Consider a church of initially 60 people embedded in a society of total 2000. That society is assumed to remain stationary. Assume society has a demand rate of 0.7% of society per year, and a supply rate of 9% of the church per year. In addition 5% of the church leave each year; less than the supply rate so as to enable church growth.
The church grows over the following 50 years, figure 1, but growth slows and exponentially tends to a limit of 245. The limit is independent of the initial size of the church. A church starting with 40 will reach the same limit, but would take longer to do so.
Church Growth Limited by Lack of Demand
Results of the Supply and Demand Model
A church which merely supplies its religion, but does no work to create demand for that religion, will ultimately be at the mercy of the demand rate. Supplying more religion will result in faster initial growth, but the church size stops at the same barrier/limit determined by society's demand and church losses. The key to raising this barrier is for the church to engage with society and increase demand for Christianity in society. That is its supply of religion helps increase demand.
Initially the growth of the church is determined by how much religion the church supplies, figure 1, curve 1 which is below curve 2. That is growth is limited by how hard the church works to seek out people, whether by contact, or advertisement, looking for interest in their religion. There will be people demanding religion, whose aspirations are not met. Demand exceeds supply.
From about 22 years supply exceeds demand and the hard work of the church is partially wasted as there are insufficient people outside church who have an interest in the church's religion. Growth is then limited by lack of demand and stops when those who join the church match those that leave figure 3. The balance of demand rate and leaving rate determines the ultimate church size.
Allow the supply rate to vary from 3% to 7% with other parameters as above, figure 4. For supply rate less than leaving rate, curves 1-2, the church declines to extinction. A church with an insufficient supply of religion will fail whatever the demand for religion. For supply rate equal to the leaving rate the church stays at its starting value, line 3.
If the supply rate exceeds the leaving rate, curves 4 and 5, the church grows to the same fixed equilibrium. This limit, or barrier, to growth is determined by the demand rate and leaving rate alone. It is independent of supply rate, which determines how fast the limit is achieved.
Thus, for a given leaving rate, the supply determines survival, but demand determines the limit to church growth. A church must have sufficient supply to avoid extinction, but to raise the barrier to growth it must find a way of increasing demand in society.
If society is losing interest in religion over time then the supply rate will partly determine the limit to church growth. A church with a higher supply rate will be able to capitalise on a society with higher demand before they lose interest. Let the supply rate vary from 6% to 9% with the other parameters as above, but now include a loss from those outside church who may demand religion of 1% per year. These become people who are hardened to religious beliefs. Figure 5 shows that the largest growth is when the supply rate is the largest, 9%, curve 4. The lowest growth, and the one that takes the longest to achieve, is curve 1, when supply is the least, 6%.
In this particular scenario church will always decline as there is no mechanism for hardened people to become open to demanding religion again.
This model suggests two strategies that raise the limit the church numbers reach.
1. Reduce Losses
As the limit depends on the leaving rate, then reducing losses will raise that limit. However reducing leaving rates only has limited scope as the rates include deaths which cannot be reduced. Nevertheless loss reduction must always be a part of a strategy to improve growth.
2. Increase Demand
Although the church in this model is supplying religion, the amount is independent of demand, and the church does no work to create demand. Creating demand is part of any successful business and must be a part of a church's strategy to improve its growth. This can be achieved by advertising the faith, e.g. as in mass evangelistic campaigns and ministries that meet needs of communities. However both these cases are more effective when there is personal contact between Christians and those outside church, contacts where discussion and persuasion take place. Churches must not take demand for religion for granted, but expect to convince unbelievers to demand what they offer.
From a system dynamics point of view the balancing feedback loop B1 needs opposing, SD model figure 1. In this model the number joining the church is either due to supply, R1, or demand, B1. Instead these loops need to interact so that R opposes B1 and is not just replaced by it. This strategy is examined in the Limited Enthusiasm Model.