Stage 113 — Purchasing-power sensitivity frontiers

Main result

Preserving spending relative to a declining control is not preserving its initial level. In the external-financing control, the minimum annual consumption of the two displaced cohorts is respectively 64.12% and 50.67% of control year 1. No tested tax case preserves at least 90% of that year-1 anchor in every year for both cohorts.

This does not prove that automation necessarily reduces purchasing power. It is a conditional result for the frozen source trajectory, housing tenure and financing experiment inherited from stages 108–110.

Declared design

Before execution, the script specifies common q values 0, 0.05, …, 1; three household tax allocations; quarter-end or December collection; and floors 90%, 95%, 97.5%, 99%. There are 126 household-tax cases plus 42 matched external-financing controls.

Both displaced cohorts must meet a floor. Three metrics remain separate:

1. Total twenty-year real consumption divided by total matched-control consumption.
2. Minimum of the twenty annual consumption ratios against the same year's matched control.
3. Minimum annual consumption divided by matched-control year-1 consumption.

The year-1 anchor is not a pre-automation baseline. The cumulative metric is an undiscounted sum, not welfare. Floors are declared research thresholds, not standards of living.

Each candidate must also pass the inherited surcharge receipt-schedule gate. This gate checks financing receipts needed by stage 108, not full government or macroeconomic sustainability. Unsupported cases remain in the archive.

Discrete frontier at 99% of matched control

Ranges summarize tested points spaced by 0.05 only. They are not continuous break-even estimates or calibrated parameter bounds. The JSON includes every passing point; no interpolation or monotonicity assumption is used.

For December/displacement-cohort taxation, q ≤ 0.70 fails the receipt schedule (15 cases). Higher tested q passes that gate, but none passes even the 90% matched-control floor for both cohorts. Thus this cell combines funding failure at some assumptions and spending failure at others; it is not a single uniform mechanism.

Across all 126 cases, 111 pass the receipt gate. Taxation of owners only preserves displaced-cohort spending relative to the control under this prototype's assumptions; that does not make it welfare-optimal, empirically validated, or sufficient to preserve initial purchasing power.

Reproduction and validation

Run:

```sh python scripts/purchasing_power_frontier_v113.py --output data/processed/purchasing_power_frontier_v113.json python scripts/test_purchasing_power_frontier_v113.py

`

Six new tests cover a temporary loss hidden by cumulative totals, mandatory funding exclusion, both-cohort acceptance, grid coverage and cash identity, nested floors and archive reproduction. Existing research, web and frontend CI remain required.

Structured results retain annual spending, ratios, funding gaps, liquidity shortfall counts, controls, 72 frontier summaries and source hashes. The stage-110 simulator is unchanged; the new script imports it. No estimated coefficients were added.

Limits and next research step

Common q alone does not represent group heterogeneity. Prices, external income and dividends follow the fixed source path; there is no new macro feedback, labor-market estimate or empirical calibration. Reported ratios are cohort aggregates with fixed masses, not population deciles.

The next priority is to decompose the declining control: income and transfers, prices, debt service, maintenance and consumption. Explain why the control itself misses the year-1 floor before changing policy parameters or extending the frontier to heterogeneous q. That decomposition directly addresses the thesis mechanism rather than treating a relative comparison as proof of preservation.