Strategic Modelling and Business Dynamics: A Feedback Systems Approach

7.11. Appendix – Gain of a Reinforcing Loop

Gain is a technical term used to describe the strength of a reinforcing loop. The procedure for calculating gain is outlined in Figure 7.34. There is a reinforcing loop A-B-C-D. What it represents is immaterial. What matters is whether the causal links amplify or attenuate a change that originates in the loop. To test this property we first imagine the loop is cut at some convenient point and then unfolded to form a linear chain or 'open loop'. In this case a cut is made in the link connecting D and A. The gain of the open loop is defined as the size of the change transmitted back to A when the value of A itself changes by one unit. Alternatively, if A changes by a small amount ΔA, then the gain is the size of the change transmitted back to A divided by ΔA. The calculation assumes a steady state is achieved, so enough time elapses for any stock adjustment processes to run their course. The full name for the calculation is the 'open loop steady state gain'.

Figure 7.34. The gain of a reinforcing loop

The concept is best illustrated with a practical example. Figure 7.35 shows the sales growth loop from the market growth model, including the parameters that determine the strength of causal links. In this case, imagine the loop is cut at a point in the link between revenue and sales budget. Suppose there is a small increase in the sales ...