Saturday, January 29, 2011

Marginal Cost - Production of the Fractal

Marginal Cost - derived from the fractal



Original Post
The fractal demonstrates cost.
To demonstrate the increasing cost - in effort and time - at each iteration (see my first blog on marginal analysis and the fractal) to produce the fractal, I decided to use the the reciprocal and invert the Marginal Area, MA. The rationale for this choice is based on: the more area to the snowflake, the more the cost. I am sure there are other ways of doing this, but I figured that this method is as simple and as easy as calculating the MC again, it should be okay.
Fig. 2 shows the original MA TA diagram with the MC.

Background
One thing about computer generated fractals is that they appear to be produced with ease, we simply forget that they would not be viewable if it were not for the memory and processing power of our modern computer. To see how complex and slow they are to draw one only has to take a pen and paper and have a go at drawing the Koch snowflake progression - step by step. It is easy from the beginning, but it progressively gets harder and harder with each iteration or level: there is a 'cost' in time, and it takes patience too - adding hundreds of triangles and rubbing out old lines.
What we don't see when we use the modern computer to draw them is that they too will start to labour, and slow - after (around) the 8th iteration, and probably crash after the 12th . This all due to the added complexity at each iteration.





In my next entry I will analyse this fractal equilibrium.
Figure 2b shows the MC MA equilibrium in closeup.

Update May 2017
This is by far my best idea; I have written it up in a working paper at my academia.edu and vixra, and named it:  Quantum Mechanics, Information and Knowledge, all Aspects of Fractal Geometry and Revealed in an Understanding of Marginal Economics.
I shall post the Abstract, followed by the original post, followed by the paper. I hope to have some collaborate and review my work in time.
Abstract
Fractal geometry is found universally and is said to be one of the best descriptions of our reality – from clouds and trees, to market price behaviour. As a fractal structure emerges – the repeating of a simple rule – it appears to share direct properties familiar to classical economics, including production, consumption, and equilibrium. This paper was an investigation into whether the mathematical principles behind ‘the market’ – known as marginalism – is an aspect or manifestation of a fractal geometry or attractor. Total and marginal areas (assumed to stand for utility) and the cost of production were graphed as the fractal grew and compared to a classical interpretation of diminishing marginal utility theory, and the market supply and demand. PED and PES was also calculated and analysed with respect to (iteration) time and decay.  It was found the fractal attractor demonstrates properties and best models classical economic theory and from this it was deduced the market is a fractal attractor phenomenon where all properties are inextricably linked. The fractal, at equilibrium, appears to be a convergent – zeta function – series, able to be described by Fourier analysis, and involves Pi, i, e, 0, and 1 (of Euler’s identity) in one model. It also demonstrated growth, development, evolution and Say’s Law – production before consumption. Insights from the fractal on knowledge and knowing are also revealed, with implications on the question of what exactly is ‘science’ – and what is ‘art’? A connect between reality and quantum mechanics was identified. It was concluded marginal, classical economics is an aspect of a fractal geometry.  
 Keywords
Marginal, Fractal, Elasticity, Utility, Cost, Production, Price, Growth and Development, Say’s Law




No comments:

Post a Comment