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diff --git a/Resources/econ-ark-logo-small.xbb b/Resources/econ-ark-logo-small.xbb
@@ -2,5 +2,5 @@
 %%Creator: extractbb 20220710
 %%BoundingBox: 0 0 140 96
 %%HiResBoundingBox: 0.000000 0.000000 139.982502 95.988001
-%%CreationDate: Thu May 23 19:35:26 2024
+%%CreationDate: Fri May 24 15:05:00 2024
 
diff --git a/SolvingMicroDSOPs-clean-clean.tex b/SolvingMicroDSOPs-clean-clean.tex
diff --git a/SolvingMicroDSOPs-clean.tex b/SolvingMicroDSOPs-clean.tex
diff --git a/binder/environment.yml b/binder/environment.yml
@@ -3,7 +3,7 @@ channels:
   - conda-forge
 dependencies:
   - python=3.9
-  - econ-ark=0.12
+  - econ-ark=0.14
   - ipywidgets
   - jupyterlab
   - matplotlib

diff --git a/cctwMoM-clean.tex b/cctwMoM-clean.tex
diff --git a/cctwMoM.pdf b/cctwMoM.pdf
diff --git a/docs/.gitignore b/docs/.gitignore
@@ -49,9 +49,6 @@ flycheck_*.el
 # projectiles files
 .projectile
 
-# directory configuration
-.dir-locals.el
-
 # network security
 /network-security.data
 

diff --git a/docs/Equations/MoM-Inequalities-clean.tex b/docs/Equations/MoM-Inequalities-clean.tex
@@ -1,9 +1,9 @@
 
   \begin{center}
     \begin{tabular}{rcl}
-      $ \aboveMin \mNrm_{\prd} \MPCmin_{\prd} < $ & $ \cFunc_{\prd}(\ushort{m}_{\prd}+\aboveMin \mNrm_{\prd}) $  $< (\aboveMin \mNrm_{\prd}+\aboveMin \hNrm_{\EndStp})\MPCmin_{\prd} $
-      \\  $- \aboveMin \mNrm_{\prd} \MPCmin_{\prd} > $ & $ -\cFunc_{\prd}(\ushort{m}_{\prd}+\aboveMin \mNrm_{\prd}) $ & $> -(\aboveMin \mNrm_{\prd}+\aboveMin \hNrm_{\EndStp})\MPCmin_{\prd} $
-      \\  $ \aboveMin \hNrm_{\EndStp} \MPCmin_{\prd} > $ & $ \bar{\cFunc}_{\prd}(\ushort{m}_{\prd}+\aboveMin \mNrm_{\prd})-\cFunc_{\prd}(\ushort{m}_{\prd}+\aboveMin \mNrm_{\prd}) $ & $> 0$
-      \\  $1 > $ & $ \underbrace{\left(\frac{\bar{\cFunc}_{\prd}(\ushort{m}_{\prd}+\aboveMin \mNrm_{\prd})-\cFunc_{\prd}(\ushort{m}_{\prd}+\aboveMin \mNrm_{\prd})}{\aboveMin \hNrm_{\EndStp} \MPCmin_{\prd}}\right)}_{\equiv \Hi{\koppa}_{\prd}} $ & $> 0$
+      $ \aboveMin \mNrm_{\prd} \MPCmin_{\prd} < $ & $ \cFunc_{\prd}(\Lo{m}_{\prd}+\aboveMin \mNrm_{\prd}) $  $< (\aboveMin \mNrm_{\prd}+\aboveMin \hNrm_{\EndStg})\MPCmin_{\prd} $
+      \\  $- \aboveMin \mNrm_{\prd} \MPCmin_{\prd} > $ & $ -\cFunc_{\prd}(\Lo{m}_{\prd}+\aboveMin \mNrm_{\prd}) $ & $> -(\aboveMin \mNrm_{\prd}+\aboveMin \hNrm_{\EndStg})\MPCmin_{\prd} $
+      \\  $ \aboveMin \hNrm_{\EndStg} \MPCmin_{\prd} > $ & $ \bar{\cFunc}_{\prd}(\Lo{m}_{\prd}+\aboveMin \mNrm_{\prd})-\cFunc_{\prd}(\Lo{m}_{\prd}+\aboveMin \mNrm_{\prd}) $ & $> 0$
+      \\  $1 > $ & $ \underbrace{\left(\frac{\bar{\cFunc}_{\prd}(\Lo{m}_{\prd}+\aboveMin \mNrm_{\prd})-\cFunc_{\prd}(\Lo{m}_{\prd}+\aboveMin \mNrm_{\prd})}{\aboveMin \hNrm_{\EndStg} \MPCmin_{\prd}}\right)}_{\equiv \Hi{\koppa}_{\prd}} $ & $> 0$
     \end{tabular}
   \end{center}
diff --git a/docs/Equations/MoM-KoppaOfMu-clean.tex b/docs/Equations/MoM-KoppaOfMu-clean.tex
@@ -1,7 +1,7 @@
   Defining $\mu_{\prd} =
   \log \aboveMin \mNrm_{\prd}$ (which can range from $-\infty$ to $\infty$), the object in the middle of the last inequality is
   \begin{equation}\begin{gathered}\begin{aligned}
-        \Hi{\koppa}_{\prd}(\mu_{\prd})   & \equiv  \left(\frac{\bar{\cFunc}_{\prd}(\ushort{m}_{\prd}+e^{\mu_{\prd}})-\cFunc_{\prd}(\ushort{m}_{\prd}+e^{\mu_{\prd}})}{\aboveMin \hNrm_{\EndStp} \MPCmin_{\prd}}\right), \label{eq:koppa}
+        \Hi{\koppa}_{\prd}(\mu_{\prd})   & \equiv  \left(\frac{\bar{\cFunc}_{\prd}(\Lo{m}_{\prd}+e^{\mu_{\prd}})-\cFunc_{\prd}(\Lo{m}_{\prd}+e^{\mu_{\prd}})}{\aboveMin \hNrm_{\EndStg} \MPCmin_{\prd}}\right), \label{eq:koppa}
       \end{aligned}\end{gathered}\end{equation}
   and we now define
   \begin{equation}\begin{gathered}\begin{aligned}

diff --git a/docs/Equations/TighterThreeEqns-clean.tex b/docs/Equations/TighterThreeEqns-clean.tex
@@ -1,7 +1,7 @@
   \begin{equation*}\begin{gathered}\begin{aligned}
-        \vctr{1}_{\text{Lo}}(\mNrm)  & = 1 \text{~if $          \mNrm \leq  \bar{\check{\mNrm}}_{\prd}^{\#} \phantom{< \mNrm <   \ushort{\hat{\mNrm}}_{\prd}^{\#}          \leq \mNrm}$}
-        \\  \vctr{1}_{\text{Mid}}(\mNrm)  & = 1 \text{~if $\phantom{ \mNrm \leq}~ \bar{\check{\mNrm}}_{\prd}^{\#}          < \mNrm <   \ushort{\hat{\mNrm}}_{\prd}^{\#} \phantom{\leq \mNrm}$}
-        \\  \vctr{1}_{\text{Hi}}(\mNrm)  & = 1 \text{~if $\phantom{ \mNrm \leq  ~\bar{\check{\mNrm}}_{\prd}^{\#}          < \mNrm < } \ushort{\hat{\mNrm}}_{\prd}^{\#}           \leq \mNrm$}
+        \vctr{1}_{\text{Lo}}(\mNrm)  & = 1 \text{~if $          \mNrm \leq  \bar{\check{\mNrm}}_{\prd}^{\#} \phantom{< \mNrm <   \Lo{\hat{\mNrm}}_{\prd}^{\#}          \leq \mNrm}$}
+        \\  \vctr{1}_{\text{Mid}}(\mNrm)  & = 1 \text{~if $\phantom{ \mNrm \leq}~ \bar{\check{\mNrm}}_{\prd}^{\#}          < \mNrm <   \Lo{\hat{\mNrm}}_{\prd}^{\#} \phantom{\leq \mNrm}$}
+        \\  \vctr{1}_{\text{Hi}}(\mNrm)  & = 1 \text{~if $\phantom{ \mNrm \leq  ~\bar{\check{\mNrm}}_{\prd}^{\#}          < \mNrm < } \Lo{\hat{\mNrm}}_{\prd}^{\#}           \leq \mNrm$}
       \end{aligned}\end{gathered}\end{equation*}
   we can define a well-behaved approximating consumption function
   \begin{equation}\begin{gathered}\begin{aligned}

diff --git a/docs/Equations/TighterUpperBound-clean.tex b/docs/Equations/TighterUpperBound-clean.tex
@@ -1,10 +1,10 @@
-  we want to construct a consumption function for $m_{\prd} \in (\ushort{m}_{\prd}, \mtCusp]$ that respects the
+  we want to construct a consumption function for $m_{\prd} \in (\Lo{m}_{\prd}, \mtCusp]$ that respects the
   tighter upper bound:
   \begin{center}
     \begin{tabular}{rcl}
-      $ \aboveMin \mNrm_{\prd} \MPCmin_{\prd} < $ & $ \cFunc_{\prd}(\ushort{m}_{\prd}+\aboveMin \mNrm_{\prd}) $  $< \MPCmax_{\prd} \aboveMin \mNrm_{\prd} $
-      % \\  $-\aboveMin \mNrm_{\prd} \MPCmin_{\prd} > $ & $ -\cFunc_{\prd}(\ushort{m}_{\prd}+\aboveMin \mNrm_{\prd}) $ & $> -\aboveMin \mNrm_{\prd} $
-      \\  $ \aboveMin \mNrm_{\prd}(\MPCmax_{\prd}- \MPCmin_{\prd}) > $ & $ \MPCmax_{\prd} \aboveMin \mNrm_{\prd}-\cFunc_{\prd}(\ushort{m}_{\prd}+\aboveMin \mNrm_{\prd}) $ & $> 0$
-      \\  $1 > $ & $ \left(\frac{\MPCmax_{\prd} \aboveMin \mNrm_{\prd}-\cFunc_{\prd}(\ushort{m}_{\prd}+\aboveMin \mNrm_{\prd})}{\aboveMin \mNrm_{\prd}(\MPCmax_{\prd}- \MPCmin_{\prd})}\right) $ & $> 0$.
+      $ \aboveMin \mNrm_{\prd} \MPCmin_{\prd} < $ & $ \cFunc_{\prd}(\Lo{m}_{\prd}+\aboveMin \mNrm_{\prd}) $  $< \MPCmax_{\prd} \aboveMin \mNrm_{\prd} $
+      % \\  $-\aboveMin \mNrm_{\prd} \MPCmin_{\prd} > $ & $ -\cFunc_{\prd}(\Lo{m}_{\prd}+\aboveMin \mNrm_{\prd}) $ & $> -\aboveMin \mNrm_{\prd} $
+      \\  $ \aboveMin \mNrm_{\prd}(\MPCmax_{\prd}- \MPCmin_{\prd}) > $ & $ \MPCmax_{\prd} \aboveMin \mNrm_{\prd}-\cFunc_{\prd}(\Lo{m}_{\prd}+\aboveMin \mNrm_{\prd}) $ & $> 0$
+      \\  $1 > $ & $ \left(\frac{\MPCmax_{\prd} \aboveMin \mNrm_{\prd}-\cFunc_{\prd}(\Lo{m}_{\prd}+\aboveMin \mNrm_{\prd})}{\aboveMin \mNrm_{\prd}(\MPCmax_{\prd}- \MPCmin_{\prd})}\right) $ & $> 0$.
     \end{tabular}
   \end{center}
diff --git a/docs/Equations/koppaLo-clean.tex b/docs/Equations/koppaLo-clean.tex
@@ -1,5 +1,5 @@
   Again defining $\mu_{\prd} =\log \aboveMin \mNrm_{\prd}$, the object in the middle of the inequality is
   \begin{equation*}\begin{gathered}\begin{aligned}
-        \Lo{\koppa}_{\prd}(\mu_{\prd})  & \equiv  \frac{\MPCmax_{\prd}-\cFunc_{\prd}(\ushort{m}_{\prd}+e^{\mu_{\prd}})e^{-\mu_{\prd}}}{\MPCmax_{\prd}-\MPCmin_{\prd}} \label{eq:koppaL}
-        \MPCMatch{\\ \Lo{\koppa}^{\mu}_{\prd}(\mu_{\prd})  & = \frac{\cFunc_{\prd}(\ushort{m}_{\prd}+e^{\mu_{\prd}})e^{-\mu_{\prd}}-\MPCFunc_{\prd}^{m}(\ushort{m}_{\prd}+e^{\mu_{\prd}})}{\MPCmax_{\prd}-\MPCmin_{\prd}}}{} .
+        \Lo{\koppa}_{\prd}(\mu_{\prd})  & \equiv  \frac{\MPCmax_{\prd}-\cFunc_{\prd}(\Lo{m}_{\prd}+e^{\mu_{\prd}})e^{-\mu_{\prd}}}{\MPCmax_{\prd}-\MPCmin_{\prd}} \label{eq:koppaL}
+        \MPCMatch{\\ \Lo{\koppa}^{\mu}_{\prd}(\mu_{\prd})  & = \frac{\cFunc_{\prd}(\Lo{m}_{\prd}+e^{\mu_{\prd}})e^{-\mu_{\prd}}-\MPCFunc_{\prd}^{m}(\Lo{m}_{\prd}+e^{\mu_{\prd}})}{\MPCmax_{\prd}-\MPCmin_{\prd}}}{} .
       \end{aligned}\end{gathered}\end{equation*}
diff --git a/docs/Resources/econ-ark-logo-small.xbb b/docs/Resources/econ-ark-logo-small.xbb
@@ -2,5 +2,5 @@
 %%Creator: extractbb 20220710
 %%BoundingBox: 0 0 140 96
 %%HiResBoundingBox: 0.000000 0.000000 139.982502 95.988001
-%%CreationDate: Thu May 23 19:35:26 2024
+%%CreationDate: Fri May 24 15:05:00 2024
 
diff --git a/docs/SolvingMicroDSOPs.bib b/docs/SolvingMicroDSOPs.bib
@@ -60,3 +60,234 @@ @article{SolvingMicroDSOPs
   url =           {https://llorracc.github.io/SolvingMicroDSOPs},
 }
 
+@article{merton:restat,
+  author =        {Merton, Robert C.},
+  journal =       {Review of Economics and Statistics},
+  pages =         {247--257},
+  title =         {Lifetime Portfolio Selection under Uncertainty: The
+                   Continuous Time Case},
+  volume =        {51},
+  year =          {1969},
+}
+
+@article{samuelson:portfolio,
+  author =        {Samuelson, Paul A.},
+  journal =       {Review of Economics and Statistics},
+  pages =         {239--46},
+  title =         {Lifetime Portfolio Selection by Dynamic Stochastic
+                   Programming},
+  volume =        {51},
+  year =          {1969},
+}
+
+@book{deatonUnderstandingC,
+  address =       {New York},
+  author =        {Deaton, Angus S.},
+  publisher =     {Oxford University Press},
+  title =         {{U}nderstanding {C}onsumption},
+  year =          {1992},
+}
+
+@article{Tanaka2013-bc,
+  author =        {Tanaka, Ken'ichiro and Toda, Alexis Akira},
+  journal =       {Economics letters},
+  month =         mar,
+  number =        {3},
+  pages =         {445--450},
+  publisher =     {Elsevier},
+  title =         {{Discrete approximations of continuous distributions
+                   by maximum entropy}},
+  volume =        {118},
+  year =          {2013},
+  abstract =      {PDF | On Mar 1, 2013, Ken'ichiro Tanaka and others
+                   published Discrete approximations of continuous
+                   distributions by maximum entropy | Find, read and
+                   cite all the research you need on ResearchGate},
+  doi =           {10.1016/j.econlet.2012.12.020},
+  issn =          {0165-1765},
+  url =           {https://www.researchgate.net/publication/
+  256994855_Discrete_approximations_of_continuous_distributions_by_maximum_entropy},
+}
+
+@article{kopecky2010finite,
+  author =        {Kopecky, Karen A. and Suen, Richard M.H.},
+  journal =       {Review of Economic Dynamics},
+  note =              {\url{http://www.karenkopecky.net/RouwenhorstPaper.pdf}},
+  number =        {3},
+  pages =         {701--714},
+  publisher =     {Elsevier},
+  title =         {Finite State Markov-Chain Approximations To Highly
+                   Persistent Processes},
+  volume =        {13},
+  year =          {2010},
+  url =           {http://www.karenkopecky.net/RouwenhorstPaper.pdf},
+}
+
+@article{denHaanMarcet:parameterized,
+  author =        {den Haan, Wouter J and Marcet, Albert},
+  journal =       {Journal of Business and Economic Statistics},
+  month =         {January},
+  note =          {Available at
+  {\url{http://ideas.repec.org/a/bes/jnlbes/v8y1990i1p31-34.html}}},
+  number =        {1},
+  pages =         {31--34},
+  title =         {Solving the Stochastic Growth Model by Parameterizing
+                   Expectations},
+  volume =        {8},
+  year =          {1990},
+}
+
+@article{ckConcavity,
+  author =        {Carroll, Christo{\-}pher D. and
+                   Kim{\-}ball, Miles S.},
+  journal =       {Econometrica},
+  note =
+  {\url{https://www.econ2.jhu.edu/people/ccarroll/concavity.pdf}},
+  number =        {4},
+  pages =         {981--992},
+  title =         {On the {C}on{\-}cav{\-}ity of the {C}onsumption
+                   {F}unction},
+  volume =        {64},
+  year =          {1996},
+  url =           {https://www.econ2.jhu.edu/people/ccarroll/concavity.pdf},
+}
+
+@article{zeldesStochastic,
+  author =        {Zeldes, Stephen P.},
+  journal =       {Quarterly Journal of Economics},
+  month =         {May},
+  number =        {2},
+  pages =         {275--298},
+  title =         {Optimal Consumption with Stochastic Income:
+                   {D}eviations from Certainty Equivalence},
+  volume =        {104},
+  year =          {1989},
+}
+
+@article{BufferStockTheory,
+  author =        {Christopher D. Carroll},
+  journal =       {Revise and Resubmit, Quantitative Economics},
+  title =         {Theoretical Foundations of Buffer Stock Saving},
+  year =          {2023},
+  doi =           {https://zenodo.org/badge/latestdoi/304124725},
+  url =           {https://econ-ark.github.io/BufferStockTheory},
+}
+
+@article{deatonLiqConstr,
+  author =        {Deaton, Angus S.},
+  journal =       {Econometrica},
+  note =          {\url{https://www.jstor.org/stable/2938366}},
+  pages =         {1221-1248},
+  title =         {Saving and Liquidity Constraints},
+  volume =        {59},
+  year =          {1991},
+  url =           {http://www.jstor.org/stable/2938366},
+}
+
+@article{carroll:brookings,
+  author =        {Carroll, Christopher D.},
+  journal =       {Brookings Papers on Economic Activity},
+  note =
+  {\url{https://www.econ2.jhu.edu/people/ccarroll/BufferStockBPEA.pdf}},
+  number =        {2},
+  pages =         {61--156},
+  title =         {The Buffer-Stock Theory of Saving: Some Macroeconomic
+                   Evidence},
+  volume =        {1992},
+  year =          {1992},
+  url =           {https://www.econ2.jhu.edu/people/ccarroll/
+                  BufferStockBPEA.pdf},
+}
+
+@article{carrollBSLCPIH,
+  author =        {Carroll, Christopher D.},
+  journal =       {Quarterly Journal of Economics},
+  number =        {1},
+  pages =         {1--56},
+  title =         {Buffer Stock Saving and the Life Cycle/Permanent
+                   Income Hypothesis},
+  volume =        {CXII},
+  year =          {1997},
+}
+
+@incollection{carroll:richportfolios,
+  address =       {Cambridge, MA},
+  author =        {Carroll, Christopher D.},
+  booktitle =     {Household Portfolios: Theory and Evidence},
+  note =
+  {\url{https://www.econ2.jhu.edu/people/ccarroll/richportfolios.pdf}},
+  publisher =     {MIT Press},
+  title =         {Portfolios of the Rich},
+  year =          {2002},
+  url =           {https://www.econ2.jhu.edu/people/ccarroll/
+                  richportfolios.pdf},
+}
+
+@article{palumbo:medical,
+  author =        {Palumbo, Michael G},
+  journal =       {Review of Economic Studies},
+  note =          {Available at
+  {\url{http://ideas.repec.org/a/bla/restud/v66y1999i2p395-421.html}}},
+  number =        {2},
+  pages =         {395--421},
+  title =         {Uncertain Medical Expenses and Precautionary Saving
+                   Near the End of the Life Cycle},
+  volume =        {66},
+  year =          {1999},
+}
+
+@article{carroll&samwick:nature,
+  author =        {Carroll, Christopher D. and Samwick, Andrew A.},
+  journal =       {Journal of Monetary Economics},
+  number =        {1},
+  pages =         {41--71},
+  title =         {The {N}ature of {P}recautionary {W}ealth},
+  volume =        {40},
+  year =          {1997},
+  url =           {https://www.econ2.jhu.edu/people/ccarroll/papers/
+                  nature.pdf},
+}
+
+@article{AttanasioBanksMeghirWeber,
+  author =        {Attanasio, O.P. and Banks, J. and Meghir, C. and
+                   Weber, G.},
+  journal =       {Journal of Business and Economic Statistics},
+  number =        {1},
+  pages =         {22--35},
+  publisher =     {JSTOR},
+  title =         {Humps and Bumps in Lifetime Consumption},
+  volume =        {17},
+  year =          {1999},
+}
+
+@inproceedings{horowitzBootstrap,
+  author =        {Joel L. Horowitz},
+  booktitle =     {Handbook of Econometrics},
+  editor =        {James J. Heckman and Edward Leamer},
+  publisher =     {Elsevier/North Holland},
+  title =         {The Bootstrap},
+  volume =        {5},
+  year =          {2001},
+}
+
+@article{andrews2017measuring,
+  author =        {Andrews, Isaiah and Gentzkow, Matthew and
+                   Shapiro, Jesse M},
+  journal =       {The Quarterly Journal of Economics},
+  number =        {4},
+  pages =         {1553--1592},
+  publisher =     {Oxford University Press},
+  title =         {Measuring the sensitivity of parameter estimates to
+                   estimation moments},
+  volume =        {132},
+  year =          {2017},
+}
+
+@book{judd:book,
+  address =       {Cambridge, Massachusetts},
+  author =        {Judd, Kenneth L.},
+  publisher =     {The MIT Press},
+  title =         {Numerical Methods in Economics},
+  year =          {1998},
+}
+
diff --git a/docs/SolvingMicroDSOPs.pdf b/docs/SolvingMicroDSOPs.pdf
diff --git a/docs/SolvingMicroDSOPs100x.svg b/docs/SolvingMicroDSOPs100x.svg