# Phase 71 — reconnecting the automation thesis

**Status: illustrative coupled accounting scenarios. No estimated parameters, probabilities, causal results or calibrated fiscal forecast.**

This step returns to the thesis question: can a world with20% unemployment preserve purchasing power through productivity gains, lower prices and transfers? It links wages, prices, profits, cash taxes, benefits and government net debt. Earlier firm-data audits remain supporting measurement work; their rates are not used to calibrate this model.

## Reference and units

Annual net output/value added is normalized to100 and potential workforce to1. The stylized reference has full employment, wage compensation60 and residual profit40. These are scenario assumptions, not observed global employment or income shares. This is not an economy measured in shekels or dollars.

Wage tax is20%, initial profit tax25%, profit-base capture100%, initial government net debt60 and annual financing rate3%. Initial cash revenue is22. Existing real primary spending is20.2, leaving1.8 for interest and an initially balanced overall budget. Existing spending is retained; the full22 is not reused to finance a new benefit.

There are20 annual periods plus reference year0. Automation progress ramps linearly to1 over10 years, then stays fixed. Unemployment reaches20% by year10; no endogenous labor-supply or job-creation mechanism is estimated. The benefit covers unemployed modeled workers only. It is **not universal basic income** for all households, children or retirees.

## Equations and closure

Let progress be a, terminal unemployment u*, cumulative efficiency gain g, nominal wage gain h, price pass-through λ, and baseline labor share s=0.6:

- u = a u*; efficiency A=1+ga; wage index w=1+ha.
- Real output Q=A(1−u), relative to reference output.
- Price P=1−λs(1−w/A). Other unit costs are fixed; this is an imposed unit-cost pass-through rule, not market-clearing price formation.
- Nominal output Y=100PQ; wages W=60w(1−u); profit surplus Π=Y−W.
- Wage cash tax Rw=0.20W. Profit cash tax Rπ=τκ max(Π,0), where τ and accessible-base share κ interpolate from reference values to their stated scenario endpoints.

Profit cannot independently grow on an unrelated path: price reductions change nominal output and the residual profit base. There is one profit tax; no second automation/capital tax is applied to the same surplus. Accessible share κ is a scenario abstraction, not an estimate of evasion, foreign profit shifting or tax-law coverage. There is no delayed collection account or tax-loss carryforward. Potential profit remaining after cash tax is recorded, but its ownership, retention and distribution across households are not modeled.

The protected worker has no capital income. Reference after-tax wage is48. With a fixed annual nominal debt payment d, reference disposable purchasing capacity is48−d. Required benefit after job loss is:

**B* = P(48−d)+d.**

Thus (B*−d)/P=48−d. Deflation raises the required nominal benefit relative to a debt-free worker by d(1−P). This is a fixed-payment illustration, not a household loan-stock or amortization model. Negative disposable capacity would indicate a cash shortfall, not negative physical consumption. Employed-worker purchasing capacity is reported separately.

Existing spending is G=20.2P (constant real services). Available funds after existing spending and interest are F=Rw+Rπ−G−rD_previous.

Two alternative policy rules are simulated with their **own debt histories**:

1. **Protect:** pay B* to every unemployed worker and finance the remaining deficit through government net debt. Preserved purchasing power is true by construction; sustainability is not.
2. **Budget:** pay min(B*, max(0,F/u)) when u>0. No new borrowing is used to top up the benefit. If F is negative, existing commitments already have a deficit and debt still rises despite zero benefit. This is not a guarantee of a balanced overall budget.

Benefit cost is uB. Primary balance is cash revenue−G−uB; overall balance subtracts rD_previous; D_next=D_previous−overall balance. The reported ratio uses nominal output Y, not real output. D is a signed net liability; negative values are financial assets. The same fixed rate is assumed for assets and liabilities, which amplifies strong-case long-run surpluses and is not a financial forecast. No debt ceiling, default, endogenous risk premium, investment response, monetary response, household saving allocation or goods-market equilibrium is solved.

Year0 is a reference observation, not an additional simulated budget period. Purchasing power of an unemployed worker is undefined there because modeled unemployment is zero.

## Results from selected assumptions, year20

All transition cases reach20% unemployment. “Reference” below is a chosen transition case, not the no-automation control.

| Case | Efficiency gain over10yr | Pass-through | Terminal profit tax | Accessible profit share | Price index | Real output index | Unemployed power under budget rule | Net debt/output under protect rule |
|---|---:|---:|---:|---:|---:|---:|---:|---:|
| Reference transition | 50% | 75% | 25% | 100% | 85 | 120 | 50.61% | 132.49% |
| Strong efficiency/collection | 100% | 100% | 35% | 100% | 70 | 160 | 100% | −114.57% |
| Limited accessible base | 50% | 75% | 25% | 50% | 85 | 120 | 0% | 258.37% |
| Reference with nominal debt payment8 | 50% | 75% | 25% | 100% | 85 | 120 | 37.21% | 136.60% |
| No pass-through | 50% | 0% | 25% | 100% | 100 | 120 | 58.33% | 109.84% |

The reference transition is a counterexample to “more productivity automatically finances protection”: real output increases20%, but fully protecting job losers raises net debt/output from60% to132.49%. Restricting benefits to available funds retains only50.61% of their reference purchasing capacity. The same real-output path with a fixed nominal debt payment leaves37.21% of that household's lower reference disposable capacity under the budget rule.

The strong case requires a doubling of labor efficiency over10 years and a35% tax on a fully accessible modeled profit base. Its success is conditional on those imposed assumptions. The large negative net-debt endpoint depends on sustained surpluses and fixed returns on accumulated assets; it is not a plausible central forecast established by this work. A no-automation control retains output100, price100, revenue22 and net debt60 throughout.

Pass-through can create a fiscal tradeoff here: stronger price reductions reduce the benefit required for real protection but also reduce nominal profit and tax receipts. The net result depends on the imposed rules. This is not evidence that price reductions should be prevented or that a particular tax rate is optimal.

## Sensitivity grid

The deterministic grid crosses efficiency gains {0,25,50,75,100%}, pass-through {0,50,100%}, terminal profit tax {15,25,35%}, accessible share {50,75,100%} and fixed debt payment {0,8}. All other inputs are held at the documented defaults. There are270 selected combinations. Forty fund the required benefit without an overall deficit in every one of the20 simulated annual periods under the protect path. **40/270 is a grid count, not a probability, empirical success rate or confidence level.** Grid outcomes depend on selected ranges and the constant-real-spending closure.

A conditional required tax rate is also recorded by solving the current year's budget with its existing debt and profit base held fixed. It is not an optimized or behaviorally feasible tax recommendation, and cannot establish an all-years feasible policy on its own.

## Reproduce and next research question

Run `python scripts/coupled_thesis_v71.py` to rebuild the public JSON (no network or empirical data required). Run `python -m unittest discover -s calibration -p 'test_*v[67]*.py'`. Tests check production-income identities, government stock-flow consistency, the reference control, benefit targeting, fiscal constraints, deflation with nominal payments and input validation. The browser displays precomputed paths from this same JSON; there is no second browser implementation of the equations.

Use `/thesis.html#research=scenarios` to select six cases and compare policy rules. All outputs remain hypothetical. They establish conditional accounting feasibility and counterexamples, not a causal macro theory or the probability of20% global unemployment. The next substantive extension should examine heterogeneous households and capital ownership, with explicit treatment of rents/housing and fixed nominal liabilities; then identify which assumptions need empirical bounds. Fiscal calibration remains unapproved.