# Stage 115 — Resources required for declared consumption floors

## Result

Closing the baseline consumption gap requires a material resource flow. At the inherited spending rule, the peak static nominal-income requirement for the two displaced cohorts is **2.21%, 2.55% or 2.90% of annual model output**, depending on the floor.

| Floor relative to each cohort's control year 1 | First gap year | Years with any gap, out of 20 | Peak income requirement / output | Requirement / existing benefits in peak year |
| --- | ---: | ---: | ---: | ---: |
| 90% | 6 | 15 | 2.21% | 54.46% |
| 95% | 4 | 17 | 2.55% | 62.98% |
| 100% | 3 | 18 | 2.90% | 71.51% |

All three output-share peaks occur in year 10. The last column is an incremental requirement divided by existing source-model benefits, not an already available funding source. It does not mean total benefits are that percentage.

## What is being measured

This stage retains the stage-114 external-financing control and each cohort's own year-1 real nonhousing consumption as the reference. It is not a pre-automation reference, a minimum living standard, or an empirical welfare criterion. Results concern the two fixed cohorts together, not the entire population receiving a universal payment.

For cohort g and year t, with baseline real consumption C_gt, year-1 reference C_g1, declared floor f and source price P_t:

- Real consumption gap: G_gt = max(0, f C_g1 − C_gt).
- Direct nominal consumption cost: D_gt = P_t G_gt.
- Static extra nominal-income requirement: R_gt = D_gt / 0.90.

D is the nominal value of missing consumption. R is larger because the inherited average income-spending rule allocates 90% of incremental spendable income to desired consumption at the fixed state. The rule is not an estimated MPC. Both requirements are cohort aggregates in model units; neither is a currency amount or an executed transfer.

The algebraic inversion holds prices, other income, maintenance, debt and the baseline cash constraint fixed. The baseline has no cash-constrained months in these cohorts. It does not establish how a new transfer would change debt repayment, asset accumulation, interest income or later spending.

## Scale across the twenty-year window

| Floor | Sum of direct nominal consumption costs | Sum of static nominal-income requirements |
| --- | ---: | ---: |
| 90% | 24.3012 | 27.0014 |
| 95% | 29.1928 | 32.4364 |
| 100% | 34.5295 | 38.3661 |

These are undiscounted sums of nominal model units, not present values or annual budget amounts. The annual output shares in the first table are the clearer scale comparison.

The archive retains the full annual path, separate cohort gaps, per-cohort-member real gaps and denominators. Conversion from real to nominal is performed year by year, before summation.

## What remains unproven

Funding is **not verified**, and supplemental transfers are **not simulated**. A gap cannot be closed by writing a payment into household income without its payer. Nor can existing benefits, bond redemption or treasury cash automatically be counted as uncommitted funding. Tax incidence can reduce other households' spending and affect collectability.

The next step is a separate funded monthly experiment: collect an explicit levy from an identified household payer, pay targeted supplements, record both sides of every flow, rerun spending and private debt service, and test whether annual floors and payment schedules still hold. Keep a matched no-supplement baseline and all failed cases. This stage's static schedule can be a declared starting proposal, not a guaranteed solution.

## Validation and reproduction

```sh
python scripts/consumption_floor_gap_v115.py --output data/processed/consumption_floor_gap_v115.json
python scripts/test_consumption_floor_gap_v115.py
```

Six new tests check units and income-rule inversion, zero gaps and price scaling, invalid inputs, aggregation and nested floors, explicit unfunded status and archive reproduction. The source baseline was checked against main before publication. Repository CI covers this script alongside prior research, web and frontend tests.

[Structured requirements](data/processed/consumption_floor_gap_v115.json) include source hashes and all annual calculations. No original source equations, spending parameters or calibrated coefficients were changed.