(cobweb)=

# The Cobweb Model

The cobweb model is a model of prices and quantities in a given market, and how they evolve over time.

## Overview

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.

```{code-cell} ipython3

The price dynamics depend on the parameter values and also on the function $f$ that determines how producers form expectations.

## Naive expectations

To go further in our analysis we need to specify the function $f$; that is, how expectations are formed.

g(p) = - \frac{1}{b} [ S(p) - a]

```

Here we represent the function $g$

```{code-cell} ipython3

p_t = - \frac{1}{b} [ S(\alpha p_{t-1} + (1-\alpha) p^e_{t-1}) - a]

$$

Let's try to simulate the price and observe the dynamics using different values of $\alpha$.

```{code-cell} ipython3

This increased stability can be seen in the figures.

## Exercises

```{exercise-start}

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```{solution-end}

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```{code-cell} ipython3

```

```