Improve cake eating lecture clarity and mathematical notation

[jstac]

Summary

• Simplifies language in introductory paragraphs for better readability
• Adds formal note explaining the intertemporal elasticity of substitution (IES = 1/γ)
• Improves mathematical notation by adding explicit constraints to argmax expressions
• Enhances formatting of multi-line explanations throughout the lecture
• Clarifies definitions and conditions for better understanding

Test plan

• Review all changes in cake_eating.md
• Verify mathematical notation is correct
• Check that the lecture builds correctly
• Ensure all explanations remain accurate

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[jstac]

This PR builds on the recent improvements to the cake eating lecture (#718) by further refining the mathematical notation and adding important economic context around the intertemporal elasticity of substitution. The changes make the lecture more rigorous while maintaining accessibility.

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[jstac]

This commit improves the code quality and documentation in the cake eating numerical lecture:

Key Changes:

1. Jupytext Compatibility - Fixed code cell language inconsistency (changed ipython to python3 in the first code cell) to ensure clean conversion with jupytext

2. Algorithm Clarity - Enhanced the description of the value function iteration process with clearer step-by-step explanation, particularly around interpolation and Bellman equation evaluation

3. Type Hints - Added comprehensive type annotations to all function signatures:

   • create_cake_eating_model
   • state_action_value
   • T (Bellman operator)
   • compute_value_function
   • σ (policy function)

4. Documentation - Improved docstrings and inline comments throughout for better code readability

5. Code Structure - Better parameter formatting in create_cake_eating_model and cleaner code organization

6. Mathematical Insights - Added explanation about why policy function iteration can be more effective (policy functions have less curvature than value functions)

7. Visualization - Enhanced the value function iteration plot with an additional final iteration to show convergence

8. Bug Fix - Corrected function parameter order in σ call from σ(model, v) to σ(v, model) for consistency with function signature

All changes maintain backward compatibility while improving code quality and educational clarity.

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