## Monday, May 2, 2016

### An Alternative SIM Equation

Wynne Godley and Marc Lavoie's book "Monetary Economics" provides an excellent introduction to SFC analysis. Chapter 3 introduces model SIM (for simplest) and introduces the reader to a system of equations suitable for entry into a spreadsheet. Unfortunately, the system introduced is interlaced with the premise that people have a tendency to spend part of their income [1] . While undoubtedly true, this premise leads the reader down a difficult path. This path leads to the arithmetic of diminishing series which requires enabling the iteration capabilities of the spreadsheet and complicated, interactive calculations.

The possibility that an alternate path may exist is inferred from the knowledge that a diminishing series (such as we have here) will converge to a limit. The fact that a limit does exist should give us confidence that any path found can be coequal with series-based-pathways .

A Monetary Relationship

A relationship between taxes, value exchanged and money is easily found. Ask yourself "If I have money, say $\\{$100} $, how much can I and all the people I trade with buy before the government takes the$ \\{$100}$ away with taxes?"

We can answer that question easily. Assume a tax rate of 20% (like the income tax) that is extracted at each exchange. We set up an equation in the form of unknown amount times tax rate equals $\\{$100} $. We can write that in a conventional format by letting X = the unknown amount and θ = the tax rate . We would write (1)$ \theta X = 100 $The reader can see that if θ is 20%, X will be$ \\{$500}$ .

We can relate this to the general economy. Government is the source of much of the money that powers our economy. When government pays wages, the wages count toward the Gross National Product (GDP). Government typical collects taxes on those wages in the form of an income tax collected before the worker actually holds those wages in his hands. (The tax collected does not have to be an "income tax" but the concept is easier to accept when we use familiar terms and conditions.) If we let T represent any tax repetitively collected at each transaction, we can write

(2)    $GDP = \frac{T}{θ}$

Equation 2 gives us a simple, intuitive way to relate GDP, taxes and a tax rate. It also provides a relationship to the money supply.

The Money Supply