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Mr.Keynes and the...Complexity! A suggested model for the General Theory

This paper proposes a mathematical model of J.M. Keynes' *The General Theory* that strictly adheres to the original text to demonstrate how liquidity preference, the marginal efficiency of capital, and the marginal propensity to consume collectively determine aggregate income and employment.

Original authors: Alessio Emanuele Biondo

Published 2026-08-31

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Alessio Emanuele Biondo

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Economics often tries to understand the world by imagining a perfect machine where every part fits together perfectly at the same moment. In this view, if people want to buy more, prices rise, and everyone finds work; if they want to save more, interest rates drop, and investment flows in. It is a tidy picture of balance, but it struggles to explain why unemployment can persist for years even when people are willing to work and businesses are willing to sell. For decades, a different perspective has argued that the economy is not a machine that settles into place, but a sequence of events where timing and uncertainty matter deeply. This is the core of the work of John Maynard Keynes, who suggested that our decisions about money, spending, and investing happen one after another, not all at once, and that these choices are driven by how we feel about the future. When we do not know what will happen tomorrow, we might hold onto our cash instead of spending it, which can cause the whole system to slow down. Understanding this sequence is crucial because it changes how we see recessions and why simple fixes often fail to bring jobs back.

A new study by Alessio Emanuele Biondo attempts to rebuild Keynes's famous theory from the ground up, not just as a set of ideas, but as a working computer model that mimics how real people and businesses interact over time. The researcher created a digital society populated by thousands of individuals who act as workers and business owners, each making their own choices based on their own hopes and fears. Unlike older models that assume everyone acts simultaneously to reach a perfect balance, this model forces the participants to move in a specific order. First, business owners decide what they hope to sell in the future. Then, they decide whether to hire workers and buy equipment based on those hopes and the current cost of borrowing money. Only after production happens and wages are paid do the workers decide how much of their new income to spend, how much to keep as cash, and how much to lend out. This step-by-step process is designed to capture the "complexity" of a real economy, where one person's decision immediately changes the options available to the next person.

The results of these computer simulations reveal that the economy is far more fragile and sensitive to mood than the old machine-like models suggest. The study shows that the willingness of business owners to take risks, a feeling Keynes called "animal spirits," is a powerful engine for growth. When these spirits are high, businesses expect to sell more, they hire more workers, and the entire economy expands. However, this expansion depends entirely on a chain reaction. If the businesses that make machinery are optimistic but the businesses that make consumer goods are pessimistic, the machinery sits unused, and the workers remain unemployed. The model demonstrates that optimism in just one part of the economy is not enough; the different sectors must be in sync for the system to work. It is similar to a relay race where the first runner must successfully pass the baton to the second; if the second runner is not ready to receive it, the race stops, regardless of how fast the first runner was.

A key finding of the research is the role of money and interest rates in stopping this chain reaction before it even begins. The model shows that business owners will only invest if they expect a return that is higher than both the interest rate they would have to pay to borrow money and their own personal desire to keep cash in hand because they are worried about the future. This creates a "financial threshold." If the interest rate is too high, or if people are too nervous and want to hoard their cash, the threshold becomes too high for many businesses to cross. In a world where all businesses are exactly the same, the model shows that crossing this threshold is a sudden event: either everyone invests and everyone works, or the threshold is crossed and almost everyone stops investing at once, leading to a sharp spike in unemployment.

However, the study adds a layer of realism by introducing differences between the businesses. In the real world, not all companies are identical; some have better technology, some have lower costs, and some are more confident than others. When the model includes these differences, the sudden stop disappears. Instead, as the financial threshold rises, businesses begin to drop out one by one. The most efficient or confident firms keep investing, while the others stop, leading to a gradual increase in unemployment rather than a sudden collapse. This suggests that the economy does not crash all at once but erodes slowly as conditions worsen. The research confirms that money is not just a neutral tool for counting value; it is a fundamental part of the decision-making process that determines whether production happens at all. By showing how individual fears and hopes, filtered through the cost of money, can ripple through the entire system, the study provides a clearer picture of why economies get stuck in unemployment and why the timing of decisions matters more than the final balance sheet.

Technical Summary: Mr. Keynes and the...Complexity! A suggested model for the General Theory

Problem and Motivation
The paper addresses the challenge of formally reconstructing J.M. Keynes's The General Theory of Employment, Interest and Money (gt) within a mathematical framework that preserves its original sequential and monetary logic. While previous formalizations, such as the IS-LM model (Hicks, 1937) or Meade's (1937) equilibrium systems, have dominated the transmission of Keynesian ideas, the author argues they often suppress the "disequilibrium message" and the sequential nature of economic processes central to Keynes's original text. The paper posits that the distinguishing feature of the Keynesian revolution lies not in methodological heterodoxy (agents are modeled as optimizing individuals) but in the sequentiality of interactions among economic participants. This sequentiality, the author argues, is the fundamental ingredient of complexity, where aggregate outcomes emerge from decentralized, time-dependent decisions rather than simultaneous equilibrium conditions.

Methodology: The KCX Model
The author proposes the Keynes-CompleXity (KCX) model, an agent-based computational framework designed to align as closely as possible with the original text of the General Theory.

Agent Structure: The economy consists of $n_p$ individuals divided into workers (consumers) and entrepreneurs (owners of $n_f$ firms). Firms are categorized into capital-goods producers ( $k$ -firms) and consumption-goods producers ( $c$ -firms).
Exogenous Variables: Following Keynes (gt, p. 245), the model treats as given: the skill and quantity of labor, technology, degree of competition, consumer tastes, and the social structure. The wage-unit is also fixed.
Sequential Decision Process: The model operates in discrete time steps where agents act sequentially, not simultaneously:
1. Expectations: Firms form sales expectations ( $E_t[q]$ ).
2. Factor Demand: Firms minimize costs to meet expected output, determining labor and capital demand.
3. Pricing and MEK: Firms calculate the Marginal Efficiency of Capital (MEK) based on expected proceeds and supply prices.
4. Investment Decision: Entrepreneurs compare the MEK against a financial threshold defined by the maximum of the interest rate ( $r$ ) and their individual liquidity preference ( $L^2$ ). Investment occurs only if $MEK > \max(r, L^2)$ .
5. Production and Income: Production occurs, labor is hired, and income is distributed.
6. Household Allocation: Households allocate income between consumption, speculative money demand, and bonds based on their utility functions and liquidity preferences.
Utility and Optimization: Agents maximize utility functions (Cobb-Douglas form) subject to budget constraints. The model incorporates Keynes's three attributes of assets: yield ( $q$ ), carrying cost ( $c$ ), and liquidity premium ( $l$ ).
Simulation Design: The paper utilizes Monte Carlo simulations with both homogeneous and heterogeneous agents. Heterogeneity is introduced in animal spirits, liquidity preferences, and technology prices to observe emergent macroeconomic patterns.

Key Contributions

Formalization of Sequentiality: The paper provides a micro-founded model where the order of decisions (expectations $\to$ investment $\to$ production $\to$ income $\to$ allocation) is explicit. This structure ensures that monetary variables (interest rates, liquidity preference) act as causal determinants of real variables (employment, income), rather than mere nominal adjustments.
Integration of Complexity: By modeling agents as optimizing individuals within a non-ergodic, sequential environment, the paper demonstrates how "animal spirits" and subjective probabilities lead to emergent aggregate outcomes that differ qualitatively from the sum of individual parts.
Rejection of the Homogeneity Postulate: The model explicitly rejects the classical assumption of homogeneity, showing how heterogeneous technology prices and liquidity preferences transform sharp, discontinuous economic transitions into gradual, empirically plausible distributions.

Results
The simulations yield three primary findings:

Sectoral Complementarity: Aggregate income and employment depend on the coordination of expectations across sectors. High "animal spirits" in the consumption sector ( $c$ -firms) cannot generate full employment if the capital-goods sector ( $k$ -firms) is pessimistic and fails to supply necessary inputs. The relationship is monotone and complementary; optimism in one sector alone is insufficient.
The Financial Threshold and Investment Selection: The operative threshold for investment is $h = \max(r, L^2)$ $h = max (r, L^{2})$ .
- In a homogeneous economy, this threshold creates a nearly discontinuous transition: if $h$ exceeds the common MEK, the entire $c$ -sector shuts down, causing a jump in unemployment.
- In a heterogeneous economy (specifically with varying technology prices), the same threshold results in a gradual selection of firms. As $h$ rises, firms are progressively filtered out of production, leading to a smooth increase in unemployment rather than a binary collapse.
Liquidity Preference and Monetary Allocation: Liquidity preference ( $L^2$ ) governs the allocation of residual income between speculative money and bonds. The model confirms that the interest rate is a monetary phenomenon that precedes and conditions real investment decisions. When $L^2 > r$ , agents prefer holding cash, reducing funds available for bond financing and potentially raising the effective cost of capital for firms.

Significance and Claims
The paper claims that the KCX model successfully reconstructs the General Theory by demonstrating that sequentiality is the structural feature distinguishing Keynesian economics from equilibrium macroeconomics.

Money is Non-Neutral: The results confirm that monetary variables (interest rates and liquidity preferences) enter the causal structure of production. They determine the financial feasibility of investment, which in turn dictates the level of aggregate income and employment.
Endogenous Fluctuations: The model shows that fluctuations in employment are not merely the result of "ad hoc" shocks to a representative agent but emerge from the interaction of decentralized, sequential decisions under uncertainty.
Heterogeneity as a Mechanism: The paper argues that heterogeneity is not just a realistic detail but a crucial mechanism that transforms theoretical discontinuities into continuous, observable economic patterns. The model suggests that the "Keynesian revolution" is best understood through the lens of complexity theory, where the non-ergodic nature of the economy prevents precise numeric predictions and necessitates a focus on the state of confidence and the sequential flow of events.

The author concludes that this micro-designed representation validates the original message of the General Theory: aggregate income and employment are determined by the interaction of the propensity to consume, the marginal efficiency of capital, and the rate of interest (itself determined by liquidity preference and the quantity of money), all operating within a sequential, non-ergodic framework.

Technical Summary: Mr. Keynes and the...Complexity! A suggested model for the General Theory

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