[ak2] improvements in lecture and conversion to JAX

[bishmaybarik]

• Fix typos in the lecture

Typo 1:

There's a minor typo in Equation (69.6). The equations written are:

$$ \begin{aligned} C_{yt} &= \beta \Bigl[ W_t (1 - \tau_t) - \delta_{yt} - \frac{\delta_{ot}}{1 + r_{t+1}(1 - \tau_{t+1})} \Bigr], \\ \frac{C_{0,t+1}}{1 + r_{t+1}(1 - \tau_{t+1})} &= (1 - \beta) \Bigl[ W_t (1 - \tau_t) - \delta_{yt} - \frac{\delta_{ot}}{1 + r_{t+1}(1 - \tau_{t+1})} \Bigr]. \end{aligned} $$

The correct version should be:

$$ \begin{aligned} C_{yt} &= \beta \Bigl[ W_t (1 - \tau_t) - \delta_{yt} - \frac{\delta_{ot}}{1 + r_{t+1}(1 - \tau_{t+1})} \Bigr], \\ \frac{C_{o,t+1}}{1 + r_{t+1}(1 - \tau_{t+1})} &= (1 - \beta) \Bigl[ W_t (1 - \tau_t) - \delta_{yt} - \frac{\delta_{ot}}{1 + r_{t+1}(1 - \tau_{t+1})} \Bigr]. \end{aligned} $$

TLDR: Replace 0 in $C_{0,t+1}$ with o. So it should be $C_{o,t+1}$

• Improve reading and flow of the lecture
• Make sure lecture follows Quantecon style guidelines
• Convert the lecture to JAX