# Balancing Loops: Growth and Decline

Early on in a system dynamics (SD) course, it is usual for a learner to be introduced to two types of first-order balancing loops: one where the stock grows, and one where the stock declines.

### Death Process

Take the decline situation first. If there are no births or migration, a population will decline over time through deaths, figure 1:

The population declines exponentially, figure 2. I have sometimes heard it said that the stock declines because of the balancing loop. But this is not true. The role of the balancing loop is to SLOW the decline. The stock declines because deaths are an outflow subtracting people from the stock! If there were no loop, the decline would be straight. By the way, there are issues with this model, which I will return to at the end.

In figure 1 note that loop B has one positive polarity and one negative polarity. The plus is a same way link, and the minus is a subtract from link because it is attached to a stock. It is the subtract from link that ensures the stock declines. You could read this as: the fewer in the population, the fewer deaths, thus fewer are subtracted from the population. The “fewer subtracted” is the control that slows the decline. Do not say: the more population, the more deaths, thus the less population! Firstly, in this case, there cannot be “more population” as there is only an outflow. Secondly, even if there were an inflow that could allow more population, the last part should then read: “the more is subtracted from the stock.” It is then clear the action of the loop is opposing the initial intention, thus is giving control.

### Goal-Seeking Process

The other example of a balancing loop SD learners usually see is the goal-seeking process. Employees are recruited with the rate of recruitment proportional to the vacancies. There is a target number of employees. Thus, the vacancies are the target minus the shortfall, figure 3.

The population grows as new employees are recruited, but the growth slows down as the vacancies are reduced, figure 4. The more employees, the fewer vacancies, thus less recruitment, therefore the fewer employees added. As in the death process, the role of the balancing loop is to slow the changes, but this time it slows the growth of the stock. If there were no loop, then growth would be linear. The curve is negative exponential, but it approaches the limit from below, unlike figure 2, where it is approached from above.