[ak_aiyagari] Fix inconsistent household reference (hh → household)

[sudayuga]

Summary

Several functions incorrectly referenced a global variable hh instead of using the household argument passed to them.
This caused silent inconsistency and potential runtime failure if hh is not defined in the global scope.

Fix

• Replaced all hh.* references with household.*
• Ensured dimensional consistency (J, num_state)
• Updated calls to backwards_opt, popu_dist, compute_aggregates,
  and solve_backwards to use the injected household object

[jstac]

many thanks @sudayuga !

@HumphreyYang , could you please review?

[HumphreyYang]

Many thanks @sudayuga, this looks perfect to me!

Hi @mmcky, I think this is ready to merge. I will do some minor cleanups on other parts of the lecture once it is merged!

[jstac]

🤖 Status note for a future session — from a maintainer investigation on 2026-07-08 into why open-PR previews 404. Context only, not instructions.

Netlify preview: none — and there never was one. This PR is from a fork (sudayuga), and fork PRs don't receive the repo's NETLIFY_AUTH_TOKEN, so the preview job can't deploy. To get a preview, a maintainer can push this branch to the main repo as an internal PR, or build locally.

Why previews are down (repo-wide findings)

1. This branch is stale — 126 commits behind main. A preview build compiles the whole site from this branch. This branch's lectures/house_auction.md still has unpinned !pip install prettytable, which now breaks on a wcwidth incompatibility. main fixed this on 2026-06-28 by pinning prettytable<3.18 (#939). This alone fails any rebuild of this branch until it's updated to main.

2. The arviz failure was a red herring — do NOT pin arviz or rewrite plotting. A 2026-07-07 rebuild also failed in ar1_bayes/ar1_turningpts with an arviz_plots figsize ValueError. That was a transient bug in an intermediate arviz-plots 1.x release, already fixed in arviz 1.2.0. Verified locally on a clean latest-stack venv: the real az.plot_trace(trace) cell (pymc + numpyro InferenceData) runs green. The lectures use only 1.x-compatible arviz APIs (plot_trace, summary, from_numpyro, compare).

Recommended first step for this PR

Update the fork branch to main (it's 126 commits behind) to clear the house_auction breakage, then review. A live preview requires re-hosting the branch in the main repo (fork limitation above).

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This PR touches: ak_aiyagari.md. Last CI build: n/a (fork). Branch: 126 commits behind main as of 2026-07-08.