Incremental Increase Method of Population Forecasting (Method of Varying Increment)

Incremental increase method combines concepts of both – arithmetic and geometric increase methods of population forecasting.

The results of incremental increase method lies in between the results of arithmetic increase method and geometric increase method.

In This Article,

Concept
Formula
Assumption
Advantages
When to Use?
Derivation
Example

Incremental Increase Method for Population Forecasting: Concept

First of all, actual increase in each decade is calculated from the known values of population from the past decade.
Increment in increase for each decade is then calculated.
Average of increment in increase is then found.
Average increase and average incremental increase are both added to the present population to estimate the present population.

Incremental Increase Method Formula

Formula of incremental increase method is –

$P_{n}=P+nI+\frac{n(n+1)}{2}\times r$

P = present population

n = number of decades

I = average increase per decade

R = average incremental increase

Assumption behind Incremental Increase Method

“The growth rate of population from decade to decade is not constant. It is either increasing or decreasing depending upon the increase or decrease in incremental increases of the past data being positive or negative.”

Advantages of Incremental Increase Method

The pros of both the arithmetic and geometric increase method are included in this incremental increase method.
It can be applied to areas where growth rate is not constant.

When do we Use Incremental Increase Population Method?

For an average sized town in normal condition, this method can be applied to carry out estimation. These towns normally do not have a constant growth rate.

Constant growth rate can be found in saturated cities, where a different method of population forecast is used.

Besides, incremental increase method can be used for both old and new cities.

Incremental Increase Method Derivation

I = incremental increase per decade

r = average incremental increase

From the concept of incremental increase method, the arithmetic increase (I) is added to the last known population. Furthermore, average of incremental increases (r) is added once for first decade, twice for second decade, and so on.

Thus, the population after first decade P₁will be –

P₁ = Population after 1 decade from present (or last known census)

$P_{1}=P_{0}+(\bar{x}+1\,.\,\bar{y})$

P₂ = Population after 2 decades

$P_{2}=P_{1}+(\bar{x}+2\,.\,\bar{y})\\\\=P_{0}+(2\bar{x}+3\,.\,\bar{y})\\\\P_{2}=[P_{0}+2\bar{x}+2\,.\,\frac{2+1}{2}\;\bar{y}]$

Proceeding in above way, we can derive a general formula; as:

$\mathbf{P_{n}=[P_{0}+n\bar{x}+\frac{n(n+1)}{2}\,.\,\bar{y}]}\\$

In the above equation,

P_n = Population after n decade from present (or last known census)

$\bar{x}$ = Average increase of population of known decades

$\bar{y}$ = Average incremental increase of population of known decades

Incremental Increase Method Example

Find the population of Delhi, India for the year 2011 from the population census data:

Year	1971	1981	1991	2001	2011
Population	40,65,698	62,20,406	94,20,644	1,38,50,507
					1,67,87,941

Step-1: Given Data

Population of last decade (2001) P = 1,38,50,507

Number of decades

$n=\frac{2011-2001}{10}=1$

Step-2: Find average incremental increase per decade

Year	Population	Increment per Decade	Incremental Increase
1971	40,65,698	–	–
1981	62,20,406	21,54,708	–
1991	94,20,644	32,00,238	3200238-2154708=
2001	1,38,50,507	44,29,863	47.02%
2011	1,67,87,941	29,37,434	21.21%
Average incremental increase =		R =1,27,22,243/4 =31,80,560.75 = 31,80,561	I =172.68/4 =43.17%

Step-3: Calculate Pn from the formula

$P_{n}=P+nI+\frac{n(n+1)}{2}*r\\\\P_{2011}=1,67,87,941+(1\times 3180561)+[\frac{1+43.17}{100}]1$

= 1,67,87,941 + (1)( 31,80,561)

= 1,99,68,502

Summary

As incremental increase method of population forecasting combines the concepts of two of the most common methods of population forecast, i.e., arithmetic increase method and geometric increase method, its results lie in between the results of these two.

The growth rate of population from decade to decade is not constant in incremental increase method. When the growth rate of a city/town is not constant, incremental increase method can be applied.

$\mathbf{P_{n}=[P_{0}+n\bar{x}+\frac{n(n+1)}{2}\,.\,\bar{y}]}$

FAQ

Where incremental increase method formula is not used?

Incremental increase method formula for population forecast cannot be used where the population growth rate is constant. Saturated towns have constant growth rate, where incremental increase formula cannot be used. Use this method instead.