Updates to lake model lecture required

[jstac]

Endogenous flows need to be brought up to date with changes in QuantEcon/lecture-source-py#793.

[Harveyt47]

Point of possible confusion.

d is used in McCall for the expected value of unemployment tomorrow,

while in lake model d is used to denote labour market exit rate.

[Harveyt47]

in lake u is used to denote both unemployment rate and the utility function

[Harveyt47]

Change links to McCall model to McCall search and separation model. I think the search lecture is more connected than McCall 1.

[Harveyt47]

Move utility function and update_bellman function into MccallModel class and jitclass the class.

Also make sure variables are consistent across lectures.

split MccallModel and solve_mccall_model into different cells.

[Harveyt47]

I think at minimum we should do the following which can be found in this notebook.

Main changes are in endogenous flow section

I also add a random_state=seed in the markov chain [simulation] (https://python-intro.quantecon.org/lake_model.html#Convergence-Rate)

CC @shlff @mtiley @sayaikegawa if you guys have time to look over this issue and discuss changes.

I have left out any changes to variables and their notation. Discussion of consistence of variable notation across lake model and McCall model is needed.

[Harveyt47]

@sayaikegawa and I have discussed a number of changes to be made not only to the lake model but other lectures to maintain notational consistency.

Finite Markov changes

• change \alpha -> \lambda
• change \beta -> \alpha
• change \lambda -> \pi here Job Search 2 changes
• change d -> f Lake Model changes
• remove @property from class
• change sentences above the class regarding @property.
• add code in this notebook to here
• change exercise to account of class changes

[jstac]

Sounds good guys, looking forward to seeing the PRs.