Marxian Value Tensor

Overview 

The ValueTensor4x3 is the core data structure for Marxian economic analysis in Babylon. It represents the 4x3 reproduction schema: 4 departments × 3 value categories (constant capital, variable capital, surplus value).

Classes 

DepartmentRow 

class babylon.economics.tensor.DepartmentRow[source]

Value composition for a single Marxian department.

Represents the three-fold decomposition of commodity value:

c (constant capital): Value transferred from machinery/materials
v (variable capital): Value paid to workers as wages
s (surplus value): Unpaid labor appropriated by capital

c: Currency: Constant capital (dead labor: machinery, raw materials). Must be non-negative.

v: Currency: Variable capital (living labor: wages). Must be non-negative.

s: Currency: Surplus value (unpaid labor). Must be non-negative.

total_value: Currency: Computed property: c + v + s

organic_composition: float

Computed property: c / v

Marx’s measure of capital intensity. Higher values indicate more mechanization. Returns float('inf') if v = 0.

exploitation_rate: float

Computed property: s / v

The ratio of unpaid labor to paid labor. Returns float('inf') if v = 0.

Example:

>>> from babylon.economics.tensor import DepartmentRow
>>> row = DepartmentRow(c=100.0, v=50.0, s=75.0)
>>> row.total_value
225.0
>>> row.organic_composition  # c/v = 100/50
2.0
>>> row.exploitation_rate  # s/v = 75/50
1.5

ValueTensor4x3 

class babylon.economics.tensor.ValueTensor4x3[source]

4x3 Marxian value tensor for a county-year.

Represents the complete reproduction schema with four departments, each decomposed into constant capital (c), variable capital (v), and surplus value (s).

Fields:

fips_code: str: 5-digit FIPS county code (e.g., “26163” for Wayne County, MI). Validated to be exactly 5 numeric digits.

year: int: Data year. Must be >= 1900.

dept_I: DepartmentRow: Department I: Means of Production (capital goods). Output consumed productively by capital.

dept_IIa: DepartmentRow: Department IIa: Necessary Consumption (wage goods). Reproduces labor power.

dept_IIb: DepartmentRow: Department IIb: Luxury Consumption (bourgeois goods). Absorbs surplus value without expanding reproduction.

dept_III: DepartmentRow: Department III: Social Reproduction (care work). Maintains/creates workers outside commodity exchange.

naics_granularity: Probability: Data quality metric: fraction of wages with 6-digit NAICS mapping. Range: [0.0, 1.0].

excluded_wages: Currency: Wages excluded from allocation (e.g., government NAICS 92).

visibility_g33: float

Added in Sprint 2.1

Visibility scalar for Department III reproductive labor. Controls what fraction of care work is visible to the price system:

1.0: Fully monetized (backward compatible default)
0.0: Fully unwaged (all shadow labor)
0.5: Half visible, half shadow

Range: [0.0, 1.0]. Default: 1.0.

Based on Fortunati’s The Arcane of Reproduction (1981).

Computed Properties:

total_value: Currency: Sum of all department total_values.

total_v: Currency: Total variable capital (wages) across all departments.

total_s: Currency

Added in Sprint 2.1

Total surplus value across all departments.

profit_rate: float: Economy-wide return on capital: total_s / (total_c + total_v). Returns float('inf') if denominator is zero.

monetized_value: Currency

Added in Sprint 2.1

Total value visible to the price system. Includes full value of Depts I, IIa, IIb, but only the visible fraction of Dept III.

Formula: Σ dept.total + dept_III.total × g₃₃

monetized_v: Currency

Added in Sprint 2.1

Wages actually paid. Only includes the visible fraction of Dept III.

Formula: v_I + v_IIa + v_IIb + (v_III × g₃₃)

shadow_subsidy: Currency

Added in Sprint 2.1

Unpaid reproductive labor appropriated as surplus.

Formula: v_III × (1 - g₃₃)

In Fortunati’s framework, shadow labor is appropriated surplus value, not merely “unpaid costs”.

exploitation_rate_fortunati: float

Added in Sprint 2.1

Expanded exploitation rate including shadow labor as appropriated surplus.

Formula: e' = (total_s + shadow_subsidy) / monetized_v

Returns float('inf') when monetized_v = 0 (pure extraction).

See Reproductive Labor for theoretical context.

Example:

>>> from babylon.economics.tensor import DepartmentRow, ValueTensor4x3
>>> tensor = ValueTensor4x3(
...     fips_code="26163",
...     year=2022,
...     dept_I=DepartmentRow(c=300.0, v=100.0, s=200.0),
...     dept_IIa=DepartmentRow(c=150.0, v=100.0, s=100.0),
...     dept_IIb=DepartmentRow(c=250.0, v=100.0, s=300.0),
...     dept_III=DepartmentRow(c=50.0, v=100.0, s=70.0),
...     naics_granularity=0.85,
...     excluded_wages=50000.0,
...     visibility_g33=0.5,
... )
>>> tensor.profit_rate
0.5826086956521739
>>> tensor.shadow_subsidy  # 100 * (1 - 0.5)
50.0
>>> tensor.exploitation_rate_fortunati
1.9428571428571428

The Four Departments 

Marxian Departments
Dept	Name	Purpose	Examples
I	Means of Production	Output consumed productively by capital	Mining, Industrial Machinery, Semiconductors
IIa	Necessary Consumption	Wage goods for proletariat reproduction	Grocery Stores, Fast Food, Basic Healthcare
IIb	Luxury Consumption	Surplus value sink, bourgeois consumption	Jewelry Stores, Fine Dining, Golf Courses
III	Social Reproduction	Produces labor power itself	Child Care, Private Households, K-12 Schools

Department III and Shadow Labor 

Department III is unique in containing both paid care work (visible to markets) and unpaid domestic labor (invisible shadow subsidy). The visibility scalar g₃₃ controls this split.

Key insight from proletarian feminist theory: shadow labor is necessary for capital accumulation but invisible to economic measurement.

The Infinity Case 

When monetized_v = 0, the Fortunati exploitation rate returns float('inf').

This is not an edge case to be sanitized. It represents a qualitative transformation from exploitation (wage relation) to expropriation (pure extraction).

Historical conditions of infinite exploitation include:

Chattel slavery
Fully unwaged domestic labor
Prison labor
Colonial extraction

See Reproductive Labor for full theoretical discussion.