Texas Investment Network


Recent Blog


Pitching Help Desk


Testimonials

"Joined, submitted, we're moving forward. Excellent site, thanks again... "
Steve Smith - EquipmentFX

 BLOG >> February 2021

Varieties of Growth [Growth
Posted on February 4, 2021 @ 06:44:00 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.

Permalink 

 Archive 
 

Archive


 November 2023 [1]
 June 2023 [1]
 May 2023 [1]
 April 2023 [1]
 March 2023 [6]
 February 2023 [1]
 November 2022 [2]
 October 2022 [2]
 August 2022 [2]
 May 2022 [2]
 April 2022 [4]
 March 2022 [1]
 February 2022 [1]
 January 2022 [2]
 December 2021 [1]
 November 2021 [2]
 October 2021 [1]
 July 2021 [1]
 June 2021 [1]
 May 2021 [3]
 April 2021 [3]
 March 2021 [4]
 February 2021 [1]
 January 2021 [1]
 December 2020 [2]
 November 2020 [1]
 August 2020 [1]
 June 2020 [4]
 May 2020 [1]
 April 2020 [2]
 March 2020 [2]
 February 2020 [1]
 January 2020 [2]
 December 2019 [1]
 November 2019 [2]
 October 2019 [2]
 September 2019 [1]
 July 2019 [1]
 June 2019 [2]
 May 2019 [3]
 April 2019 [5]
 March 2019 [4]
 February 2019 [3]
 January 2019 [3]
 December 2018 [4]
 November 2018 [2]
 September 2018 [2]
 August 2018 [1]
 July 2018 [1]
 June 2018 [1]
 May 2018 [5]
 April 2018 [4]
 March 2018 [2]
 February 2018 [4]
 January 2018 [4]
 December 2017 [2]
 November 2017 [6]
 October 2017 [6]
 September 2017 [6]
 August 2017 [2]
 July 2017 [2]
 June 2017 [5]
 May 2017 [7]
 April 2017 [6]
 March 2017 [8]
 February 2017 [7]
 January 2017 [9]
 December 2016 [7]
 November 2016 [7]
 October 2016 [5]
 September 2016 [5]
 August 2016 [4]
 July 2016 [6]
 June 2016 [5]
 May 2016 [10]
 April 2016 [12]
 March 2016 [10]
 February 2016 [11]
 January 2016 [12]
 December 2015 [6]
 November 2015 [8]
 October 2015 [12]
 September 2015 [10]
 August 2015 [14]
 July 2015 [9]
 June 2015 [9]
 May 2015 [10]
 April 2015 [9]
 March 2015 [8]
 February 2015 [8]
 January 2015 [5]
 December 2014 [11]
 November 2014 [10]
 October 2014 [10]
 September 2014 [8]
 August 2014 [7]
 July 2014 [5]
 June 2014 [7]
 May 2014 [6]
 April 2014 [3]
 March 2014 [8]
 February 2014 [6]
 January 2014 [5]
 December 2013 [5]
 November 2013 [3]
 October 2013 [4]
 September 2013 [11]
 August 2013 [4]
 July 2013 [8]
 June 2013 [10]
 May 2013 [14]
 April 2013 [12]
 March 2013 [11]
 February 2013 [19]
 January 2013 [20]
 December 2012 [5]
 November 2012 [1]
 October 2012 [3]
 September 2012 [1]
 August 2012 [1]
 July 2012 [1]
 June 2012 [2]


Categories


 Agriculture [77]
 Bayesian Inference [14]
 Books [18]
 Business Models [24]
 Causal Inference [2]
 Creativity [7]
 Decision Making [17]
 Decision Trees [8]
 Definitions [1]
 Design [38]
 Eco-Green [4]
 Economics [14]
 Education [10]
 Energy [0]
 Entrepreneurship [74]
 Events [7]
 Farming [21]
 Finance [30]
 Future [15]
 Growth [19]
 Investing [25]
 Lean Startup [10]
 Leisure [5]
 Lens Model [9]
 Making [1]
 Management [12]
 Motivation [3]
 Nature [22]
 Patents & Trademarks [1]
 Permaculture [36]
 Psychology [2]
 Real Estate [5]
 Robots [1]
 Selling [12]
 Site News [17]
 Startups [12]
 Statistics [3]
 Systems Thinking [3]
 Trends [11]
 Useful Links [3]
 Valuation [1]
 Venture Capital [5]
 Video [2]
 Writing [2]