# V110 — Declared heterogeneity in spending responses to the financing tax

30 October 2026. Sensitivity experiment, not empirical calibration or policy optimization.

## Question and isolated change
V109's common spending rule made aggregate consumption cuts almost invariant to surcharge allocation. This step asks whether that comparison survives different declared responses to the same financing tax.

The baseline income-spending share remains .90. Only the incremental response to accrued extra tax varies by cohort:
```
desired nonhousing consumption =
    max(0, .90 * max(0, pretax spendable income) - q[group] * accrued surcharge)
```
Pretax spendable income still deducts maintenance and contractual personal interest and includes owner interest receipts as in v109. Actual spending is then constrained by cash. The surcharge expense accrues uniformly, while cash due dates retain the quarter-end or December profile.

q measures the desired nominal spending reduction per nominal unit of this recurring modeled tax expense. It is not an estimated one-month transfer MPC, a new average income-spending share or a parameter imported from the UI paper. Bounds zero to one are restrictions of this prototype. Baseline income heterogeneity, anticipatory behavior, price feedback and dividends from changed holdings are not calibrated here.

## Declared profiles and controls
Six profiles were specified for sensitivity:

| Profile | Workers | Displaced-free | Displaced-debt | Owners |
|---|---:|---:|---:|---:|
| common_000 | 0 | 0 | 0 | 0 |
| common_050 | .50 | .50 | .50 | .50 |
| common_090 | .90 | .90 | .90 | .90 |
| common_100 | 1 | 1 | 1 | 1 |
| owners_low | .90 | .90 | .90 | .25 |
| owners_high | .30 | .30 | .30 | 1 |

The last two labels describe assumed responses, not observed characteristics of wealthy households.

Cross six profiles, two financing-tax collection profiles and the four v109 incidence rules (external-payer control, owners-only, per-capita, displacement cohorts): 48 cases. Twelve are matched external-payer controls and 36 allocate tax to modeled households. These are chosen combinations, not independent observations or a probability distribution.

Every tax allocation uses a control with the same response vector and source resources. Since the control charges no extra tax to the measured households, its household spending is unchanged across these vectors. Common .90 reproduces v109 to rounding tolerance. The baseline source remains the unchanged default v100 annual path, stable owner-free housing, concentrated ownership and zero corporate credit/workout.

Annual financing bills and due dates remain those of v108's cost-funded 4% scenario. The two collection profiles have different financing bills, so comparing them is not a timing-only experiment with equal tax cost.

## Comparison reversal
For quarter-end collection, all three household-tax allocations support the prescribed receipt schedule in both heterogeneous profiles. Change in cumulative aggregate real nonhousing consumption over twenty years relative to the matched external-payer control:

| Assumed response profile | Owners-only tax | Per-capita tax | Displacement-cohort tax |
|---|---:|---:|---:|
| Owners respond less | -.8844 | -2.9540 | -3.1840 |
| Owners respond more | -3.5378 | -1.3090 | -1.0613 |

Units are normalized real aggregate model units, not currency amounts or percentage growth rates. More negative values mean a larger cut in measured consumption.

The pairwise comparison reverses: owners-only taxation has the smaller aggregate cut in the first row and the larger cut in the second. This is an expected consequence of assigning different response coefficients, not independent evidence about which group actually responds less. It invalidates treating the v109 aggregate comparison as a stable, empirically supported tax ranking.

With common .50, .90 or 1 responses and no binding cash constraint, aggregate cuts remain effectively tied across allocations. That invariance is structural. Distributional burdens remain different even when aggregate spending ties. None of these comparisons is a welfare criterion or a recommendation to tax a particular cohort.

## Collection feasibility remains a separate gate
Of the 36 declared household-tax cases, three do not support v108's prescribed receipt schedule: December collection with displacement-cohort taxation under common_000, common_050 and owners_high. These cases are retained in the archive but excluded from the conditional spending comparison that assumes funded receipts.

The gate is conservative: a missing scheduled tax receipt means the ready-made v108 fiscal path cannot simply be reused. It does not itself prove sovereign insolvency; the treasury buffer and government payment path would need resimulation using actual receipts.

Low or zero desired spending response does not guarantee zero actual consumption loss. Cash may instead be exhausted, purchases clipped and taxes collected late; consumption can become liquidity constrained. In common_000/December/displacement-cohort taxation, actual spending falls and collection is delayed despite zero direct tax response in desired spending. No external payer fills this gap.

An eligible case with the highest aggregate consumption among the three declared allocations is labeled only as such. Controls funded outside the measured cohorts are excluded from this comparison; their external payer's consumption is not modeled. Ineligible low-collection cases cannot be presented as fully financed alternatives.

## Accounting, tests and reproducibility
The v109 monthly cash mechanics are retained in a separate generalized engine, leaving historical code/artifacts unchanged. Counterparty payments, personal interest/principal, arrears, nonnegative cash, calendar carry and source income/price assumptions remain explicit.

Eleven new tests passed with the previous sixty-one component tests. They verify recovery of v109 at common .90, matched controls, the pairwise reversal, common-response invariance, exclusion of unsupported collection, liquidity constraints at q=0, all cash tapes and creditor claims, no external backfill, rejected coefficient vectors, grid dimensions and exact archive reproduction.

Run:
```
python scripts/test_household_tax_response_v110.py
python scripts/household_tax_response_v110.py --output data/processed/household_tax_response_v110.json
```

The public artifact contains all 48 case summaries, twelve conditional comparisons, response vectors and source fingerprints. Full monthly/annual paths and transaction tapes are reproducible via build(); they are not all duplicated in the summary archive.

## Consequence for the thesis and next action
The thesis requires both a fundable transfer system and household spending responses that are not chosen to deliver the desired outcome. This sensitivity step shows that tax-incidence conclusions depend materially on an unidentified response assumption.

Keep the calibration and macro-validation gates closed. The next research action is to seek primary empirical evidence specifically comparable to recurring tax changes and spending, recording direction of shock, population, time horizon, anticipation and outcome basket. A temporary UI transfer response cannot automatically identify this tax-response coefficient.

Source outside income, prices, benefits and future dividends remain frozen, even when holdings change. The baseline income-spending share remains common at .90. No complete heterogeneous-income model, firm feedback, public-finance equilibrium or empirical proof of debt protection is supplied. No restricted records were used.

[Case summaries and fingerprints](data/processed/household_tax_response_v110.json) · [V109 incidence audit](HOUSEHOLD_TAX_INCIDENCE_V109.md) · [V108 financing cost](FINANCED_FISCAL_BUFFER_V108.md)