Extension to basic McCall model -- response to volatility (#707) (#709)

* Add continuous distribution and volatility analysis to McCall model (#707)

This commit addresses issue #707 by extending the basic McCall model:

- Add "Continuous Offer Distribution" section
  - Move continuous wage distribution from exercises to main content
  - Implement lognormal wage distribution with Monte Carlo integration
  - Show how reservation wage varies with c and β using contour plots

- Add "Volatility" section
  - Demonstrate that reservation wage increases with volatility
  - Use mean-preserving spread with lognormal distribution
  - Illustrate how workers prefer more volatile distributions

- Update exercise mm_ex1 solution
  - Change from discrete to continuous distribution
  - Use JAX implementation with continuous wage draws

- Remove exercise mm_ex2 (now covered in main text)

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Co-Authored-By: Claude <noreply@anthropic.com>

* misc

* misc

* Add lifetime value analysis for volatility in McCall model

- Add new section showing expected lifetime value increases with volatility
- Implement parallel JAX code for simulating job search with optimal policy
- Use jax.vmap to vectorize 10,000 simulation replications
- Compute reservation wage and lifetime value across volatility levels
- Plot demonstrates option value of search under uncertainty
- Fix LaTeX escape sequence warnings in xlabel (use raw strings)

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Co-Authored-By: Claude <noreply@anthropic.com>

* Simplify lifetime value simulation to fixed 100 periods

- Replace while_loop with fixed-period simulation (100 periods)
- Draw all wage offers upfront using vectorized operations
- Use cumsum to track employment status from first acceptance
- Simpler logic that's easier to parallelize (same path length)
- Cleaner code without nested loop functions
- Update description to reflect simplified approach

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Co-Authored-By: Claude <noreply@anthropic.com>

* misc

* misc

---------

Co-authored-by: Claude <noreply@anthropic.com>

Author: jstac

lectures/mccall_fitted_vfi.md

@@ -44,7 +44,7 @@ $$
 
 and $\{Z_t\}$ is IID and standard normal.
 
-While we already considered continuous wage distributions briefly in Exercise {ref}`mm_ex2` of the {doc}`first job search lecture <mccall_model>`, the change was relatively trivial in that case.
+While we already considered continuous wage distributions briefly in {doc}`mccall_model`, the change was relatively trivial in that case.
 
 The reason is that we were able to reduce the problem to solving for a single scalar value (the continuation value).