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 BLOG >> February 2021

Varieties of Growth [Growth
Posted on February 4, 2021 @ 07:44:00 PM by Paul Meagher

Currently reading Vaclav Smil's book Growth: From Microorganisms to Megacities (2019).

As you can see from the book cover, Bill Gates is a big fan of Vaclav's many books and has reviewed and recommended this book on his website.

The book could be interesting/useful reading for entrepreneurs and investors for the simple reason that growth is a central concern for both. A better and more detailed understanding of growth might allow us to 1) better understand how the world works, and 2) apply growth-related ideas to our own circumstance.

Chapter 1 of the book is called Trajectories: or common patterns of growth. The chapter is 69 pages long with relatively small typeface so there is alot of content in this first chapter to the extent you might consider it a book. My strategy for reading this 634 pg. book is to consider each chapter as equivalent to reading a small book. When I finish the first chapter, it should result in a sense of accomplishment and allow me to drop the book for awhile until I have time to focus on it again.

Chapter 1 sets a technical background for the book. Vaclav discusses some math and models that have been used to account for and explain the trajectories of growth. Growth is generally plotted as some labelled variable on the y axis that increases over time plotted on the x axis. Within this view of growth, many possible trajectories can be plotted and many different maths can be used to describe these trajectories. The math used to describe these trajectories can in turn be explained by different models and theories of how that trajectory came about. The varieties of growth refer to this diversity of maths, models, and theories that are used to describe and explain growth phenomenon.

If you study visual representations of growth in many different areas like Vaclav and others have, you will begin to notice common patterns. One common pattern is an S-shaped or a Sigmoid growth pattern involving slow growth at first, followed by exponential growth, and then trailing off to slow growth again. The model explanation of this pattern might involve a positive feedback loop accounting for the exponential aspect of growth with a countervailing negative feedback loop accounting for the slowing of growth at the end. Growth can also appear in a more modest linear form involving a constant amount of growth each year perhaps plateauing at points along the way. Growth can also be fast right from the start without any slow buildup - what startups and investors might wish was the case. The pandemic has caused many micro and macro economic growth curves to oscillate off trend.

In the remainder of this blog, I want to do a deep dive into one of ideas mentioned in this chapter that interested me.

Explaining Technological Change

In 1971, Fisher and Fry published a classic paper called "A Simple Substitution Model of Technological Change" (1971) which you may be able to download if you google it.

The objective of the paper was to provide the reader with a simple-to-understand model that might be used to explain how the technologies we use change over time.

Fisher and Fry summarize their model as follows:

The Model

The model is based on three assumptions:

  1. Many technological advances can be considered as competitive substitutions of one method of satisfying a need for another.
  2. If a substitution has progressed as far as a few percent, it will proceed to completion.
  3. The fractional rate of fractional substitution of new for old is proportional to the remaining amount of the old left to be substituted.

.... Experience shows that substitutions tend to proceed exponentially (i.e., with a constant percentage annual growth increment) in the early years, and to follow an S-shaped curve. (p. 75-76).

This substitution model can be used to generate S-shaped curves using logistic type equations. The particular version of these equations Fisher and Fry used allows you to enter a point in time and return the market fraction (f) of a new method. Vaclav summarized the rest of Fisher and Fry's paper by saying they "used their substitution method to forecast the outcome of simple two-variable substitutions and applied it initially to competitions between synthetic and natural fibers, plastics and leather, open hearth furnaces and Bessemer converters, electric arc furnaces and open-hearth steelmaking, and water-based and oil-based paints" (p. 48).

The variety of technology changes they modelled in this paper is one reason the paper is considered a classic. Also the simplicity of the proposed model is a good starting point for thinking about technology change before formulating more complex models.

To better understand some of the concepts in Chapter 1, I felt the need to deep dive into some of the primary research Vaclav cited. If you decide to read this book, you might want to anticipate doing so as well out of interest and/or to more fully understand the concepts.




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