# Complexity Economics and the Accounting Framework

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Frederico Botafogo

Southern Institute of Technology, New Zealand

Please cite the paper as:

*Frederico Botafogo, (2017), Complexity Economics and the Accounting Framework, World Economics Association (WEA) Conferences, No. 2 2017, Economic Philosophy: Complexities in Economics, 2nd October to 30th November 2017*

## Abstract

This working paper introduces a formal language to frame the concept of complexity within economic theory. The purpose is to provide a consistent analytical framework within which the varied aspects of complexity may be given expression.

The intuition underlying the framework is provided by double-entry bookkeeping and the accounting equation whereby assets equal liabilities for all possible agents in the economic system. The discussion is focused on foundational issues; markets, preferences, convexity in production, general equilibrium are not deemed to be required in describing an economic system. The basis for developing the framework is given solely by accounting theory. Linear algebra, in particular vector and tensor analyses, provide the mathematical elements required to construct said framework.

Complexity in economics is understood to imply subjective beliefs by interacting agents, who chose strategies given their particular goals, and further who update said strategies as time goes by. The resulting framework is, accordingly, dynamic and inherently uncertain. Therein, the accounting equation is seen as the expression of a solution concept, as this is defined in Game Theory. And economic value is a measurement scale which informs how distinct resource subsets relate to each other as input to output given a strategic economic process consisting of production, trade, or both.

The epistemological background which supports the framework relies on the representational theories of measurement.

The paper is organised as a list of talking points. Three appendices cover the methodological approach being used, the mathematics knowledge being required, and a short review of what the representational approach to measurement entails.

As we have discussed previously I am very delighted to see a reasonable and comprehensive framework that does not require any G.E assumptions to function. This is much more in line with what I imagine “complex” economics to be like.

I would like to explore this framework via agent modelling; that is, to imbue some agents with the mental model described here “goal -> prices” and to build in some simple decision making AI. When we meet up next time, let’s discuss how we can make this happen? I have in mind a simple “toyworld” scenario where we make a n x m tile terrain that agents must traverse in order to reach their predetermined goals, and in each tile they have the ability to perform simple functions like trade, pay tolls, etc. In this scenario we might be able to see how prices can be determined from goals.

Thanks Max. Please notice that to deal with several agents we must first develop the notation beyond what is presented in the appendix to this working paper. The appendix refers to a single agent only. To allow multiple agents one has to partition the given partition. The process of partitioning is accounted for by introducing additional indices, as sub-indices of the given initial indices. For example, if ‘i’ index the goods at t = 1, then ‘alpha’ could index agents such that x(i,alpha) informs how much of the ith good is controlled by the alpha th agent. Note further that the DEB consistency condition now reads as a tensor contraction of both indices such that 1 is the end result of the contraction.

I believe the notation issue is the key to a clear understanding of this framework.