Commit e2c1183
Update Job Search III: Add utility function to mathematical formulation (#690)
* Update Job Search III: Add utility function to match mathematical formulation
Modified mccall_model_with_sep_markov.md to correctly apply the CRRA utility function u(c, γ) = (c^(1-γ) - 1)/(1-γ) throughout the code implementation.
Key changes:
- Updated Bellman operator T() to use u(w_vals, γ) and u(c, γ)
- Updated get_greedy() policy function to apply utility transformation
- Modified plotting code to use utility-transformed values
- Added γ parameter unpacking in all relevant functions
- Fixed missing comma in create_js_with_sep_model() parameter list
The code now correctly matches the mathematical formulation where wages and unemployment compensation enter the value functions through the utility function rather than directly.
🤖 Generated with [Claude Code](https://claude.com/claude-code)
Co-Authored-By: Claude <noreply@anthropic.com>
* Complete Job Search IV lecture: Add utility function and fitted VFI implementation
Updated mccall_fitted_vfi.md to implement the continuous wage offer model with CRRA utility.
Key changes:
- Added CRRA utility function u(c, γ) = (c^(1-γ) - 1)/(1-γ) to mathematical formulation
- Updated Model class to include ρ, ν, and γ parameters
- Implemented Monte Carlo integration for computing conditional expectations (Pv_u)(w)
- Updated Bellman operator T() to use u(w, γ) and u(c, γ)
- Added get_greedy() function for computing optimal policy
- Fixed all model unpacking throughout code
- Implemented compute_expectation() using w' = w^ρ * exp(ν * z) with standard normal draws
- Added Exercise 3: Exploring reservation wage as function of risk aversion γ
- Reformatted text: each sentence on separate line for better version control
Mathematical consistency:
- Code now matches theory where wages and unemployment compensation enter through utility function
- Monte Carlo approximation: (Pv_u)(w) ≈ (1/N) Σ v_u(w^ρ exp(ν z_i))
- Proper JAX implementation with interpolation for fitted value function iteration
🤖 Generated with [Claude Code](https://claude.com/claude-code)
Co-Authored-By: Claude <noreply@anthropic.com>
* Fix missing equation label 'bell2mcmc' in mccall_fitted_vfi.md
Added the label 🏷️ bell2mcmc to the Bellman operator equation and
converted it from $$ delimiters to the {math} directive to support
cross-references. This fixes the build warning:
WARNING: equation not found: bell2mcmc
🤖 Generated with [Claude Code](https://claude.com/claude-code)
Co-Authored-By: Claude <noreply@anthropic.com>
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Co-authored-by: Claude <noreply@anthropic.com>
Co-authored-by: Matt McKay <mmcky@users.noreply.github.com>1 parent 065fb58 commit e2c1183
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