[cass_fiscal] Updates (#436)

* update cass_fiscal

* simplify plotting function

* simplify code

* move code up to the equation

* improve clarity of the code and algorithm

* small updates to the formula

* update terminology

* update cass fiscal

* updates

* update case fiscal

* update cass_fiscal

* update lecture

* update cass_fiscal

* Tom's Dec 31 edits of cass_fiscal lecture

* install sphinx-proof for google collab compat

* Revert "install sphinx-proof for google collab compat"

This reverts commit 0077cda.

* add sphinx-proof to collab env

---------

Co-authored-by: Humphrey Yang <u6474961@anu.edu.au>
Co-authored-by: thomassargent30 <ts43@nyu.edu>

Author: 3 people

Diff for: .github/workflows/collab.yml

@@ -32,7 +32,7 @@ jobs:
       - name: Install Build Software
         shell: bash -l {0}
         run: |
-          pip install jupyter-book==0.15.1 docutils==0.17.1 quantecon-book-theme==0.7.2 sphinx-tojupyter==0.3.0 sphinxext-rediraffe==0.2.7 sphinx-reredirects sphinx-exercise==0.4.1 sphinxcontrib-youtube==1.1.0 sphinx-togglebutton==0.3.1 arviz==0.13.0
+          pip install jupyter-book==0.15.1 docutils==0.17.1 quantecon-book-theme==0.7.2 sphinx-tojupyter==0.3.0 sphinxext-rediraffe==0.2.7 sphinx-reredirects sphinx-exercise==0.4.1 sphinxcontrib-youtube==1.1.0 sphinx-togglebutton==0.3.1 arviz==0.13.0 sphinx-proof
       # Build of HTML (Execution Testing)
       - name: Build HTML
         shell: bash -l {0}

Diff for: lectures/_config.yml

@@ -32,7 +32,7 @@ latex:
       targetname: quantecon-python.tex
 
 sphinx:
-  extra_extensions: [sphinx_multitoc_numbering, sphinxext.rediraffe, sphinx_tojupyter, sphinxcontrib.youtube, sphinx.ext.todo, sphinx_exercise, sphinx_togglebutton, sphinx.ext.intersphinx, sphinx_reredirects]
+  extra_extensions: [sphinx_multitoc_numbering, sphinxext.rediraffe, sphinx_tojupyter, sphinxcontrib.youtube, sphinx.ext.todo, sphinx_exercise, sphinx_proof, sphinx_togglebutton, sphinx.ext.intersphinx, sphinx_reredirects]
   config:
     # false-positive links
     linkcheck_ignore: ['https://online.stat.psu.edu/stat415/book/export/html/834']

Diff for: lectures/_static/quant-econ.bib

@@ -2547,4 +2547,15 @@ @book{auerbach1987dynamic
   publisher = {Cambridge University Press},
   address = {Cambridge},
   year    = {1987}
+}
+
+@article{hall1971dynamic,
+  title={The dynamic effects of fiscal policy in an economy with foresight},
+  author={Hall, Robert E},
+  journal={The Review of Economic Studies},
+  volume={38},
+  number={2},
+  pages={229--244},
+  year={1971},
+  publisher={Wiley-Blackwell}
 }

Diff for: lectures/_toc.yml

@@ -54,6 +54,7 @@ parts:
   chapters:
   - file: cass_koopmans_1
   - file: cass_koopmans_2
+  - file: cass_fiscal
   - file: ak2
   - file: cake_eating_problem
   - file: cake_eating_numerical