מסמך טכני מיומן המחקר · באנגלית, כפי שנכתב בשלב העבודה
Step 277: breakeven productivity instead of shares of cells
Why. The third referee report showed that the grid's preservation count samples a threshold coarsely. Along the productivity gain, the outcome is close to a step: either the debt cap binds and the benefit is rationed, or it does not. So "49% of cells" mostly counts cells on one side of a threshold. The informative result is the threshold itself.
Generated by scripts/breakeven_v277.py; archived in data/processed/breakeven_v277.json. Model of step 276. Illustrative; not a forecast.
Method
- Sweep. For each of the 144 distinct combinations of the other factors, the productivity gain g is
swept from 0 to 1.5 in steps of 0.025.
- Breakeven gain. g\* is the smallest gain at which both displaced cohorts keep 90% of their initial
consumption in every year.
- Government rules. Three are compared:
- benefits only: the step-271 rule, in which only the benefit is cut when the 90% cap binds; - revised: present-value equity, plus a profit levy of up to 15% of profits when the cap binds (step 276); - revised with a levy of up to 30%.
What g means in output. g is not total-factor productivity. It is the efficiency gain in a scenario that also displaces 20% of workers. Real output at year 20, relative to the no-automation control (pass-through 0.5, broad ownership, renters, revised rule):
| g | 0 | 0.1 | 0.2 | 0.25 | 0.3 | 0.4 | 0.5 | 0.75 | 1 |
|---|---|---|---|---|---|---|---|---|---|
| Output vs control | 0.63 | 0.74 | 0.81 | 0.85 | 0.89 | 1.04 | 1.22 | 1.49 | 1.74 |
At g ≈ 0.38 the automation scenario produces as much as the economy without automation. Below that, displacing 20% of workers lowers output.
Results
| Rule | Median g\* (quartiles) | Output at the median g\* | Never preserved (of 144) | Preserved at g = 0.25 | at g = 0.4 | at g = 0.5 |
|---|---|---|---|---|---|---|
| Benefits only | 0.50 (0.35–0.68) | 1.22 | 7 | 14% | 33% | 44% |
| Revised (levy 15%) | 0.33 (0.20–0.45) | 0.913 | 6 | 29% | 61% | 73% |
| Revised, levy 30% | 0.20 (0.13–0.30) | 0.81 | 5 | 56% | 76% | 81% |
"Preserved at g" counts combinations with g\* at or below g that stay preserved at every higher gain.
Median g\* by factor, revised rule:
| Factor | Values | Median g\* |
|---|---|---|
| Tax reach | 0.5 / 1 | 0.43 / 0.20 |
| Tax rate | 25% / 35% | 0.35 / 0.30 |
| Ownership | concentrated / broad | 0.39 / 0.30 |
| Pass-through | 0 / 0.5 / 1 | 0.30 / 0.33 / 0.36 |
| Tenure | renters / outright owners / fixed / reset mortgage | 0.35 / 0.34 / 0.30 / 0.35 |
Not monotone. In 15 combinations under the revised rule, preservation is lost again at higher gains. These are full pass-through with concentrated ownership. A larger gain lowers prices further, and nominal rent and mortgage payments do not fall with them (step 272).
How much tax is needed. The smallest levy cap that preserves the displaced, revised rule, by productivity gain:
| g | Median levy cap needed (quartiles) | Not possible with a levy up to 50% |
|---|---|---|
| 0.10 | 30% (20%–45%) | 86 of 144 |
| 0.25 | 17.5% (5%–29%) | 28 |
| 0.40 | 7.5% (0%–17.5%) | 12 |
What it shows
- **With benefits as the only margin, protection requires automation that raises output well above the
economy without it.** The median breakeven gain implies output about 21% higher.
- If the profit tax may rise by up to 15% of profits when the budget binds, the breakeven falls to a
gain at which output is about 9% lower than without automation (0.913 in the reference case, computed with breakeven_v277.output_ratio(0.325) and archived in data/processed/breakeven_median_output_v277.json). With 30%, about 19% lower.
- The answer to the research question is therefore conditional on two numbers: how much automation
raises output, and how far the profit tax may rise. The breakeven surface gives the trade-off directly. In the median combination, an automation that cuts output by about a quarter (g = 0.1) needs a levy cap of 30%. One that cuts it by about 15% (g = 0.25) needs 17.5%. One that leaves output roughly unchanged (g = 0.4) needs 7.5%.
- Tax reach is the strongest institutional lever. Full reach lowers the breakeven gain from 0.43 to
0.20.