# Verification checks (P4)
| # | check | outcome |
|---|---|---|
| 1 | Clean rerun (delete results.json, rerun analysis.py, byte compare) | PASS: identical |
| 2 | Market clearing good 1: x1_A+x1_B-12 | PASS: 0.0 |
| 3 | Market clearing good 2: x2_A+x2_B-10 | PASS: 0.0 |
| 4 | Budget constraints A and B hold with equality | PASS: 0.0, 0.0 |
| 5 | MRS_A = MRS_B = p (Pareto efficiency / tangency) | PASS: 0.875 each |
| 6 | Closed form vs Brent root of z1(p) on [1e-6,1e6] | PASS: abs diff 1.1e-16 |
| 7 | Walras' law at eq. (0.0) and on 41-point off-equilibrium grid p in [0.01,100] | PASS: max abs 5.7e-14 |
| 8 | Hand calculation p = (0.4*2+0.6*8)/(0.6*8+0.4*4) = 5.6/6.4 | PASS: 0.875 |
| 9 | All allocations strictly positive (interior) | PASS |
| 10 | n_raw(2) - removed(0) = n_analysed(2) | PASS |
| 11 | Uniqueness: Cobb-Douglas z1(p) strictly decreasing (z1 = 5.6/p - 6.4 with sum-of-endowment data), so there is a single root | PASS (analytic) |
| 12 | Input inconsistency (aggregate good1 14 vs 12) recorded in data_issues | PASS |