# Phase 73 — saving, asset sales and valuation sensitivity

**Rule-based financial experiments, not calibrated household optimization or a general-equilibrium growth model.** This step varies the closures that previously fixed household wealth outcomes. It does not identify actual deciles or estimate investment returns.

## What changes from phase72

The four cohort masses, initial productive-equity ownership alternatives and phase71 production/tax path are retained. Equity positions can now change through saving and sales, cash buffers can be spent, and borrowers can voluntarily repay principal. The fiscal experiment uses budget-limited benefits only, to isolate saving and valuation assumptions. Phase72's full-protection scenarios remain separate.

Government bonds are no longer a forced signed position that can make the financial cohort borrow when government net debt becomes negative. Surplus first redeems outstanding gross bonds at par, then accumulates zero-return Treasury cash. Interest is paid only on remaining gross bonds. Existing spending and debt service are retained before benefits. If existing commitments cannot be financed from current revenue and Treasury cash, the path stops and is marked incomplete; it is not assumed to borrow from an invisible financier.

The Treasury measure excludes monetary-base liabilities; it is not a consolidated public-sector balance sheet. Initial cash50 is held by households20 and firms30, with Treasury cash0. This fixed monetary base has an outside issuer and is conserved within the modeled holders. Household wealth now includes explicit cash, so raw wealth levels must not be compared directly with phase72 as if initial endowments were identical.

## Two behavioral rules, both hypothetical

1. **Income share:** attempt to consume90% of current income after contractual loan interest.
2. **Reference smoothing:** attempt to consume90% of the group's initial real disposable income, maintaining this real target through the price path.

The initial reference differs across the two initial ownership systems. A100 consumption index refers to each group's own initial consumption target, not equal living standards.

Cash buffer targets are three months of desired consumption. Cash above consumption and this buffer is invested; the indebted cohort first uses50% of that surplus to repay principal. Both percentages are assumptions, not estimated propensities. Initial household cash is20 per normalized person in all groups, independent of ownership; the initial target buffers may therefore require adjustment.

Contractual private interest has priority. A household can draw cash and liquidate existing equity to meet interest and consumption needs. Interest actually paid is income to the lender; principal repayments and bond redemptions are asset transactions, not income. Unpaid interest capitalizes into the private loan and the lender's par-value claim. No credit-loss, bankruptcy, refinancing or recovery model is supplied.

If resources plus the value of all existing equity cannot fund desired consumption, consumption is reduced and the shortfall recorded. A negative income-after-contractual-interest index is a liquidity gap, not negative consumption. The experiments do not borrow new private principal to preserve a consumption target.

## Four quoted-price rules

The initial equity unit price is200 and initial outstanding units total1. Dividends are the phase71 residual profit after cash profit tax, allocated to beginning-of-period shareholders. Capital gains do not enter current income or fiscal benefit calculations.

- **Constant real unit price:** q=200P.
- **Fixed nominal unit price:** q=200.
- **Profit multiple:** q=(200/30) × current total distributed profit / beginning equity units. Thirty is the reference distributed profit. New issuance can dilute future per-unit dividends and quotes.
- **Drawdown:** q=200P(1−0.5a), where a ramps from0 to1 over10 years. This is an imposed50% fall in the real unit price, not a probability or forecast.

Quotes are imposed; they are not obtained from rational expectations, an endogenous risk premium or household optimal portfolio choice. Rules invest surplus even when the quoted-price mapping later produces disappointing returns. The profit-multiple rule is therefore a valuation sensitivity experiment, not an investment recommendation.

## Who buys assets? Explicit residual corporate financing

All orders clear at the declared quote. Cohort purchases can absorb other cohorts' sales. Net purchases beyond secondary sales are newly issued equity; net sales beyond purchases are corporate equity redemption. No actor can sell more units than it owns. Corporate redemption/issuance has cash and real-capital constraints; exhausted capacity stops the path.

For each annual period after reference year0:

- Net investment I = nominal output Y − household consumption C − government goods G.
- Net equity cash E is the sum of cohort equity purchases minus sales.
- Corporate cash changes by E−I.
- Real capital changes by I/P. Negative I is disinvestment under an assumed common output/investment good; capital must remain nonnegative.
- Total household cash + corporate cash + Treasury cash remains at its initial50.

Thus cash hoarding has a corporate cash counterpart, investment has a financing counterpart, and an asset sale is never free income. Initial real capital is200. Equity market valuation and physical/book capital need not coincide under the quoted-price rules.

This closure assumes the firm sector accepts residual investment/disinvestment. Output and employment remain on the phase71 imposed path and **do not respond to the new capital stock or consumption**. Consequently the experiment checks financial/resource identities and distributional sensitivity, not expected returns, optimal investment demand, a production function with endogenous capital or a solved economic equilibrium. Passing the identities does not validate this absorption assumption.

A separate stress test with stronger output growth exhausts corporate liquidity under the finite monetary base and Treasury accumulation rule. The model flags that constraint instead of extending an unfunded path. All16 displayed reference-transition experiments and their16 matched controls complete20 years under their stated inputs; this is not a universal feasibility result.

## Matched controls are necessary

Saving can build wealth even without automation. Each ownership/saving/valuation combination is therefore also run with unemployment and efficiency changes set to zero, while retaining the same financial behavior and price mapping. The drawdown remains a time-based price stress in the control; it is not silently removed.

The exported year20 wealth difference is transition wealth minus this matched control, only when both paths complete. It is a model-conditioned comparison, not an empirically identified causal effect. Raw wealth growth since year0 cannot be attributed wholly to automation. The control's economic and financial assumptions are part of the comparison.

## Selected results: concentrated initial equity, year20

All examples here use the phase71 reference transition:20% unemployment,50% efficiency gain,75% price pass-through,25% terminal profit tax and full modeled base access. This is one economic parameterization, not a broad empirical robustness claim.

With the income-share rule:

| Valuation | Displaced debt-free consumption index | Displaced indebted index | Financial group's real wealth change since reference |
|---|---:|---:|---:|
| Constant real unit price | 69.07 | 56.52 | +1,046.17 |
| Fixed nominal unit price | 68.15 | 55.71 | +1,428.40 |
| Profit multiple | 68.15 | 55.64 | +596.86 |
| Real unit-price drawdown | 72.44 | 59.55 | −83.80 |

Consumption indices are relative to each group's initial90%-of-income consumption, not income indices from phase72. In the constant-real-price example, workers' real wealth increases130.56 per person; their share of productive equity reaches23.91%. The financial group's equity share falls from100% to72.88%. This demonstrates that zero wealth accumulation among workers in phase72 was a consumption/financing closure, not an invariant finding.

The same example's financial-group wealth difference versus the matched no-transition control is+397.54, substantially below its raw+1,046.17 increase. With the drawdown, raw wealth falls83.80 even though its consumption/income index rises; its matched-control difference is positive because the control fares worse. Income, consumption, absolute wealth changes and counterfactual differences answer different questions.

Reference smoothing can sustain consumption temporarily through buffers and sales, but it can also deplete productive claims and subsequent dividend income. For example, broad initial equity with constant-real unit pricing ends with displaced consumption indices34.51 and25.26 under smoothing, versus82.76 and75.93 under the income-share rule. This does not prove smoothing is irrational or broad ownership harmful: initial income targets differ across ownership systems and behavior, saving, resale and investment rules are imposed. It shows that broad initial ownership alone does not guarantee long-run protection under every chosen consumption strategy.

## Interpretation for the thesis

Access to capital and freedom from nominal obligations can matter, but their consequences depend on saving behavior, asset prices, credit service and public financing. An initially capital-rich group need not gain absolute wealth when asset valuations fall. Workers can acquire capital when saving and issuance are allowed. These are conditional mechanism results; the model does not yet establish actual winners, an observed top decile or the social desirability/feasibility of a redistribution policy.

## Reproduce and inspect

`python scripts/saving_asset_sensitivity_v73.py` rebuilds the compact public JSON:16 transition experiments, matched-control summaries and year20 differences. Group row arrays are described by `group_columns`; stock and flow units are annual normalized values. `python -m unittest discover -s calibration -p 'test_*v[67]*.py'` checks money, investment, equity, credit and fiscal identities, saving/acquisition, sales versus income, matched controls and infeasible-path handling. Year0 is a reference observation, not an additional settled annual flow.

The phase73 section appears first in `/thesis.html#research=scenarios`. The next extension should test investment/output feedback and credit losses or housing before using these paths as long-run welfare predictions. All parameters remain assumptions; fiscal calibration remains unapproved.