lq_inventories#

  • Series: lecture-python.myst

  • File: lectures/lq_inventories.md

  • Audit date: 2026-08-26

  • Corpus snapshot: e25fdf2345

  • Categories audited: writing, math, code, figures, references, links, admonitions (JAX out of scope)

  • Overall score: 7.2 / 10

  • Priority: HIGH

Score breakdown#

Category

Score

One-line note

Writing

3/10

qe-writing-006 ×2; qe-writing-001 ×4; qe-writing-005 ×4, +4 more.

Math

3/10

qe-math-002 ×15; qe-math-003 ×17.

Code

7.5/10

qe-code-001 ×7.

JAX

out of scope

JAX rules target lecture-jax.

Figures

7/10

qe-fig-003 ×4; qe-fig-008 ×10; qe-fig-001 ×1.

References

10/10

no mechanical violations detected.

Links

10/10

no mechanical violations detected.

Admonitions

10/10

no mechanical violations detected.

Issues#

Critical#

None found.

High severity#

  • [qe-code-001] (reviewer) — Follow PEP8 unless closer to mathematical notation. Count: 7. Lines: 298, 299, 315, 322, 333, 335, 743. Example: c2 * Q_path ** 2 (298) and d2 * (S_path - I_path) ** 2 (299) put spaces around **, which qe-code-001 names explicitly as the one operator that should be written closed up; set_ylim(0-span*1.1, 0+span*1.1) (315, 322) drops the spaces around -, + and * in the same expression; the two plot labels at 333-336 are continued with a backslash inside the string literal, which both violates PEP8’s preference for parenthesised continuation and injects a run of spaces into the rendered legend text; and A22 =[[1,  0,  0], (743) has no space after = and continues at column 10 under an opening bracket at column 6. Three inline comments also sit one space from the code rather than two (646, 680, 753).

  • [qe-fig-008] — Use lw=2 for line charts. Count: 10. Lines: 306, 307, 308, 312, 326, 327, 328, 332, 333, 335. Example: plot() without lw=.

  • [qe-math-002] — Use \top for transpose notation. Count: 15. Lines: 131, 137, 148, 149, 151, 153, 661, 720. Example: apostrophe transpose x_t'.

  • [qe-math-003] — Use square brackets for matrix notation. Count: 17. Lines: 114, 150, 151, 154, 157, 158, 161, 164, 165, 168, …. Example: array used as matrix.

  • [qe-writing-006] — Capitalize lecture titles properly. Count: 2. Lines: 417, 448. Example: H2 Title Case: ‘Inventories Not Useful’ (Not, Useful).

Medium severity#

  • [qe-fig-003] — No matplotlib embedded titles. Count: 4. Lines: 310, 316, 330, 338. Example: .set_title.

  • [qe-writing-001] — Use one sentence per paragraph. Count: 4. Lines: 489, 716, 722, 769. Example: 2 sentences in one paragraph.

  • [qe-writing-002] (reviewer) — Keep writing clear, concise, and valuable. Count: 3. Lines: 481, 71, 564. Example: line 481-487 is one 75-word sentence describing three production paths and their three colours, and it is ungrammatical in the middle (‘as well with an optimal production path’); the bullet at 71-72 says the same object is two different things - ‘\(c(Q_t) = c_1 Q_t + c_2 Q_t^2\), be a cost of production function, where \(c_1>0, c_2>0\), be an inventory cost function’ - so the definition of the production cost function reads as a definition of the inventory cost function; and 564-571 packs the stability caveat, the optimal output level, its economic meaning and an aside about negative production into a single 48-word sentence with two nested parentheticals.

  • [qe-writing-003] (reviewer) — Maintain logical flow. Count: 2. Lines: 417, 481. Example: the two alternative-technology models are given their own H2 sections, ‘Inventories Not Useful’ (417) and ‘Inventories Useful but are Hardwired to be Zero Always’ (448), which sit between ‘## Example 1’ (353) and ‘## Example 2’ (517) at the same heading level - so the Example 1…6 sequence is broken in the middle by two sections that are not examples. Worse, the discussion inside the second of them (481-511) is about the bottom-right panel of Example 1’s figure and ends by re-running Example 1 at 514, so Example 1’s analysis is completed under a heading about a different model. The two concepts are also introduced a third time, at 404-415, before either section defines them.

  • [qe-writing-005] (reviewer) — Use bold for definitions, italic for emphasis. Count: 4. Lines: 565, 590, 592, 685. Example: bold is used for emphasis throughout the later sections, and the lecture uses italic for emphasis nowhere: stability (565) emphasises a term that is not being defined here, run a Ponzi scheme (590) and going short in / borrowing (592-593) are rhetorical emphasis, and season (685) marks a word in an ordinary sentence. The genuine definitions earlier in the lecture, state (98) and control (104), are bolded correctly - it is the emphasis that has taken the wrong markup.

  • [qe-writing-008] — Remove excessive whitespace between words. Count: 4. Lines: 56, 62, 432, 507. Example: 2 spaces.

Low severity#

  • [qe-fig-001] — Do not set figure size unless necessary. Count: 1. Lines: 304. Example: figsize=.

  • [qe-writing-007] (reviewer) — Use visual elements to enhance understanding. Count: 1. Lines: 304. Example: all twelve figures in the lecture come from one hard-coded four-panel layout inside SmoothingExample.simulate (304-340), the same four panels whatever the example is about, and none of them is captioned or named. The prose is therefore forced to navigate by position - ‘The figures above’ (391), ‘The lower right panel’ (404), ‘The bottom right panel’ (481), ‘the following figures confirm’ (595) - and Example 4’s point, that inventories run down without limit, has to be found in one panel of a 15x10 grid. Example 6 then prints four more of the same four-panel figures (681, 689, 694, 699) that differ only in the initial season, with nothing in or around them saying which is which.

Strengths#

  • The reduction of the firm’s profit function to the LQ matrices is shown rather than asserted: the \underset{...}{\underbrace{...}} annotations at 148-149 tag each group of terms with the matrix it lands in, and 150-171 then displays \(R\), \(Q\) and \(N\) with the same tags, so every entry can be traced back to a primitive.

  • The lecture warns the reader about the two notation collisions it cannot avoid - that \(Q_t\) is production while \(Q\) is the control cost matrix (129-132), and that the cross-product matrix is called \(N\) in the QuantEcon library (177-178).

  • The six examples change exactly one feature of the environment each - AR(1) shock (353), no randomness (517), \(d_1 = 0\) (535), \(d_1 = d_2 = 0\) (554), linear trend (614), deterministic seasonal (650) - and all of them go through keyword arguments to a single class, so any difference between figures is attributable to the stated change.

  • Example 4 teaches a failure instead of hiding it: switching off both inventory costs violates the stability conditions, and the lecture follows the absurd optimum through the law of motion (573-590) and then shortens the horizon to \(T = 30\) so the divergence is visible (607-611).