A FRACTAL MODEL OF CREATIVE DESTRUCTION

Johnnie B. Linn III Concord University, Athens, WV

Creative Destruction as Industrial Mutation

• The opening up of new markets, foreign or domestic, and the organizational development from the craft shop and factory to such concerns as U.S. Steel illustrate the same process of industrial mutation—if I may use that biological term—that incessantly revolutionizes the economic structure from within, incessantly destroying the old one, incessantly creating a new one. (p 83)

Occupying a Niche

• Popularizing a little and recognizing that by doing so we lose much of the meaning, we may say that it is our daily work which forms our minds, and that it is our location within the productive process which determines our outlook on things—or on the sides of things we see—and the social elbow-room at the command of each of us. (p. 12)

Schumpeterian Universe

• Creative destruction changes structure in the economic universe but does not change its number of dimensions.

• So what is the number of dimensions of the Schumpterian universe?

A Fractal Model of Niche Creation

• Each new firm selects a niche in the Schumpterian universe.

• In doing so, it alters its environment and creates new niches.

• When new niches are filled, even more new niches are created.

• An endless process, suggesting a fractal.

Hypothesis: Schumpeterian Universe is a Sierpinski Triangle.

• Animated_construction_of_Sierpinski_Triangle– This file is licensed under the Creative Commons

Attribution-Share Alike 3.0 Unported license.– Attribution: Dino at en.wikipedia

An Empty Simplex

BRAKES TIRES

MUFFLERS

First Niche Dweller

BRAKES TIRES

MUFFLERS

Occupying Central Void

BRAKES TIRES

MUFFLERS

First Three Orders

BRAKES TIRES

MUFFLERS

Primality and Duality

• The concept of creative destruction can be applied to either primal or dual economic dimensions.

• Primal dimensions apply to the kinds of output that are made available.

• Dual dimensions apply to the kinds of inputs that are drawn upon.

The Model

• Calculate a Herfindahl-Hirschman index (HHI) for value added generated by the firms in a simplex.

• Infer the number of dimensions of the Schumpeterian universe by finding the simplex whose HHI best approximates the observed HHI.

Testing the Model

• Compare the number of dimensions we derive for the Sierpinski triangle to a number of dimensions that is inferred by some other means.

Market Share and its Square

HHI for a Full Simplex

𝐻 (𝑛)= 1(𝑛+1 ) [ 1

1−(𝑛+1 )

(𝑛+2 )2

−1]= 1

(𝑛+2 )2− (𝑛+1 ).

Number of Effective Participants

• This number is the same as the number of voids to the first three levels.

Number of Dimensions

𝑛=−3+√9+4 (𝐻− 1−3 )

2.

Testing the Model: Perception of Class

• The distribution of members in each class, when compared with what would be expected in a Sierpinski triangle for a predicted value of n, will give us a test of the fitness of a Sierpinski triangle.

Testing the Model: Lorenz Curve

q

p

Gini Coefficent for First Three Orders

𝑔=𝑞−𝑝 .

Geographic Variation

• Hargrove and Hoffman: 9 Dimensions at one-kilometer resolution.

• More dimensions could be expected at higher resolution.

• We should expect Schumpeter universe to exploit all geographic variation.

• These dimensions can be regarded as dual.

Biosphere, Biomes, Ecoregions

• 1 Biosphere, 14 Biomes, 125 Ecoregions (Ricketts, 1999).

• 9 Dimensions is best fit.• These dimensions can be regarded as primal

or dual.

Socioeconomic Class

• Primal: Degree of Specialization– Central Void filled by least differentiated– Working Poor or Underclass– 12% to 20% of labor force (Thompson and Hickey,

Beeghley, Gilbert)– Best fit: one primal dimension (likely education).

• Dual: Consumption– U.S. Gini coefficient is about 0.468– Best fit for dual number of dimensions is 3.3

Manufacturing Concentration Data

• Effective global number of participating firms is about 439. (Linn, 2010)

• Corresponding number of primal dimensions is 19.

• Likely overstated because of geographic dispersion of firms.

Make-Use Tables

• Problem of intermediation of firms avoided.• Make table: Effective number of commodities

about 50. (Linn, 2010)– Number of primal dimensions about 5.

• Use Table: Effective number of industry purchasers of commodites about 479. (Linn, 2010)– Number of dual dimensions about 20.

Best Comprehensive Estimate

• 5 primal dimensions• 20 dual dimensions

Further Study

• Sports and Games– Abundance of data on distribution of winnings– Abundance of analysis of the number of

dimensions of a sport or game– Will the fractal model match these up well?