## Exercises

(career_ex1)=

### Exercise 1

```{exercise-start}

:label: career_ex1

```

Using the default parameterization in the class `CareerWorkerProblem`,

generate and plot typical sample paths for $\theta$ and $\epsilon$

In particular, modulo randomness, reproduce the following figure (where the horizontal axis represents time)

```{figure} /_static/lecture_specific/career/career_solutions_ex1_py.png

```

Hint: To generate the draws from the distributions $F$ and $G$, use `quantecon.random.draw()`.

(career_ex2)=

### Exercise 2

```{exercise-end}

```

```{exercise}

:label: career_ex2

Let's now consider how long it takes for the worker to settle down to a

permanent job, given a starting point of $(\theta, \epsilon) = (0, 0)$.

Collect 25,000 draws of this random variable and compute the median (which should be about 7).

Repeat the exercise with $\beta=0.99$ and interpret the change.

```

(career_ex3)=

### Exercise 3

```{exercise}

:label: career_ex3

Set the parameterization to `G_a = G_b = 100` and generate a new optimal policy

figure -- interpret.

```

## Solutions

### Exercise 1

```{solution-start} career_ex1

:class: dropdown

```

Simulate job/career paths.

plt.show()

```

### Exercise 2

```{solution-end}

```

```{solution-start} career_ex2

:class: dropdown

```

The median for the original parameterization can be computed as follows

Not surprisingly, more patient workers will wait longer to settle down to their final job.

### Exercise 3

```{solution-end}

```

```{solution-start} career_ex3

:class: dropdown

```

```{code-cell} python3

cw = CareerWorkerProblem(G_a=100, G_b=100)

stays put has grown because the distribution for $\epsilon$

has become more concentrated around the mean, making high-paying jobs

less realistic.

```{solution-end}

```