Interconnected islands symbolizing business growth and market expansion.

Deconstructing Growth: Unveiling the Secrets of How Companies Really Evolve

Nico Varela in Business & Economy September 2025 • 4 min read.

"Move beyond traditional business models and explore how compositional growth models offer a more realistic view of firm dynamics and market concentration."

Traditional economic analysis often simplifies the business world by focusing on single-product firms. This approach, while straightforward, misses the complex reality of most modern companies. As early as the 1950s, economist Joan Robinson pointed out the limitations of this 'one-commodity firm' view, noting that it restricts the scope of economic analysis.

In the late 1970s, a new trend emerged: models that recognized firms as collections of multiple, often independent units. These early multi-product firm models, however, tended to overlook the strategic interactions between these units in order to maintain mathematical simplicity. Economist John Sutton famously described these as 'island models,' where markets are isolated and dominated by a single firm behaving like a local monopolist.

A significant leap forward occurred at the turn of the century with the rise of 'compositional models,' pioneered by Gene Stanley and his colleagues. These models consider both the 'intensive' and 'extensive' margins of firm growth, offering a more nuanced understanding of how companies evolve and markets become concentrated. Compositional models provide valuable insights into firm growth, market concentration, and overall economic dynamics.

What are Compositional Growth Models and Why Do They Matter?

Interconnected islands symbolizing business growth and market expansion.

Compositional growth models represent a significant shift in how we understand firm dynamics. Instead of treating a company as a monolithic entity, these models recognize that firms are often composed of multiple, semi-independent units, each operating in different markets or producing different products. This perspective allows for a more detailed analysis of how firms grow, adapt, and contribute to the overall economy.

The 'intensive margin' in these models refers to the size of a company within a specific market. A simple example of this dates back to 1960. The 'extensive margin' refers to the number of different markets a company operates in. The way a company allocates its resources across these opportunities is often modeled using a Bose-Einstein process, which helps to explain how firms diversify and expand their reach.

More Realistic View: They offer a more accurate representation of how companies actually operate and grow.
Better Predictions: By considering the internal structure of firms, these models can improve economic forecasts.
Strategic Insights: They provide valuable insights for business leaders looking to understand market concentration and competitive dynamics.
Understanding Diversification: They explain how firms diversify across different markets and product lines.

At a micro level, compositional models highlight the number of transactions versus the value of transactions. At a macro level, GDP growth is influenced by firm-specific shocks. Therefore, in compositional models, shocks at the micro level can have a persistent effect on the performance at the aggregate level from firms to the national economies.

The Future of Growth Modeling

Compositional growth models have already played a vital role in reshaping our understanding of economic systems. By recognizing that economic systems are composed of heterogeneous units, with skewed size distribution, these models offer a more realistic perspective than traditional approaches. Compositional models help explain deviations from Gibrat's growth model at the company level. At the macro level, these models provide an explanation for the excessive volatility of composite economies whose effective diversification is bounded away from the predictions of the law of large numbers.

About this Article -

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This article is based on research published under:

DOI-LINK: https://doi.org/10.48550/arXiv.2404.07935,

Title: Compositional Growth Models

Subject: econ.gn physics.soc-ph q-fin.ec

Authors: José Moran, Massimo Riccaboni

Published: 11-04-2024

Everything You Need To Know

What are Compositional Growth Models, and how do they differ from the traditional economic approaches to understanding businesses?

Compositional Growth Models depart from the traditional 'one-commodity firm' view that simplifies companies into single entities. Pioneered by Gene Stanley, these models view firms as collections of multiple, semi-independent units. Unlike early multi-product firm models, compositional models consider both the 'intensive' and 'extensive' margins of firm growth. This approach offers a more nuanced understanding of how companies evolve, adapt, and contribute to the overall economy, providing a more realistic view compared to traditional methods.

How do Compositional Growth Models explain the concepts of 'intensive margin' and 'extensive margin' in firm growth?

In Compositional Growth Models, the 'intensive margin' refers to the size of a company within a specific market, using example dating back to 1960. The 'extensive margin,' on the other hand, refers to the number of different markets a company operates in. These models often use a Bose-Einstein process to explain how firms allocate resources across these opportunities, driving diversification and expansion. This dual perspective allows for a detailed analysis of how firms grow and adapt.

How do Compositional Growth Models offer insights that can improve economic forecasts?

Compositional Growth Models provide more realistic insights by considering the internal structure of firms and their various units. By recognizing that firms are composed of heterogeneous units, these models provide a better understanding of market concentration and competitive dynamics. This detailed approach improves economic forecasts by accounting for the complex realities of how companies operate and grow, leading to more accurate predictions.

What is the significance of micro-level shocks in Compositional Growth Models, and how do they impact macro-level economic performance?

In Compositional Growth Models, the micro-level focuses on the number and value of transactions. These models reveal that shocks at the micro level can have a persistent effect on aggregate performance, influencing economic indicators like GDP. The models highlight how these micro-level shocks, which affect individual firms, can cause fluctuations in national economies.

How have Compositional Growth Models reshaped our understanding of economic systems, and what are the future implications?

Compositional Growth Models have already transformed our understanding of economic systems. By recognizing that economic systems are composed of heterogeneous units, with skewed size distribution, these models offer a more realistic perspective than traditional approaches. They explain deviations from Gibrat's growth model at the company level and provide an explanation for the excessive volatility of composite economies. The future implications suggest further development in understanding economic dynamics, market concentration, and firm evolution.