsZSuX9uC9o2ksWyGnwsAmkoFjF8oAgIF9C9H6CJatkNNyWGBbLBYsXrwY\niYmJmD59Ovbs2eOopyaSNasg4KSxDHpvd4T3uvnJ7cmOZSvkrBwW2Dt37oRer8eWLVuwbt06vPnm\nm456aiJZyymoRn2TBfdEGaBQuE5Zyq91bdnKWwdZtkLy5rDAnjBhAlJSUgAAgiBApeIh4ES343Re\nBQBgcESAyJPIT2vZSmLMNNjAshWSN4elplZr37O1rq4OKSkpWLBggaOemkjWsvMqoVQoMLCvn9ij\nyJJCocCokHsxQB+JTSxbIRlT2By4fai4uBh/+MMfMGfOHEyZMsVRT0skW/WNZsz+SyYGhvvjnT+O\nEXsc2RMEAV+c242MrJ2wClY8HDkGyUOegofaQ+zRiG7JYWvYZWVlePbZZ/Hqq69i5MiRt/240tLa\nHpzKuQQGenN5dYEcltexC6UQbEB0qI+os8phWd2uUYb70HdYODaeycBu4/c4XnQGc+NmIsI3vNue\nw5mWlyNweV0VGHjzHUsd9h72mjVrUFNTg9WrVyMpKQnJyckwmVgjSNSZM3n2PZtjw/UiT+Jc2pet\nlDdW4K8sWyEZcOgm8TvBv7puH/9K7Ro5LK+l6w+irLoRq166Hyo38WoT5LCs7tSFylxsyv4YFU2V\nCNOFYO5dsxDs1etX/ZvOvLx6ApfXVZJYwyairqmua0ZRWT0GhPmJGtbOrkPZSl2RvWzl8ncsWyHJ\n4W8BIonKKawBAAwM497hPe1q2cpce9lKzi6sPLaOZSskKQxsIokyFlUDACJCfEWexHUMCbwLS0cs\nwmBDHM5XGfHWwQ9wsPgoy1ZIEhjYRBJlLKyGQgH0D2YdqSN5a3R4YfBcJMb8FjYI2JT9MdZnbUad\niWUrJC7WjRFJkMUqIO9KLfoE6uCh4Y+po9nLVhLaylaOl55CbnUeEmOmYZAhVuzxyEVxDZtIgvJL\n6mC2CIgM5eZwMRm0/nhp6Av4TeRENJgb8PeT/4t/nv0UTZZmsUcjF8TAJpKg3CL7DmeRIT4iT0JK\nhRLjw8diccJ8hHj1xg9FB5F6+EPkVl8SezRyMQxsIgkyFtp3OOMatnSE6oKvK1vZybIVciAGNpEE\nGYuq4eWhQi+9VuxRqB21UoUpUY8jJf4F+Hv44etLe/DekVUoqrsi9mjkAhjYRBJTU29CaVUTIkN9\nef5riYrWR+CVexfgvuAE5NcVYfmRFSxboR7HwCaSmLbN4Xz/WtK0Kg/Mif0ty1bIYRjYRBJjbNnh\nLILvX8tCa9nK3Ya72spW9l08wLIV6nYMbCKJMRZWQwEgIphr2HLhrdHhd4OTMaelbCXt0Easz0pn\n2Qp1KzYyEEmIVRBw8UoNQgK9oHXnj6ecKBQK3BeSgGh9JDJyPsHx0iwYq/MwJ+a3LFuhbsE1bCIJ\nKSiph8ksIJL94bJl0PrjtbEL8JvIiWg0N+LvJ/8X/59lK9QNGNhEEpJbxB3OnIFS2bFsZX9b2Uqe\n2KORjDGwiSSk9ZSaLExxDq1lK+P7jm0pW/k7y1bojjGwiSTEWFQNT3cVegd4ij0KdRO1UoXfRE3E\nS0N/z7IV+lUY2EQSUdtgQkllIyJCfKBkYYrTifLrjz/duwCj2pWt/JtlK9QFDGwiiWg9/pqbw52X\nh8oDibG/xQstZSvbc3ZhxbG1KG9k2QrdGgObSCK4w5nruLtd2cqFqly8fegDHCw+yrIV6hQDm0gi\njC07nEUwsF3CtWUrm7I/ZtkKdYrNDEQSIAg25BbXIDjAE54earHHIQdpX7ay6czHLFuhTnENm0gC\nCsvq0Wyy8v1rF2XQ+uOloS+wbIU6xcAmkgCeoYuUiqtlK6G6YJat0HUY2EQSYGzd4Yxr2C4vVBeM\nl4f/sUPZyufGL1m2QgxsIikwFtbAQ+OGkAAvsUchCehYtqLHN5f+g3dZtuLyGNhEIqtrNONKRYO9\nMEXJwhS6yl628hJGBSeggGUrLo+BTSSy3KLWw7m4OZyu175sRevmwbIVF8bAJhJZTssOZ1F8/5o6\ncXfgXfjziIUdylYOFB9h2YoLYWATiSynoAoKAFGh3EOcOte+bAWwIT17K8tWXAiLU4hEZLEKyC2q\nQUigFwtT6La0lq0M0EdiUzbLVlwJ17CJRJRfUgeTRUB0Hz+xRyGZCdD6IyX+BUyJerxd2conLFtx\nYgxsIhFdyK8CAETz/Wu6A0qFEg/3faBd2cohpB76AMaqPLFHox7AwCYS0YXWHc76MLDpznUoW2mq\nxAc/s2zFGTGwiURis9mQU1ANP50GBl8PscchmWPZivNjYBOJpLSqEdX1JkT18YNCwcIU6h7Xla0c\n/ht2X97HshUnwMAmEsmFAvvm8GhuDqdu1qFsRaXFZzn/YtmKE2BgE4nkQkHLDmcMbOohrWUrQ1i2\n4hQY2EQiyb5UCa27Cn2DvMUehZyYt0aH5wcnY07sdLSWrazLSketqU7s0aiLWJxCJILSqkaUVjUh\nPtrAE35Qj1MoFLgveDgG+EVgU/bHOFGahdzqPCTGTMNgQ5zY49Ftcvga9okTJ5CUlOTopyWSlOxL\n9vcS4/r5izwJuZJry1Y+OrkBW7I/QZOlSezR6DY4dA17/fr1+Pzzz+HlxXP+kms7k1cBAIjrpxd5\nEnI1rWUrsf4DsPFMBn4sPoTzlTlIjpuJSL9+Yo9HnXDoGnZ4eDjS0tIc+ZREkiPYbMi+VAk/nQa9\n/T3FHodcVGvZyiPhD7JsRSYcGtjjx4+Hm5ubI5+SSHIKS+tR22BGXD9/Hn9NolIrVZgcOaFD2co7\nR1aybEWiJL/TWWAg96DtCi6vrhFjeX2fZf9lOGJwsKz+v+Q0qxTIaXkFBt6Ne/oNwMbjn2BP7n4s\nP7ICswZPxuMDx0GpcMx6nZyWl1hECeyuHANYWlrbg5M4l8BAby6vLhBref1wvBAKAOGBXrL5/+L3\nVtfIdXlN7TcZA3TR2JL9CdJPfIoDl44hKXYGArQ9u6+FXJdXT+jsDxdRjsPmZkByVbUNJuQUViOy\njy98PDVij0N0ncGGOHvZSuCglrKVv+Inlq1IgsMDOzQ0FBkZGY5+WiJJOGksh80GxEcZxB6F6Ka8\nNTo8PygJSbHTAQCbWbYiCZJ/D5vImRzPKQMA3BPNwCZpUygUGBk8HNF+EUjP3movW6nKQ2Isy1bE\nwmpSIgcxW6zIyq1AkF7Lw7lINgK0/pgf/zt72YqFZStiYmATOUhWbgWazVbERxu4HwfJSmvZyuKE\n+QjVBePH4kN4+9CHMFbliT2aS2FgEznIT2d+AQCMiOsl8iREd6Z92UoFy1YcjoFN5AANTRacyClD\ncIAnwnvxeFOSr9aylQVDX0QAy1YcioFN5ABHz5fAbBEw8q7e3BxOTiHSrx9eufcljA65F4V1xVh+\n+G/YfXkfBJsg9mhOi4FN5AAHTts3h4/k5nByIh4qD8yOmYbf3/00tGotPsv5F/52bA3KGyvEHs0p\nMbCJelhJVSPOXqpEVB9fBPppxR6HqNsNNsThz/fay1Zyqi7i7UMfsGylBzCwiXrYf34ugA3AuPhQ\nsUch6jE3LFs5tYllK92IxSlEPajZZMX3J4rh46XB8Jggscch6lHXla2UnUbuwUssW+kmXMMm6kEH\nzlxBQ7MFDwwJgcqNP27kGli20jP4G4SohwiCDd8czodSocBYbg4nF9NatrIkIaVD2UpO1UWxR5Mt\nBjZRDzlyrgTF5Q0YNbg39N7uYo9DJIoQXW8sble28uHPH2FHTibMLFvpMgY2UQ8QBBt27s+DUqHA\nE6P6iT0OkahU15StfHt5L949shKFdcVijyYrDGyiHnD4bAmKyuoxanBvBPFQLiIArWUrC9rKVt45\nvMJetiKwbOV2MLCJulmz2YpP9uZA5ca1a6JreajcrytbeX3vhyxbuQ0MbKJu9uWBSyivacYjCX25\ndk10E+3LVrJLL9jLVooOs2ylEwxsom5UUtmAzAOXofd2xxOjwsUeh0jSWstW5t2bDADYfHYb1rJs\n5aZYnELUTQTBhvX/yobFKmDGuCh4aPjjRXQrCoUCY/vfh95uoUjP/hgny07jIstWbohr2ETd5KtD\nl5FTUI3hAwORwFYzoi4J0OoxP/53eCrqCTRam1rKVraxbKUdBjZRN8gprMZn3+XCV6dB8mMxPIUm\n0R1QKpR4qO/9WDJ8PvroQvBj8WGWrbTDwCb6lSprm5G2/RQEmw3PPxEHnVYt9khEshai642Xh/8B\nj4aPY9lKOwxsol+hsdmClZ+eRHW9CdMfjEJcP3+xRyJyCiqlCk9GPoaFw1i20oqBTXSHzBYrVm0/\nhbwrtRg9uDceSQgTeyQipxPh21q2MqKtbOXbS3sh2FyvbIWBTXQHms1WpH2WhexLlYiPNuDpCXzf\nmqin2MtWpraVrewwZuLDn9e4XNkKA5uoi+qbzHg/4zhOGssxqL8/fj/5Lrgp+aNE1NNay1buCRwE\nY/VFlytb4W8Zoi64UtGA1M0/I6ewGiPiemH+tLuhVrmJPRaRy/DW6PDcoCQkx84AoHCpshU2OxDd\npqPnSvGPf51Bk8mKRxLCMH1cFJTcDE7kcAqFAiOChyHKL6JD2crsmKm4O/AuscfrMVzDJrqFhiYL\n/l9mNtI+sx+69btJcZj5UDTDmkhkrWUrU1vKVtac2ojNTly2wjVsopuw2Ww4eq4U//z3BVTWNqNv\nkA7PTYpDn0Cd2KMRUQulQolxfe9HjP8AbDyTgZ+KD+N8pRHJcTMQ5ddf7PG6FQOb6AYuXalFxr8v\n4Fx+FdyUCkz+r/54/L5wqNy4UYpIilrLVjIv7sY3l/6DD3/+CA/3fQCPRzwCtdI5os45XgVRN8kt\nqsGuH/NwPKcMAHBPlAHTx0Wht7+nyJMR0a20lq0MMsRg45mP8e3lvThTcQ5z42YiVBcs9ni/GgOb\nXJ7FKuCksRx7fi7AmbxKAEBUqC8mj+mPu9hcRiQ7Eb798ErCS9ieswv7iw7incMr8ETEo3io7/1Q\nKuS7lYyBTS6rqKwOX3xnxPcni1FdZwIAxIbrMWlUPwzs68ciFCIZay1budsQh81nt2GHMROnyrKR\nHDcDBq08/xBX2CR+xHlpaa3YI8hGYKA3l9ctXKlowOGzJTh6tgSXS+zHbWrdVRg1qDceGBKCPkHc\noexG+L3VNVxeXdPTy6vOVI9/ntuO46Wn4O6mwbToybgveLgk/ygPDPS+6de4hk1OrclkwdnLVThz\nsQKn8ypQXN4AAHBTKjA8theGRPhjeEwQ3NUsPyFyVjqNF54bNAeHrvyMrec/x5az23Cq7Axmx0yF\nt0Y+f6QzsMmp1DSYYCyshrGwBjkFVTAW1cAq2DciuavdcE+UAcMGBiI+2oDwMH+uBRG5iNaylWh9\nBNLPbMXJstPIPZiH2THTMEQmZSsMbJKt6rpm5JfWIb/E/pFbWIOSqsa2rysA9Av2Rlw/fwzq74/I\nUF8elkXk4vw99Phj/PPYm/8DPs/9CmtPbcR9wQmYGj0JWpWH2ON1ioFNkiYINlTUNOGXykb8UtmA\nXyoaUVhWh4KSOtQ0mDvc18tDhcERAYgM8UFkqC/6B/vA04Pf4kTUUfuylU1tZSs5SI6bKemyFf42\nI1EJNhtq602oqG1GRU0TKmqaUV7ThJKWgC6taoTFev1+kQZfD8RH+yIsSIc+gTqEBekQqNeyLpSI\nbluIrjf+W0ZlK9KbiJyCxSqgrtGMmnqT/aPBhJp6M2oaTKiua0ZFTTMqaptQWdt8w0AGAE93FcKC\ndOil90SQXote/p7opfdEcIAntO781iWiX09OZSv8rUedEmw2NDVbUN9kQX2TGfVNFjS0Xm80t1y3\noKHJjLpGM6rrTahtsF/vjAKAj06DsCBv+Pu4w9/bAwE+7vD38YDexx1BflrotGpJHnZBRM6ntWzl\ns5xd+EGiZSsODWybzYZly5bh3Llz0Gg0eOuttxAWFubIEZyezWaDxWqD2WJFk6n9hwXN7a43maxo\nNFlbbrNcd79Gkz2YG5ot6MqR+l4eKvh4aRBq8IKPlwY+nhr4eKnbXbd/6L3duQMYEUmKh8ods2Km\nYrAhDlvOfiK5shWHBvbu3bthMpmQkZGBEydOIDU1FatXr3bkCA4h2GywWgV7cFoFWFsuLRYBlpbb\n7ZcdPzdbBJgsAsxmK0wWASaLFSbzNbe1XJo7XLei2Wz/t5pNVvyaJhwFAHeNGzw0bvDTuSPE4AUv\nDzW8PFTwbLtUwctDbb/UdvwaQ5iI5G6QIRZ/vndhW9nK24f+KomyFYcG9tGjRzFmzBgAwJAhQ5CV\nldXp/Strm1BR0wRBsMHa7kMQbLAIgv12qw1Wm/3Sfj/h6n2ttrbw7PjYa+7b9tjWD+Hq51b7Zftw\nNbcPWosAi9Aaxvb7tR7325OUCgXUaiXcVUqoVW7w9lTDU6u2B27Lba3Ba/9QdbjurnGD9ga3a9RK\nboYmIpd3o7KVk2WnkRgzTbSyFYcGdl1dHby9r9auqVQqCIIApfLGa2XJy7521Gi3TalQQKVSQO2m\nhJubEmo3BdzVbtB5qKFyU0LlprBfqpRQKRX2y5bbrz5GCbeWz6+9n0athEblBo1KCY3aDWqVsu26\npiWINWrlDddkWYdIRNR9ri1bOVV2Bv9z8H3RylYcGtg6nQ719fVtn3cW1gDwxfuTHTGWU+msh5au\nx+V1+7isuobLq2ukvLwC4Y3/CftvsceAQ99wHDp0KPbt2wcAOH78OAYMGODIpyciIpIth56tq/1e\n4gCQmpqK/v2l2ypDREQkFZI/vSYRERE5eJM4ERER3RkGNhERkQwwsImIiGRAcoFts9nw2muvYebM\nmUhOTkZ+fr7YI0maxWLB4sWLkZiYiOnTp2PPnj1ijyQL5eXlGDt2LC5evCj2KJK3du1azJw5E1On\nTsWnn34q9jiSZrFYsGjRIsycORNz5szh91cnTpw4gaSkJADA5cuXMXv2bMyZMwevv/66yJNJl+QC\nu3196aJFi5Camir2SJK2c+dO6PV6bNmyBevWrcObb74p9kiSZ7FY8Nprr8HDQ9onq5eCQ4cO4dix\nY8jIyEB6ejqKi4vFHknS9u3bB0EQkJGRgXnz5uGDDz4QeyRJWr9+PZYuXQqz2X6SoNTUVCxcuBCb\nN2+GIAjYvXu3yBNKk+QCu6v1pa5uwoQJSElJAWAvolGpeAK2W1m+fDlmzZqFoKAgsUeRvB9++AED\nBgzAvHnz8OKLL+LBBx8UeyRJ69evH6xWK2w2G2pra6FWq8UeSZLCw8ORlpbW9vnp06cxfPhwAMD9\n99+Pn376SazRJE1yv927Wl/q6rRaLQD7cktJScGCBQtEnkjatm/fjoCAAIwePRofffSR2ONIXmVl\nJYqKirBmzRrk5+fjxRdfxFdffSX2WJLl5eWFgoICPPbYY6iqqsKaNWvEHkmSxo8fj8LCwrbP2x9d\n7OXlhdpaVizfiORSsKv1pQQUFxdj7ty5mDJlCiZOnCj2OJK2fft27N+/H0lJSTh79iyWLFmC8vJy\nsceSLD8/P4wZMwYqlQr9+/eHu7s7KioqxB5LsjZs2IAxY8bg66+/xs6dO7FkyRKYTCaxx5K89r/j\n6+vr4ePjI+I00iW5JGR9adeUlZXh2Wefxcsvv4wpU6aIPY7kbd68Genp6UhPT0dMTAyWL1+OgIAA\nsceSrGHDhuH7778HAPzyyy9oamqCXq8XeSrp8vX1hU5nP5OTt7c3LBYLBEEQeSrpi4uLw+HDhwEA\n3333HYYNGybyRNIkuU3i48ePx/79+zFz5kwA4E5nt7BmzRrU1NRg9erVSEtLg0KhwPr166HRaMQe\nTfJ4GtFbGzt2LI4cOYJp06a1HcHB5XZzc+fOxZ/+9CckJia27THOnRtvbcmSJfjLX/4Cs9mMyMhI\nPPbYY2KPJEmsJiUiIpIByW0SJyIiousxsImIiGSAgU1ERCQDDGwiIiIZYGATERHJAAObiIhIBhjY\nRE5g3LhxiImJafuIi4tDQkICnn/+eZw9e/amj4uJicEXX3zhwEmJ6E7xOGwiJzBu3DhMmjQJycnJ\nAOyVvmVlZXjjjTdw+fJlfPvtt/D09LzuceXl5fD29mbRDpEMcA2byElotVoEBAQgICAAgYGBiI2N\nbetKP3DgwA0fExAQwLAmkgkGNpETUyqVUCgU0Gg0iImJwYoVK/DAAw9g7NixKCsru26T+I4dOzBp\n0iQMGTIEEyZMwI4dO9q+duXKFcyfPx/Dhg3D6NGjsXDhQpSUlLR9/fjx45g1axbi4+MxYsQILF68\nGNXV1Q59vUTOjIFN5KTy8/Px/vvvIygoCPHx8QCAbdu2Ye3atVi5ciUMBkOH+2dmZmLp0qWYMWMG\ndu3ahWeeeQZLly7Fjz/+iMbGRiQlJcHT0xNbt27FP/7xD1gsFsydO7ftBBfz5s3D6NGjkZmZiXXr\n1iErKwvvvPOOGC+dyClJ7uQfRHRnVq9e3Xb+ZYvFAqvVitjYWKxcuRJeXl4AgKeeegoDBw684eM3\nbdqEJ598EnPmzAEAhIWFobGxEYIgYNeuXWhsbERqamrbyT/ee+89jBw5Et988w1Gjx6NyspKBAQE\nIDg4GMHBwVi1ahXMZrMDXjmRa2BgEzmJxMREzJ49GwDg5uYGPz+/63Y069Onz00ff+7cOUyeKWxp\nzwAAAdhJREFUPLnDba07sb3xxhuoqKjA0KFDO3y9ubkZRqMREydOxDPPPIPXX38dK1aswKhRozBu\n3Dg8+uij3fHSiAgMbCKn4evri7CwsE7v09mpHtVqdadfi46OxqpVq677mre3NwDg5ZdfRmJiIvbu\n3Yv9+/fjlVdewbZt27Bhw4bbewFE1Cm+h01EAICIiAhkZWV1uG3x4sV46623EBUVhYKCAvj5+SEs\nLAxhYWHQ6/V4++23cf78eeTn52PZsmUwGAyYPXs20tLSsHz5chw8eBAVFRUivSIi58LAJiIAwHPP\nPYedO3ciIyMD+fn52Lp1KzIzM/HQQw/hySefhJ+fH1JSUpCVlYXz589j0aJFOHnyJKKioqDX6/Hl\nl19i2bJlyM3NhdFoRGZmJvr27Qt/f3+xXxqRU2BgEzmB1h3Bunqf9rc9/PDDePXVV7FhwwY88cQT\nSE9Px7vvvouRI0fC3d0dGzZsgFarxdNPP43ExEQIgoCNGzfC398fOp0O69atQ35+PmbMmIHp06fD\nbDZj7dq13fo6iVwZm86IiIhkgGvYREREMsDAJiIikgEGNhERkQwwsImIiGSAgU1ERCQDDGwiIiIZ\nYGATERHJAAObiIhIBhjYREREMvB/4/7YlrZhq6cAAAAASUVORK5CYII=\n", 273 | "text/plain": [ 274 | "" 275 | ] 276 | }, 277 | "metadata": {}, 278 | "output_type": "display_data" 279 | } 280 | ], 281 | "source": [ 282 | "interactive_supply_demand_plot = ipywidgets.interact(cobweb.supply_demand_plot,\n", 283 | " D=ipywidgets.fixed(quantity_demand),\n", 284 | " S=ipywidgets.fixed(quantity_supply),\n", 285 | " a=cobweb.a_float_slider,\n", 286 | " b=cobweb.b_float_slider,\n", 287 | " gamma=cobweb.gamma_float_slider,\n", 288 | " p_bar=cobweb.p_bar_float_slider)\n" 289 | ] 290 | }, 291 | { 292 | "cell_type": "markdown", 293 | "metadata": {}, 294 | "source": [ 295 | "

Analyzing dynamics of the model via simulation...

\n", 296 | "\n", 297 | "Model has no closed form solution (i.e., we can not solve for a function that describes $p_t^e$ as a function of time and model parameters). BUT, we can simulate equation 7 above to better understand the dynamics of the model..." 298 | ] 299 | }, 300 | { 301 | "cell_type": "markdown", 302 | "metadata": {}, 303 | "source": [ 304 | "We can simulate our model and plot time series for different parameter values. Questions for discussion...\n", 305 | "\n", 306 | "
    \n", 307 | "
  1. Can you find a two-cycle? What does this mean?
    2. \n", 308 | "
  2. Can you find higher cycles? Perhaps a four-cycle? Maybe even a three-cycle?
    3. \n", 309 | "
  3. Do simulations with similar initial conditions converge or diverge over time?
    4. \n", 310 | "
\n", 311 | "\n", 312 | "Can we relate these things to other SFI MOOCS on non-linear dynamics and chaos? Surely yes!" 313 | ] 314 | }, 315 | { 316 | "cell_type": "code", 317 | "execution_count": 30, 318 | "metadata": { 319 | "collapsed": false 320 | }, 321 | "outputs": [ 322 | { 323 | "data": { 324 | "image/png": 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xo5oEQQRPXDovXIsgxwInvs6zwMn71OpHbzzx/aH2Iy5+ZixMXAuzwHG9uew2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\nLyhlg6R5n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s+eXW+TGAxGA6Gq5IXBYDDKweLFi7Flyxb09PQAANatW1dnixgMRiOhqjEv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\nKzB5YTAYDAaDESsweWEwGAwGgxEr/P9YOwWgh8V8jAAAAABJRU5ErkJggg==\n", 325 | "text/plain": [ 326 | "" 327 | ] 328 | }, 329 | "metadata": {}, 330 | "output_type": "display_data" 331 | } 332 | ], 333 | "source": [ 334 | "model = functools.partial(adaptive_expectations, inverse_demand, quantity_supply)\n", 335 | "interactive_time_series_plot = ipywidgets.interact(cobweb.time_series_plot,\n", 336 | " F=ipywidgets.fixed(model),\n", 337 | " X0=cobweb.initial_expected_price_slider,\n", 338 | " T=cobweb.T_int_slider,\n", 339 | " a=cobweb.a_float_slider,\n", 340 | " b=cobweb.b_float_slider,\n", 341 | " w=cobweb.w_float_slider,\n", 342 | " gamma=cobweb.gamma_float_slider,\n", 343 | " p_bar=cobweb.p_bar_float_slider)" 344 | ] 345 | }, 346 | { 347 | "cell_type": "markdown", 348 | "metadata": {}, 349 | "source": [ 350 | "

Forecast errors

\n", 351 | "\n", 352 | "How do we measure forecast error? What does the distribution of forecast errors look like for different parameters? Could an agent learn to avoid chaos? Specifically, suppose an agent learned to tune the value of $w$ in order to minimize its mean forecast error. Would this eliminate chaotic dynamics?" 353 | ] 354 | }, 355 | { 356 | "cell_type": "code", 357 | "execution_count": 32, 358 | "metadata": { 359 | "collapsed": false 360 | }, 361 | "outputs": [ 362 | { 363 | "ename": "NameError", 364 | "evalue": "name 'observed_price' is not defined", 365 | "output_type": "error", 366 | "traceback": [ 367 | "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", 368 | "\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)", 369 | "\u001b[0;32m/Users/drpugh/Teaching/sfi-complexity-mooc/notebooks/cobweb.py\u001b[0m in \u001b[0;36mforecast_error_plot\u001b[0;34m(D_inverse, S, F, X0, T, **params)\u001b[0m\n\u001b[1;32m 132\u001b[0m \u001b[0;34m\"\"\"Plot forecast errors.\"\"\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 133\u001b[0m \u001b[0mtrajectory\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_simulate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mF\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mT\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mparams\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 134\u001b[0;31m \u001b[0merrors\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_forecast_error\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mD_inverse\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mS\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtrajectory\u001b[0m \u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mparams\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 135\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 136\u001b[0m \u001b[0mfig\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0max\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msubplots\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", 370 | "\u001b[0;32m/Users/drpugh/Teaching/sfi-complexity-mooc/notebooks/cobweb.py\u001b[0m in \u001b[0;36m_forecast_error\u001b[0;34m(D_inverse, S, expected_price, **params)\u001b[0m\n\u001b[1;32m 56\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m_forecast_error\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mD_inverse\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mS\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mexpected_price\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mparams\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 57\u001b[0m \u001b[0;34m\"\"\"Difference between observed price and expected price.\"\"\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 58\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mobserved_price\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mD_inverse\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mS\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mexpected_price\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mparams\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mexpected_price\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 59\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 60\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n", 371 | "\u001b[0;31mNameError\u001b[0m: name 'observed_price' is not defined" 372 | ] 373 | } 374 | ], 375 | "source": [ 376 | "interactive_forecast_error_plot = ipywidgets.interact(cobweb.forecast_error_plot,\n", 377 | " D_inverse=ipywidgets.fixed(inverse_demand),\n", 378 | " S=ipywidgets.fixed(quantity_supply),\n", 379 | " F=ipywidgets.fixed(model),\n", 380 | " X0=cobweb.initial_expected_price_slider,\n", 381 | " T=cobweb.T_int_slider,\n", 382 | " a=cobweb.a_float_slider,\n", 383 | " b=cobweb.b_float_slider,\n", 384 | " w=cobweb.w_float_slider,\n", 385 | " gamma=cobweb.gamma_float_slider,\n", 386 | " p_bar=cobweb.p_bar_float_slider)" 387 | ] 388 | }, 389 | { 390 | "cell_type": "markdown", 391 | "metadata": { 392 | "collapsed": true 393 | }, 394 | "source": [ 395 | "

Other things of possible interest?

\n", 396 | "\n", 397 | "Impulse response functions?\n", 398 | "Compare constrast model predictions for rational expectations, naive expectations, adaptive expectations. Depending on what Cars might have in mind, we could also add other expectation formation rules from his more recent work and have students analyze those..." 399 | ] 400 | }, 401 | { 402 | "cell_type": "code", 403 | "execution_count": null, 404 | "metadata": { 405 | "collapsed": true 406 | }, 407 | "outputs": [], 408 | "source": [] 409 | } 410 | ], 411 | "metadata": { 412 | "kernelspec": { 413 | "display_name": "Python 3", 414 | "language": "python", 415 | "name": "python3" 416 | }, 417 | "language_info": { 418 | "codemirror_mode": { 419 | "name": "ipython", 420 | "version": 3 421 | }, 422 | "file_extension": ".py", 423 | "mimetype": "text/x-python", 424 | "name": "python", 425 | "nbconvert_exporter": "python", 426 | "pygments_lexer": "ipython3", 427 | "version": "3.4.4" 428 | } 429 | }, 430 | "nbformat": 4, 431 | "nbformat_minor": 0 432 | } 433 | --------------------------------------------------------------------------------