Strategic Modelling and Business Dynamics: A Feedback Systems Approach

3.4. Equation Formulations

The final step in developing a simulator is to write algebraic equations. Diagrams are a good starting point because they show all the variables that must appear in the equations. Nevertheless, there is skill in writing good algebra in a way that properly captures the meaning of the relationships depicted.

3.4.1. Drug-related Crime

Consider the formulation of drug-related crime. We know from the diagram that drug-related crime depends on the funds required (by addicts) to satisfy their addiction and on the average yield per crime incident. These two influences are reproduced in Figure 3.12, but how are they combined in an equation? Should they be added, subtracted, multiplied or divided? The top half of Figure 3.12 is a plausible formulation where drug-related crime is equal to funds required divided by average yield. This ratio makes sense. We would expect that if addicts require more funds they will either commit more crimes or else operate in a neighbourhood where the yield from each crime is greater. Hence, funds required appears in the numerator and average yield in the denominator. The ratio expresses precisely and mathematically what we have in mind.

An alternative formulation, such as the product of 'funds required' and 'average yield', contradicts common sense and logic. A simple numerical example shows just how ludicrous such a multiplicative formulation would be. Let's suppose there are 10 addicts in a neighbourhood and collectively they ...