# V109 — Household incidence and collection of the buffer-financing tax

30 October 2026. Four-cohort incidence audit linked to v108's required financing surcharge. No empirical calibration or full macro integration.

## Purpose and scope
V108 recorded a tax cost but assigned it to an external taxpayer account without household spending effects. This extension assesses that surcharge against explicit modeled households, debits their cash and replays their consumption, personal debt and equity purchases.

Use the unchanged complete v100 default path: concentrated ownership, income-share spending, stable owner-free housing and zero corporate credit/workout. There are four fixed cohorts: workers (.70), displaced_free (.10), displaced_debt (.10) and owners (.10). Owner-free housing excludes mortgages, not the displaced_debt group's separate personal loan.

For each of v108's quarter-end and December tax profiles, use the cost-funded buffer sized at the assumed 4% annual interest rate. Annual surcharges are approximately .155126 and .879762 normalized aggregate cash units respectively. These are financing scenarios, not market-rate or tax-policy estimates.

## Incidence rules and benchmark
| Rule | Workers | Displaced-free | Displaced-debt | Owners |
|---|---:|---:|---:|---:|
| Owners only | 0 | 0 | 0 | 1 |
| Per capita | .70 | .10 | .10 | .10 |
| Displacement cohorts | 0 | .50 | .50 | 0 |

Shares allocate the same total surcharge within each collection profile. The last rule taxes two fixed cohorts exposed to displacement; it is not a tax specifically on people currently unemployed or receiving benefits. Some cohort members remain employed during the transition.

A fourth case retains the external-payer benchmark from v108. Its cost is outside the four measured household cohorts; it is not a costless social benchmark. All eight cases use identical opening household, market and external-control cash. In household-tax cases the external-control reserve remains idle: it never fills a collection gap.

## Household accounting and behavior
Year zero supplies stocks only; twenty artificial flow years supply 240 months. Outside cash receipts and annual prices are frozen from the source path. Personal interest is removed from source net income and replayed explicitly between debtor and owner cohorts. Original government principal receipts are separate from income.

Monthly priority is current/outstanding personal interest, maintenance, current/outstanding surcharge, nonhousing consumption, scheduled personal principal and planned equity purchases. Personal principal reduces matching debtor and owner claims and is never treated as owner income. Debt principal shortfalls remain owed; interest on outstanding principal is explicit, without interest-on-arrears or write-off. Planned purchases can be clipped to cash; no asset liquidation or new credit is activated.

Desired consumption inherits the source's .90 share of positive spendable income, after maintenance, contractual personal interest and the monthly accrued surcharge expense. Cash-tax due dates follow the declared collection profile; expense accrues uniformly through each year. Actual consumption is then constrained by cash. This separates accrual response from payment-date liquidity and does not import an MPC from v103.

The tax is paid once into a surcharge-receipts account. This is an incidence/collection ledger, not an additional copy of v108's government cash balance. Do not sum the two raw ledgers together as one consolidated economy.

## Results
All eight declared cases collect the required surcharge on schedule to tolerance 1e-9. Totals are 3.1025 normalized units in the quarter-end cases and 17.5952 in the December cases over twenty years. The v108 receipt schedule is therefore supported by the modeled household payments in these cases; a deliberately excessive-tax test closes this gate and retains unpaid tax instead of supplying outside finance.

Percent change in **cumulative real nonhousing consumption over twenty years**, relative to the corresponding external-payer benchmark:

| Collection profile / incidence | Workers | Displaced-free | Displaced-debt | Owners |
|---|---:|---:|---:|---:|
| Quarter-end / owners only | 0.00% | 0.00% | 0.00% | -0.40% |
| Quarter-end / per capita | -0.29% | -0.50% | -0.70% | -0.04% |
| Quarter-end / displacement cohorts | 0.00% | -2.51% | -3.51% | 0.00% |
| December / owners only | 0.00% | 0.00% | 0.00% | -2.25% |
| December / per capita | -1.63% | -2.84% | -3.98% | -0.22% |
| December / displacement cohorts | 0.00% | -14.21% | -19.88% | 0.00% |

These are scenario outputs, not estimated effects, annual percentage growth rates or probabilities. Each profile has a different financing bill; comparing the two profiles is not a timing-only comparison with the same surcharge.

No declared case has a liquidity-induced shortfall relative to its newly reduced desired consumption. That does **not** mean consumption is preserved: desired consumption itself falls because the tax reduces modeled spendable income. Under the December displacement-cohort rule, the two taxed cohorts also end with zero cash and fewer shares than in the benchmark. Private principal follows the original path in these eight cases; the model does not find a changed debt-service outcome here.

## Structural limits that matter for the thesis
The common .90 rule and nonbinding consumption-cash limits mechanically produce virtually the same aggregate real consumption reduction across the three household-tax allocations within each profile: about 3.1840 quarter-end and 18.0574 December normalized real units.

Allocation changes who bears that reduction. This does not identify an optimal tax or heterogeneous MPCs. Equal absolute cuts to the two displacement cohorts create different percentage cuts because the debtor cohort starts from lower consumption. The larger percentage decline is not an independent estimate of the causal effect of debt.

The thesis therefore needs both financing feasibility and explicit incidence. Paying benefits on time can coexist with lower consumption among the people financing them. These results establish that distinction within the chosen rules; they do not establish purchasing-power preservation for all households.

## Validation and remaining gates
Eleven new tests passed alongside the previous fifty component tests. The external-payer controls recover each cohort's source annual consumption, closing cash, equity units and personal-loan balance. Tests also check identical initial cash, complete counterpart tapes, tax weights, no external backfill, explicit private claims/arrears, rejected inputs, calendar carry and exact archive reproduction. Cash-conservation residuals in the declared cases are below 6e-11 normalized units.

The high-tax stress test retains uncollected tax and marks v108's funded receipt schedule unsupported. In such a case the fiscal path must be resimulated; the audit does not assert that the original government payments remain feasible.

Outside income, benefit plans, prices, supplier output and equity purchase plans remain frozen. Realized holdings may change without feeding into future source dividends. Source fiscal payments and the external buffer lender's spending are not recomputed jointly with this household ledger. No household defaults, asset-sale responses, firm feedback or macro equilibrium are inferred.

Next, test the incidence result with differing **declared** spending responses and an explicit feedback rule for changed holdings/dividends, keeping calibration closed until comparable evidence is available. This will show which distributional conclusions depend on the common .90 assumption before wider sustainability claims. The restricted-data route remains unavailable.

Reproduce:
```
python scripts/test_household_tax_incidence_v109.py
python scripts/household_tax_incidence_v109.py --output data/processed/household_tax_incidence_v109.json
```

The artifact records source fingerprints, all annual group accounts, first-year months, every December and any tax-arrears/consumption-shortfall months. Full monthly tapes are reproducible through build().

[Group results and fingerprints](data/processed/household_tax_incidence_v109.json) · [V108 financing costs](FINANCED_FISCAL_BUFFER_V108.md) · [V107 fiscal settlement](MONTHLY_FISCAL_BRIDGE_V107.md)