This example shows the effects of loop impact in a limits-to-growth model.

A fixed amount of land is designated for a new trading estate in order to encourage business development in a town. Initially, the trading estate grows rapidly as more businesses attract more business developments – the urban attractiveness hypothesis *R0*. However, as growth continues, land availability falls, and business construction is reduced, *B1*. The model is first-order. See figure 1.

Simulating the model shows the classic S-shaped growth, figure 2. Comparing the loop impacts of the two loops shows that the reinforcing loop *R0 *dominates as the growth in *Business Structures* accelerates. Once that growth slows down, loop *B1* dominates. This is classic “shifting loop dominance”. Dominance shifts from the reinforcing loop (accelerating) to the balancing loop (decelerating).

The values of the loop impacts are compared in figure 3. The units are “per year”. The impact of *R0* on *Business Structures* is positive and falls throughout. First-order reinforcing loops have positive impact as impact has the same sign as loop gain in first-order loops. By contrast, the impact of *B1* on the stock is and negative increases in absolute value. Thus, *R0* gets weaker while *B1* gets stronger. Therefore *B1* eventually has a greater impact than *R0 *(in absolute terms). The loop with the greater impact has the most influence on the curvature in the stock graph. The model is non-linear due to multiplication in the flow *Business Construction*. Thus, both loops are non-linear, which is why their impacts change over time.

If buildings are demolished at a fixed rate, then a third loop, *B0*, is added, figure 4. This loop is balancing and linear, depleting the stock – a draining process.

There are now three loops influencing stock behaviour. Initially, *R0* dominates, the accelerating phase, until the combination of *B1* and *B0* has a larger impact, figure 5. In this middle phase, no single loop dominates. *R0 *still has the largest impact of the three loops, but the *sum* of the two balancing loops is larger than that of *R0* – hence the stock growth is slowing down. In the third phase, *B1* has the largest impact, thus dominates over *R0*.

The impacts of the three loops are compared in figure 6. As loop *B0 *is linear, its impact is constant (green dotted line). Initially, loop *B0* has a larger impact than *B1*, but this phase has no noticeable effect on stock behaviour as both loops are decelerating. In the middle phase where it takes both *B0* and *B1* to dominate over *R0*, the value of *B0*‘s impact has enabled *B1* to slow the growth earlier than would have happened if there had been no demolition. Thus, demolition shortens the acceleration phase. Demolition also lowers the carrying capacity, seen in the maximum value of *Business Structures*, compare figures 2 and 5.