The model consists of two groups of people: Church, either a single congregation, or a local group of congregations, or a denomination. Church may be measured by attendance or membership; Outside Church, the unbelieving society that do not practice religion by church attendance.
The dynamic hypotheses are:
Supply and Demand Model
The first hypothesis of the supply and demand model is that a church supplies religion according to its size. The bigger the church the more religion it supplies. The second hypothesis is that the unbelieving society demands religion according to its size. As people get converted the demand for religion goes down. What the church supplies is not matched to demand, neither does it create demand, thus the lower of the two determines recruitment.
In addition, losses to the church, whether deaths or people leaving, are at a constant rate per person.
The model predicts a limit to the growth of the church, with growth slowing as the limit is reached. Initially growth is limited by supply as the church is not big enough to meet demand. In time supply exceeds demand and the limit is achieved as a balance between demand and the church's leaving rate.
This is a metaphorical model whose purpose is to illustrate limits to church growth.
|Unbelieving society demands church/religion at a rate proportional to its size (B1).||Each person in society has a demand for religion, set at the average. Thus the demand in society is proportional to the number outside church. As people join the church then demand falls. Thus there is no effort by the church to increase demand.|
|Church supplies religion in proportion to its size (R).||The larger the church, the more people go into the community advertising the faith, actively finding those who demand religion, “seeking and saving the lost”. However the church only seeks those that demand what it offers, rather than persuading people to demand its religion. Thus it is the minimum of the supply and demand that determines recruitment. The church does not increase supply to meet demand, neither does it create demand to match the supply.|
|People leave church at a constant proportional rate (B2).||This includes people giving up the church, and deaths. The reason people leave are personal, thus the rate is proportional to the church size, i.e. "per capita". Those who leave are open to rejoining. Those who die are matched by births.|
|Limited pool of unbelievers.||The size of society outside the church is finite.|
Births can be considered to be part of the recycling where births balance deaths.
Unbelievers are added to the church according to the minimum of the supply (R) and demand (B1). Church members leave at a constant rate per person and are recycled back into society (B2). Thus people stay in church for a constant average length of time. The leaving rate can include deaths if balanced by an equal amount of births into society.
Without the loop B2 the church would increase with growth slowing until all of society is converted. With B2 the feedback: more church, more leave, thus less church, gives exponential deceleration. Thus growth halts before all society is converted when the number leaving rises to match the demand.
The behaviour of the model is controlled by a number of parameters that reflect the church's effectiveness, and the response of society:
|demand rate||This is the percentage of unbelievers who could join the church each year, provided there is sufficient supply by the church. This is society's demand for the religion of the church.|
|supply rate||This is the number of unbelievers who the church could supply the needs of if there is sufficient demand in society. This is the church's supply of religion per year.|
|leaving rate||The fraction of church members who leave each year.|
Church starts by growing (R), but growth slows (B1) until a limit is reached when the number leaving matches the number joining, i.e. the effect of B2 matches B1.