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lectures/cobweb.md

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(cobweb)=
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# The Cobweb Model
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The cobweb model is a model of prices and quantities in a given market, and how they evolve over time.
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## Overview
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Our discussion and simulations draw on [high quality lectures](https://comp-econ.org/CEF_2013/downloads/Complex%20Econ%20Systems%20Lecture%20II.pdf) by [Cars Hommes](https://www.uva.nl/en/profile/h/o/c.h.hommes/c.h.hommes.html).
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We will use the following imports.
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```{code-cell} ipython3
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The price dynamics depend on the parameter values and also on the function $f$ that determines how producers form expectations.
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## Naive expectations
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To go further in our analysis we need to specify the function $f$; that is, how expectations are formed.
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g(p) = - \frac{1}{b} [ S(p) - a]
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```
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Here we represent the function $g$
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```{code-cell} ipython3
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p_t = - \frac{1}{b} [ S(\alpha p_{t-1} + (1-\alpha) p^e_{t-1}) - a]
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$$
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Let's try to simulate the price and observe the dynamics using different values of $\alpha$.
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```{code-cell} ipython3
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This increased stability can be seen in the figures.
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## Exercises
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```{exercise-start}
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```
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```{solution-end}
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```
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```{code-cell} ipython3
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```
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```

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