Purchasing-age population index

The PAP is an index that draws two ceilings based on demographics. The idea is to model rational demand based on population^[1].

Assuming that every 1 person needs 1 house, that would be the demographic upper limit of purchases.
Assuming that humans mate, then each couple (2 people) would need 1 house, that would be the lower limit.

How are the limits created?

The demographic limits are created by considering the number of people between 25 and 50 years of age on a given year, and then this limits can be crossed with the number of sales or mortgages for the same year.

The upper bound is the total number of people between 25 and 50 divided by 26 (the total number of age groups).

$Upper limit equation$

The lower bound is the upper bound divided by 2 (simulates the potential number of couples).

$Lower limit equation$

Why the range between 25 and 50 years of age?

The logic comes from a decision to avoid "noise" in the data. Around 70% of purchases are concentrated in this age group (example source: Statista). The approximate landscape is the following:

Age group between 0 - 24, represents 24% of the population and 5% of purchases.
Age group between 25 - 50, represents 35% of the population and 70% of purchases.
Age group between 51 - 1xx, represents 41% of the population and 25% of purchases.

The bands could move especially upwards, towards 60 years of age. Actually, the values for the limits using the age group between 25 - 60 has been reviewed and is available in the public database. But the values do not vary significantly from those shown by the 25 - 50 group, and only serve to flatten the curve, which we interpret as noise.

Overall, the 25 - 50 age bracket occupies the majority of purchases providing the least noise.

Other notes

For the mathematical notations, the Latex Math API developed by @uechz has been used. A latex editor is accessible at TutorialsPoint.com.

^[1] However, this index is far from achieving a perfect demand side. We must consider that 85% of purchases come from individuals, but 15% are from legal entities (not considered in the demographic curve). Also, purchases made by foreign non-residents are not considered either in the demographic limits.