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---

In addition to what's in Anaconda, this lecture will need the following libraries:

```{code-cell} ipython

---

tags: [hide-output]

---

```{code-cell} ipython3

:tags: [hide-output]

!pip install --upgrade quantecon

```

We'll need the following imports:

```{code-cell} ipython

```{code-cell} ipython3

import sys

import numpy as np

import matplotlib.pyplot as plt

Description and clarifications are given below

```{code-cell} python3

```{code-cell} ipython3

# Set up a namedtuple to store data on the model economy

Economy = namedtuple('economy',

('β', # Discount factor

a0 = 0.5 * (F @ (x_vals.T @ Sm.T)**2)[0]

H = ((Sb - Sd + Sg) @ x_vals) * ((Sg - Ss) @ x_vals)

b0 = 0.5 * (F @ H.T)[0]

a0, b0 = float(a0), float(b0)

a0, b0 = float(a0[0]), float(b0[0])

else:

H = Sm.T @ Sm

a0 = 0.5 * var_quadratic_sum(A, C, H, β, x0)

Here's the code

```{code-cell} python3

```{code-cell} ipython3

# == Parameters == #

β = 1 / 1.05

ρ, mg = .7, .35

Most obvious from the figure is tax smoothing in the sense that tax revenue is

much less variable than government expenditure.

```{code-cell} python3

```{code-cell} ipython3

gen_fig_2(path)

```

Our second example adopts a discrete Markov specification for the exogenous process

```{code-cell} python3

```{code-cell} ipython3

# == Parameters == #

β = 1 / 1.05

P = np.array([[0.8, 0.2, 0.0],

The call `gen_fig_2(path)` generates

```{code-cell} python3

```{code-cell} ipython3

gen_fig_2(path)

```

:class: dropdown

```

```{code-cell} python3

```{code-cell} ipython3

# == Parameters == #

β = 1 / 1.05

ρ, mg = .95, .35

gen_fig_1(path)

```

```{code-cell} python3

```{code-cell} ipython3

gen_fig_2(path)

```

```{solution-end}

```