Source-paper checks for the gradual_trade_agreements and organizational_equilibrium lectures #397

@thomassargent30 — the review of #396 turned up three points that need checking against the source papers. None of them blocks merging #396. Both lectures are internally consistent, and every number quoted in the text matches the code output.

1. Two footnotes say the source papers are wrong

Bond and Park (2002), Figure 1(a) — footnote [^fig1a] in gradual_trade_agreements. The footnote says the caption reports λ = 1.1, δ = 0.65 and T_L > 0, but the lecture's model gives T_L ≈ −1.01 at those values, and T_L turns positive only above δ ≈ 0.70. Two possible explanations were checked, and neither accounts for the difference:

• Demand and supply parameters. T_L stays negative at λ = 1.1, δ = 0.65 across five different sets of A, B, β and α.
• Deviation timing. The lecture assumes a deviator still collects its partner's side payment in the period it deviates. Dropping that assumption changes the size of T_L but not its sign.

Could you compare the caption, and the paper's welfare and punishment definitions, with the lecture's?

Bond (2009), the two-step condition — footnote [^bond-two-step]. The footnote says Bond states the second-step condition as 3Φ(G, δ) = (1 − δ)k, and that applying his Lemma 1 to the newcomer gives (1 + 2δ)Φ(G, δ) ≥ (1 − δ)k instead. Working it through by hand under the lecture's timing gives the lecture's version. The factor 1 + 2δ comes from the newcomer's entry-date side payment not relaxing its constraint. If Bond's timing treats entry-date payments differently, his 3Φ would be correct for his model, and the footnote should say that rather than imply an error.

Proposition number. The consumption-smoothing section cites "Proposition 3 of Bond and Park (2002)" for the small country's slack incentive constraint. Please confirm the number.

2. A claim with no code behind it

organizational_equilibrium says that "a numerical search over tariff paths that repeat every two, three, or four periods finds none that gives every policymaker more than V*". The claim holds. A re-run of that search found the best paths at about 0, 0 and −3 × 10⁻⁵ relative to V*; the 2- and 3-period searches converge to the constant best tariff. Would you like the search added as a code cell, perhaps in a dropdown, or left as text?

One small code tidy-up from the review is on #396: the padding in the exercise 3 table of gradual_trade_agreements is corrected.