Add a lecture on overlapping generations

[jstac]

Set out the OLG lecture and show one way that a constant savings rate can be derived from first principles.

Use the baseline model in https://economics.mit.edu/sites/default/files/inline-files/Lecture%208%20-%20Overlapping%20Generations_1.pdf described on page 17.

Begin from page 9 and continue until page 26.

Use Python to

• show 45 degree diagram and how it changes with parameters
• simulate paths from different initial conditions
• show how the steady state

[jstac]

Also see ch 8 of https://press.lse.ac.uk/site/books/m/10.31389/lsepress.ame/

[jstac]

Also consider adding the case where production is CES rather than Cobb-Douglas, as well as other kinds of preferences.

Then we will have to solve for the savings rate numerically (I think), which will be an interesting computational problem.

References:

• https://www.minneapolisfed.org/~/media/files/research/prescott/macro_theory/cesprodfn.pdf?la=en
• https://en.wikipedia.org/wiki/Category:Utility_function_types

[jstac]

Give references in the lecture to more advanced OLG models used for policy, such as https://github.com/PSLmodels/OG-USA

[jstac]

Done.