Social network analysis, Markov Chains and input-output models: combining tools to map and measure the circulation of currency in small economies.

Abstract

Localization is posited as the antidote for globalization, but little exists in the way of quantifying the micro-scale of small communities. In this paper, the reader's attention is drawn towards understanding that social network analysis, Markov Chains and input-output models are equivalent, and that together these tools can be used to map and measure the circulation of currency in a small community. The "map" of the economy can be created using social network analysis, in a form equivalent to Markov Chains and input-output models, by representing businesses as nodes and the percentage of expenses spent by one business at another as the strength of the edges between the nodes. Markov Chain mathematics is used to measure the circulation of currency in the economy by calculating the average number of transactions (average path length) from where the dollar enters the community until it leaves. This method is equivalent to the "multiplier effect" from input-output models but more granular. An example using a simple loop is provided showing different methods of solutions, their equivalence and the impact of loops on the average number of transactions in a small economy.