Economics Pipeline Reference (Features 012–016)

Technical reference for the five economics modules that compute capital dynamics, MELT, visibility tensors, throughput position, and class transitions. These features form a dependency chain from the ValueTensor4x3 primitive (Feature 011) through to simulated class distribution evolution.

Feature 012: Capital Stock Dynamics 

Computes accumulated capital stock K via the perpetual inventory method, enabling the TRPF (tendency of the rate of profit to fall) analysis.

Depreciation Configuration 

Preset	Rate (δ)	Description
`default()`	0.07	Standard annual depreciation
`slow()`	0.05	Long-lived capital (infrastructure)
`fast()`	0.10	Short-lived capital (tech equipment)

Valid range: [0.01, 0.20].

Formulas 

Perpetual inventory method (TVT Axiom A3):

\[K_{t+1} = K_t \cdot (1 - \delta) + c_t\]

Where c_t = total_c from the ValueTensor4x3. Initial condition uses steady-state:

\[K_0 = \frac{c_0}{\delta}\]

Stock-based profit rate (TVT Section 3.6):

\[r_{\text{stock}} = \frac{\sum s_\mu}{K + \sum v_\mu}\]

Flow-based profit rate (from tensor directly):

\[r_{\text{flow}} = \frac{s}{c + v}\]

DerivedTensorMetrics 

Field	Type	Description
`capital_stock`	`float`	Accumulated K via perpetual inventory
`profit_rate_stock`	`float`	s / (K + v) — stock-based
`profit_rate_flow`	`float`	s / (c + v) — flow-based (from tensor)
`organic_composition`	`float`	c / v
`exploitation_rate`	`float`	s / v
`depreciation_rate`	`float`	δ used for this computation
`tensor`	`ValueTensor4x3`	Source tensor

Implementation: babylon.economics.capital_stock.CapitalStockCalculator

Year range: 2010–2025. Thread-safe via RLock.

Feature 013: MELT and Basket Visibility 

Computes the Monetary Expression of Labor Time (MELT), basket visibility, class position classification, and imperial rent per hour.

MELT (τ)

Formula (TVT Axiom B3):

\[\tau = \frac{\text{GDP}}{\text{employment} \times 2080}\]

Where 2080 = HOURS_PER_YEAR (40 hrs/wk × 52 wks). Units: $/labor-hour. One τ per currency zone (TVT Axiom B4).

Validation Ranges
Tier	Range	Action
Expected	$55–75/hr	Pass
Warning	$40–100/hr	Log warning
Fail	<$20 or >$200/hr	Return error

Basket Visibility (γ_basket)

Formula (TVT Axiom D3):

\[\gamma_{\text{basket}} = \frac{1} {\frac{\alpha}{\gamma_{\text{import}}} + (1 - \alpha)}\]

Where α = import share of consumption, γ_import = import visibility. Edge cases: α=0 → 1.0; α=1 → γ_import.

MVP defaults: α=0.25, γ_import=0.35 → γ_basket=0.68.

Effective MELT (TVT Axiom D4):

\[\tau_{\text{eff}} = \tau \times \gamma_{\text{basket}}\]

Imperial Rent Per Hour (Φ_hour)

Formula (TVT Axiom E3):

\[\Phi_{\text{hour}} = \frac{W}{\tau} \cdot \frac{1}{\gamma_{\text{basket}}} - 1\]

Φ_hour > 0: net extractor (labor aristocracy flow position). Φ_hour < 0: net exploited. Break-even at W = τ_eff.

Labor commanded (TVT Axiom E4):

\[L_{\text{cmd}} = \frac{W}{\tau \cdot \gamma_{\text{basket}}}\]

Class Position Classifier 

Class position is determined by wealth percentile (stock), not income (flow). Thresholds from Fed Survey of Consumer Finances:

Class	Threshold	Description
BOURGEOISIE	≥ 99th percentile	~$13M+ net worth
PETIT_BOURGEOISIE	≥ 90th percentile	~$1.88M+ net worth
LABOR_ARISTOCRACY	≥ 50th percentile	~$142K+ net worth
PROLETARIAT	< 50th percentile	Below median wealth
LUMPENPROLETARIAT	Excluded from labor	PrecarityStatus.EXCLUDED

NationalParameters 

Field	Description
`tau`	National MELT ($/labor-hour)
`alpha`	Import share of consumption
`gamma_import`	Import visibility coefficient
`gamma_basket`	Composite basket visibility
`tau_effective`	τ × γ_basket
`v_reproduction`	Labor cost of reproducing labor power
`p50_wealth_threshold`	~$142K (LA boundary)
`p90_wealth_threshold`	~$1.88M (PB boundary)
`p99_wealth_threshold`	~$13M (Bourgeoisie boundary)

Feature 014: Throughput Position 

Computes county-level throughput intensity and position relative to the national MELT, with commuter-adjusted variants.

Formulas 

Throughput intensity:

\[\tau_{\text{through}} = \frac{\text{GDP}} {\text{employment} \times 2080}\]

Throughput position (dimensionless):

\[\pi = \frac{\tau_{\text{through}}}{\tau_{\text{national}}}\]

π > 1: county produces more value per labor-hour than national average. π < 1: below average.

Commuter-adjusted residence throughput:

\[\tau_{\text{res}} = \frac{\text{GDP}} {\text{residence\_employment} \times 2080}\]

Using LODES commuter flow data to distinguish workplace vs residence employment.

Supply chain depth (employment-weighted):

\[D = \frac{\sum_{i} e_i \cdot d_i}{\sum_{i} e_i}\]

ThroughputMetrics 

Field	Description
`tau_through`	County throughput intensity ($/labor-hour)
`pi`	Position relative to national MELT
`supply_chain_depth`	Employment-weighted depth [0–5]
`data_quality`	`"high"` / `"medium"` / `"low"`

NAICS Depth Scale 

Depth	Layer	NAICS
0.0	Extraction	11 (Agriculture), 21 (Mining)
1.5	Manufacturing	31, 32, 33
2.0	Transformation	22 (Utilities), 23 (Construction)
3.0	Logistics	42, 48, 49, 56, 81
4.0	Services	44, 45, 51, 54, 61, 62, 71, 72, 92
5.0	Finance	52, 53, 55

Feature 015: Gamma Visibility Tensor 

Computes the three visibility coefficients and shadow value transfers that measure how much labor is invisible to the price system.

Gamma III (γ_III) — Reproductive Labor 

Formula (TVT Axiom I.5):

\[\gamma_{\text{III}} = \frac{L_{\text{paid care}}} {L_{\text{paid care}} + L_{\text{unpaid care}}}\]

γ_III < 1: some care labor is naturalized as unpaid (invisible). US estimate ~0.30 (70% of care work unpaid).

Fortunati exploitation rate:

\[e_F = \frac{1 - \gamma_{\text{III}}}{\gamma_{\text{III}}}\]

Ratio of invisible to visible care labor.

Data sources: ATUS (unpaid hours), QCEW (paid care sector employment).

Gamma Import (γ_import)

Formula (Emmanuel-Amin / TVT Axiom C1):

\[\gamma_{\text{import}} = \sum_i \frac{s_i}{\text{ERDI}_i}\]

Where s_i = import share from country i, ERDI = Exchange Rate Deviation Index (GDP_PPP / GDP_MER).

MVP ERDI Values (Penn World Tables 10.01)
Country	ERDI	Note
China	1.80	Second-largest import source
Mexico	1.50	NAFTA partner
Vietnam	2.50	Rising periphery source
India	2.80	Highest ERDI in top partners
Germany, Japan	1.00	Core countries (no deviation)
Rest of world	2.00	Default periphery ERDI

Shadow Value Transfers 

Phi III — reproductive shadow subsidy (TVT Axiom I.5):

\[\Phi_{\text{III}} = (1 - \gamma_{\text{III}}) \times L_{\text{unpaid}} \times \tau\]

Phi Imperial — imperial shadow subsidy (TVT Axiom I.2):

\[\Phi_{\text{imperial}} = (1 - \gamma_{\text{basket}}) \times \text{Consumption}\]

Validation Ranges
Coefficient	Expected	Warning	Fail
γ_III	[0.20, 0.40]	[0.10, 0.50]	Outside [0, 1]
γ_import	[0.40, 0.70]	[0.30, 0.80]	≤ 0
γ_basket	[0.60, 0.85]	[0.40, 0.95]	≤ 0

Feature 016: Class Dynamics Engine 

Simulates class distribution evolution through transition flows: accumulation (upward mobility), dispossession (downward mobility), precaritization, and stabilization.

Class Distribution 

Five-class distribution summing to 1.0:

Class	Typical Share	Dynamic
Bourgeoisie	1%	Fixed (structural)
Petit Bourgeoisie	9%	Fixed (structural)
Labor Aristocracy	30–50%	Dynamic: gains from accumulation, loses to dispossession
Proletariat	25–45%	Dynamic: gains from dispossession, loses to precaritization
Lumpenproletariat	10–25%	Dynamic: gains from precaritization, loses to stabilization

Transition Flow Equations 

Discrete ODE per tick:

\[\text{LA}' = \text{LA} - d \cdot \text{LA} + a \cdot \text{Prol}\]

\[\text{Prol}' = \text{Prol} + d \cdot \text{LA} - a \cdot \text{Prol} - p \cdot \text{Prol} + z \cdot \text{Lum}\]

\[\text{Lum}' = \text{Lum} + p \cdot \text{Prol} - z \cdot \text{Lum}\]

Where d = dispossession, a = accumulation, p = precaritization, z = stabilization.

Transition Rate Formulas 

Dispossession (LA → Proletariat):

\[d = 0.6 \cdot r_f + 0.3 \cdot r_b + 0.1 \cdot r_e\]

Where r_f = foreclosure rate, r_b = bankruptcy rate, r_e = eviction rate.

Accumulation (Proletariat → LA):

\[s_{\text{eff}} = s_{\text{base}} + \min\left(\frac{\Phi_h \times 2080}{W},\; \phi_{\text{cap}} \right)\]

\[A = W \cdot s_{\text{eff}}^2\]

\[a = \min\left(\frac{A}{W_{\text{threshold}}},\; 0.08\right)\]

Where W_threshold = $142K (Fed SCF p50 2022).

Savings rates (Fed SCF calibrated):

Class	Base Rate
Bourgeoisie	0.38
Petit Bourgeoisie	0.20
Labor Aristocracy	0.12
Proletariat	0.03
Lumpenproletariat	0.00

Precaritization (Proletariat → Lumpen):

\[p = u \cdot w_e + r_e \cdot (1 - w_e)\]

Where u = unemployment rate, w_e = eviction weight (default 0.5).

Stabilization (Lumpen → Proletariat):

\[z = z_0 \cdot (1 - u)\]

Where z_0 = base stabilization rate (default 0.15).

Crisis Amplification 

Phased Crisis Multipliers
Phase	Disp ×	Precari ×	Accum ×	Stab ×
NORMAL	1.0	1.0	1.0	1.0
ONSET	1.2	1.5	0.8	0.7
EARLY	1.8	2.5	0.4	0.4
DEEP	3.0	3.5	0.1	0.2
RECOVERY	1.3	1.2	0.6	0.5

Dependency Chain 

Feature 011 (ValueTensor4x3)
  ├── Feature 012 (K from total_c via perpetual inventory)
  ├── Feature 013 (τ from GDP/employment, γ_basket, Φ_hour)
  │     ├── Feature 014 (π = τ_through / τ_national)
  │     └── Feature 016 (AccumulationResult uses Φ_hour)
  └── Feature 015 (γ_III, γ_import → γ_basket, Φ_III)

All features share NoDataSentinel from babylon.economics.tensor as the universal missing-data carrier.