# Step 273: output constrained by demand

**Why.** In every earlier specification, investment was whatever output was not consumed or bought by
the government. Saving always became capital, and output never fell short of capacity. That was the
model's largest structural limitation. Here firms plan their investment, and output is the smaller of
capacity and demand.

Generated by `scripts/demand_v273.py`, with the model in `scripts/closure_model_v273.py` (a copy of
step 268; archived files untouched). Archived in `data/processed/demand_v273.json`. All 432 distinct
cases, central specification of step 271 (debt cap 90%, surpluses returned, risk premium, step-266
firms). Illustrative; not a forecast.

## The demand closure

- **Planned investment.** Firms plan P × (depreciation + g + ι) × K:
  - g is the growth of capacity. In a variant it is last year's growth of realized output, an
    accelerator on demand.
  - ι is an autonomous share, calibrated at 0.034 so that the status-quo control starts at full use of
    capacity. Without it the base economy saves more than firms want to invest, and the control itself
    runs at about 91% of capacity.
- **Demand** is consumption + government purchases + planned investment.
- **Enough demand:** output is capacity, and investment takes what is left, as before.
- **Too little demand:** output is demand. The shortfall adds nothing to capital, and firms bear it as
  a loss of cash, which their retention rule then passes on to dividends. The profit tax on the
  shortfall is refunded to firms the next year, which lowers revenue then.
- **What still follows the scenario:** employment and the price level. Step 274 adds an employment
  channel.

With demand switched off, the model reproduces step 268 exactly (tested). Money is conserved in every
run.

## Results

| Variant | Preserved (of 432) | Fiscal crises | Mean use of capacity: median / 10th pct | Median gap to control, displaced |
|---|---:|---:|---|---|
| Central, no demand constraint (step 271) | 211 | 110 | 100% / 100% | −20% / −21% |
| **Demand, calibrated investment** | **210** | 110 | 100% / 99% | −20% / −21% |
| Demand, accelerator on realized output | 212 | 110 | 100% / 98% | −19% / −19% |
| Demand, autonomous investment 0.05 | 211 | 110 | 100% / 100% | −20% / −21% |
| **Demand, investment slump with displacement** | **174 (40%)** | 190 | 95% / 91% | −39% / −50% |
| Slump, with the demand accelerator | 167 | 187 | 95% / 91% | −41% / −50% |
| Demand, no autonomous investment (uncalibrated) | 156 | 208 | 94% / 90% | −36% / −50% |
| Demand, symmetric fiscal rule | 244 | 0 | 100% / 99% | −9% / −10% |

"Fiscal crises" are cases in which peak net debt exceeds 95% of output. In the slump, autonomous net
investment falls to zero as displacement reaches 20%. The control, which has no displacement, keeps it.

**What it shows.**

- **"Saving becomes investment" was not driving the results.** When firms keep investing at the rate
  that held the economy at full use before automation, demand rarely falls short. Use of capacity stays
  at 99% or more in nine cases out of ten, and preservation is unchanged (210 against 211).
- **Investment demand is what matters.** If firms invest less as displacement rises, output falls about
  5% below capacity on average and up to 9% in a tenth of cases. Profits and tax revenue fall with it.
  Fiscal crises rise from 110 to 190, and preservation falls from 49% to 40%. The displaced end 39%–50%
  below the control at the median.
- **The ordering of factors holds.** Productivity, tax reach, tax rate and broad ownership still help.
  Pass-through still hurts. With a 25% productivity gain, no case is preserved in the slump.
- **Demand does not rescue the hoarding problem, and does not need to.** Under the central rule
  surpluses are returned, so a hoarded surplus no longer drains demand.

## Limits

- **Employment and prices** do not respond to the shortfall, so the demand effect here runs only
  through profits, dividends and taxes. Step 274 lets employment respond.
- **The investment rule is a rule,** not an optimisation. The calibration assumes the base economy
  starts at full use.
- **No inflation or monetary policy** responds to the shortfall.