# MacroVision v198: why full price pass-through lowers displaced-household preservation

5 November 2026. Analytical derivation plus measurement on the existing v98 runs. No rule changes; one in-memory counterfactual removes the initial consumer loan. Output: `data/processed/mechanism_channels_v198.json` (`python scripts/mechanism_channels_v198.py` after regenerating v98/v100).

## Summary
Full pass-through of cost savings to prices works through two channels. (A) The fiscal residual that funds benefits shrinks sharply even though real revenue barely moves, because it is a thin residual after existing spending and interest on nominal debt. (B) Households whose rent or mortgage is fixed in nominal terms lose real non-housing consumption when the benefit is indexed to goods prices. In the model, B decides preservation: for outright owners pass-through leaves joint preservation unchanged (8/16, 8/16, 8/18), for renters it falls from 8/16 to 2/18.

## Notation (year t, budget-limited closure of v98)
P goods price index; W nominal wage bill (nominal wage per worker fixed, `wage_gain = 0`); N = P·Q nominal output with real output Q; Π = N − W profits; τ_w = 0.20 wage tax; τ_π profit tax (0.25 or 0.35); κ accessible profit share (0.5 or 1); G = 20.2 existing real spending; i = 0.03; D nominal government net debt. Sources: `coupled_thesis_v71.py` lines 8–16 and 43–55; `corporate_credit_model_v98.py` lines 66–75.

Revenue R = τ_w W + τ_π κ Π. Real residual for benefits a = R/P − G − iD/P.
Pass-through enters only through P = 1 − φ·(W₀/N₀)·(1 − w/e): with φ = 1 the unit-cost saving is passed into lower prices instead of profits.

## Proposition 1 (fiscal leverage)
Holding Q, W and D fixed at the margin,
  ∂a/∂P = [(τ_π κ − τ_w)·W + i·D] / P²,  so  ∂ln a/∂ln P = [(τ_π κ − τ_w)·W/P + i·D/P] / a.

Proof. R/P = τ_w W/P + τ_π κ (Q − W/P); differentiate: −τ_w W/P² + τ_π κ W/P². The interest term −iD/P contributes +iD/P². ∎

Two consequences:
1. The interest term always pushes the same way: lower prices raise the real burden of interest on nominal debt (a fiscal form of Fisher's 1933 debt-deflation mechanism). The revenue term can go either way: when τ_π κ < τ_w, lower prices raise the real value of the nominal wage-tax base.
2. The base calibration sets G = BASE_REVENUE − i·D₀ (line 16), so a₀ = 0: the benefit fund is only the increment generated by the transition. The elasticity is divided by a small number, so a 1% change in real revenue becomes a much larger change in a.

Measured (64 matched pairs, year 10, no-credit variant): real revenue −1.2% median (IQR −3.0% to +1.2%); residual −12.6% (IQR −14.3% to −6.1%); leverage R/P ÷ a median 6.0 (IQR 3.3–8.0); 57% of the residual change comes from revenue and 43% from interest; the budget rule binds in 53 of 64 pairs at full pass-through.

## Proposition 2 (nominal obligations inside the benefit requirement)
When the budget binds, every displaced household receives the same fraction f = A/Need of its requirement, and the requirement of the indebted cohort includes its nominal debt service δ: Need/P = Σ M(1−e)(r − d/P + δ/P). Lower P raises δ/P, so f falls further. Measured: removing the initial consumer loan leaves the pass-through effect on the debt-free displaced cohort unchanged (−7.97 vs −7.92 index points), so this crowding-out is negligible; for the indebted cohort the loan adds about 2.5 points (−10.46 vs −7.92), roughly a quarter of its loss.

## Proposition 3 (nominal housing payments)
For a displaced household whose benefit is fully funded at P·r and whose housing payment H is nominal, real non-housing consumption is c = r − H/P, so ∂c/∂P = H/P² > 0: a fall in goods prices raises the real cost of a fixed rent or mortgage one-for-one. Outright owners pay only fixed nominal maintenance of 2 against rent of 12. Measured pass-through effect on terminal consumption of the debt-free displaced cohort (median index points): owner_free −1.5, renter −11.3, mortgage_fixed −9.9, mortgage_reset −11.3.

| Tenure | Joint preservation at pass-through 0 / 0.5 / 1 |
|---|---|
| Outright owner | 8/16 · 8/16 · 8/18 |
| Renter | 8/16 · 8/18 · 2/18 |
| Fixed-rate mortgage | 8/16 · 6/16 · 6/18 |
| Reset mortgage | 6/16 · 4/16 · 3/18 |

## Interpretation and limits
- Channel B rests on assumptions: rent is nominal and moves only with the housing stress path, mortgage payments are nominal, and the required benefit is indexed to goods prices. If rents followed goods prices, channel B would largely disappear. The finding is therefore conditional: cheaper goods protect displaced households only if their housing obligations fall too, or if benefits are indexed to a price measure that includes housing costs.
- Channel A is structural in this model (it follows from a₀ = 0 and nominal debt), but its effect on preservation is small on its own: outright owners face the same fiscal residual yet keep the same preservation count.
- Comparisons are descriptive across matched model cases, not causal estimates of real economies. Q and D are not held fixed in the simulations; Proposition 1 is a local guide to direction and magnitude, verified numerically above.