The central hypothesis of the bounded resource model is that church members generate resources that, in turn, drive the growth of the church through conversion/recruitment. Conversion is proportional to resource size. Resource generation is proportional to church size but is increasingly harder to generate at higher resource levels. Assume the resources has an upper bound. Essentially, the church supplies religion to society in proportion to a generated resource.
Additionally, losses to the church, whether deaths or people leaving, are at a constant rate per person. The resource will naturally deplete over time if not generated.
Limited resources include physical buildings, staff time, church reputation, opportunities to serve.
The model predicts a limit to the growth of the church, with growth slowing as the limit is reached. Initially, both church growth and resource generation may accelerate, but eventually, each slows down until the conversion rate matches the leaving rate. The resource always falls short of its upper bound.
This is a metaphorical model whose purpose is to illustrate limits to church growth.
System Dynamics Model
Unbelievers are added to the church according to the amount of resource (R). Church members leave at a constant rate per person (B1). The resource is generated according to the size of the church (R). The resource is harder to generate the larger it becomes (B3), measured next to its maximum resource (capacity). Resource depletes at a constant per capita rate (B2).
The leaving feedback loop B1 has a constant impact. However, because loop B3 slows the generation of the resource, the reinforcing loop R has a diminishing impact on recruitment. Church growth reaches its limit when the recruitment rate matches the leaving rate.
If the church subsequently declines because, for example, the leaving rate increases, then the smaller church will generate less resources as some of the existing resources will deplete in time, B2. A new lower equilibrium would be reached.
Results of the Bounded Resource Model
Church starts by growing, with the resource also growing, loop R dominates. However, the resource becomes harder to generate as it gets closer to capacity, thus its growth slows, loop B3. The slowing resource growth slows the increase in recruitment until it matches the losses from the church, loop B1. Thus, the church stops growing. The resource does not reach capacity due to its natural depletion, loop B2.