{% extends "base.html" %} {% block title %}About Markov Economics - Marx, Piketty, and Wealth Inequality Theory{% endblock %} {% block meta_description %}Learn about the economic theory behind the Markov chain simulation. Understand Marx's M-C-M' model and Piketty's r > g inequality principle.{% endblock %} {% block og_title %}About Markov Economics - Marx, Piketty, and Wealth Inequality Theory{% endblock %} {% block og_description %}Learn about the economic theory behind the Markov chain simulation. Understand Marx's M-C-M' model and Piketty's r > g inequality principle.{% endblock %} {% block twitter_title %}About Markov Economics - Marx, Piketty, and Wealth Inequality Theory{% endblock %} {% block twitter_description %}Learn about the economic theory behind the Markov chain simulation. Understand Marx's M-C-M' model and Piketty's r > g inequality principle.{% endblock %} {% block content %}

๐ŸŽฏ About Markov Economics

Understanding how capitalism "eats the world" through Markov chain analysis

๐Ÿ“š Theoretical Foundation

Marx's Economic Cycles

Karl Marx identified two fundamental economic circulation patterns:

M-C-M' (Capitalist Circuit)

Money โ†’ Commodities โ†’ More Money

Capital is invested in production to generate surplus value. The goal is accumulation - turning M into M' where M' > M.
C-M-C (Consumer Circuit)

Commodities โ†’ Money โ†’ Commodities

Goods are sold to acquire money to purchase other goods. The goal is consumption and use-value satisfaction.
Piketty's Inequality Principle

Thomas Piketty demonstrated that wealth inequality increases when:

r > g

Capital Return Rate > Economic Growth Rate

When capital generates returns faster than the overall economy grows, wealth concentrates among capital owners, leading to increasing inequality.
Key Parameters:
  • r: Rate of return on capital (stocks, real estate, business)
  • g: Economic growth rate (GDP growth)

โš™๏ธ Markov Chain Implementation

This simulation models economic behavior as Markov chains with state-dependent transition probabilities:

Capitalist Chain States
Money (M)
Initial capital seeking investment opportunities
Commodities (C)
Capital invested in production/goods
Enhanced Money (M')
Capital with accumulated returns
Transition Probability Matrix:
M โ†’ C: r (capital rate)
C โ†’ M': 1 (always)
M' โ†’ M: 1 (reinvestment)
Consumer Chain States
Commodities (C)
Goods available for consumption
Money (M)
Liquid currency from sales
New Commodities (C')
Purchased goods for consumption
Transition Probability Matrix:
C โ†’ M: g (growth rate)
M โ†’ C': 1 (always)
C' โ†’ C: 1 (consumption cycle)

๐Ÿ”ฌ Simulation Mechanics

How the Simulation Works
  1. Agent Initialization: Each economic agent starts with equal capital and consumption capacity
  2. Dual Chain Operation: Every agent runs both capitalist (M-C-M') and consumer (C-M-C) chains simultaneously
  3. Wealth Accumulation: Capitalist chains multiply wealth by (1 + r) on each complete cycle
  4. Consumption Growth: Consumer chains grow by (1 + g) on each complete cycle
  5. Inequality Emergence: When r > g, capital wealth grows faster than consumption, concentrating among fewer agents
Key Metrics
Gini Coefficient
Measures inequality (0 = perfect equality, 1 = perfect inequality)
Top 10% Share
Percentage of total wealth held by richest 10%
Capital Share
Proportion of wealth from capital vs consumption

๐Ÿงช Experimental Parameters

Try These Scenarios
Scenario 1: Stable Economy (r โ‰ˆ g)
  • Capital Rate: 3%
  • Growth Rate: 3%
  • Expected: Moderate inequality growth
Scenario 2: Modern Capitalism (r > g)
  • Capital Rate: 5%
  • Growth Rate: 2%
  • Expected: Increasing inequality
Scenario 3: Extreme Inequality (r >> g)
  • Capital Rate: 8%
  • Growth Rate: 1%
  • Expected: Rapid wealth concentration
Historical Context

Real-world examples of r vs g:

Period r (Capital) g (Growth) Inequality
Gilded Age (1870-1914) 4-5% 1-1.5% Very High
Post-War Era (1950-1980) 2-3% 3-4% Decreasing
Modern Era (1980-2020) 4-6% 1-2% Increasing

โšก Technical Implementation

Technology Stack
  • Backend: Python Flask with SocketIO
  • Modeling: NumPy for matrix operations
  • Visualization: Chart.js for real-time charts
  • Frontend: Bootstrap 5 with responsive design
  • Real-time: WebSocket connections for live updates
Performance Characteristics
  • Scalability: Up to 10,000 agents
  • Speed: Real-time visualization of state transitions
  • Accuracy: Precise Markov chain calculations
  • Export: JSON and CSV data export
๐Ÿš€ Start Your Simulation
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