DEFINITION

Growth rate is an indicator that reflects the ratio of the value of a certain economic or statistical indicator for the corresponding period of time to its original value, that is, to the value taken as the basis (base) of reference.

The growth rate indicator can be measured as a percentage or in relative values.

The rate of economic growth directly depends on type of economic growth. In economics, there are two types of economic growth:

• Extensive type of growth, in which the increase in production volume occurs due to the introduction of a certain, large number of factors (raw materials, fuel, labor, equipment, etc.).
• Intensive growth type increases production volume by improving quality indicators (qualifications, technologies, achievements of scientific and technological progress). In this type of growth, change occurs through improvements in quality rather than quantity.

If an intensive type of growth occurs in the economy, then the pace may even decrease slightly when compared with the extensive type. However, this does not indicate a decline in economic development or that it is slowing down.

There are several features of growth types:

• In the case of an extensive type of growth, the economy can maintain its proportions and its structural characteristics, while continuing to develop in breadth.
• In the process of intensive type of growth, the economy can become dynamic due to the expansion of production, as well as due to progressive structural changes.

Percentage growth rate formula

In general, the percentage growth rate formula is as follows:

Tr=Pnp/Pkp

Here Tp is the growth rate indicator,

Rnp – indicator at the beginning of the period,

RKP – indicator at the end of the period.

In order to get a more visual result, the resulting value is usually multiplied by 100% to express the formula for the growth rate as a percentage.

Growth rate values

The growth rate reflects the dynamics by what percentage the statistical indicator of the current period changes (grows) when comparing it with the value of the previous period.

If you use different values ​​of the formula, you can see 3 options for the dynamics of values:

1) If the growth rate is more than 100%, then positive dynamics can be observed.

2) Growth rate = 100% does not mean any change.

3) A growth rate of less than 100% indicates negative dynamics.

Growth rate and growth rate

There is often confusion when defining the concepts of growth rate and increment, since their formulas are easy to confuse.

In order to determine the growth rate, the indicator of the base period is subtracted from the indicators of the calculation period, subsequently this result is divided by the indicator of the base period and multiplied by 100%. As a result, we get the growth rate as a percentage.

In order to avoid confusion in these concepts, it can be noted that the growth rate shows the increase in the indicator itself, that is, how many times it has changed in a certain time period.

The growth rate shows how much the value of the indicator has grown over this period of time (comparison).

Examples of problem solving

EXAMPLE 1

EXAMPLE 2

Exercise	To more accurately understand the difference between the growth rate and the growth rate, calculate the growth and growth rate using the following indicators: The basic indicator is 140,000 rubles, The reporting figure is 380,000 rubles.
Solution	To avoid confusion between the concepts of growth and increment, it should be noted that the growth rate is expressed as a percentage of the change in value in the current period when comparing it with the previous one. For calculations we use the following formula: Тп=((П2-П1)/П1)*100% Тп=((380000-140000)/140000) * 100%=171.43% Growth rate formula in percentage: Tr=P 1 /P 2 * 100% Tr = 140000/380000 * 100% = 36.84% Conclusion. We see that the growth rate and the growth rate are different indicators. The growth rate characterizes the indicator in dynamics, and the growth rate characterizes the amount of change in the indicator over a selected period. That is, the indicator increased by 36.84%, while increasing by 171.43% compared to the base one.
Answer	Tr = 36.84%, Tp = 171.43%

Part 2

Calculation of the average growth rate over equal periods of time

Enter the data into the table. This is not required, but the table will allow you to organize your data according to time periods. Create a simple table with two columns; Enter time intervals in the first column, and the corresponding values ​​of a certain quantity in the second.

1. Use a growth rate formula that takes into account the number of time intervals in your data. You need to use standard values ​​for time intervals. What exactly will be used as these values ​​is not important. This method works for information collected over minutes, seconds, days, and so on. In our example, the time period is 1 year. Substitute the initial and final values ​​given to you into the formula: (Final value) = (Initial value) * (1 + Growth rate) n, Where n - number of time intervals.

   • This formula will take you to the average growth rate over one time period (i.e., assuming a steady growth rate). Since in our example the time period is 1 year, we will get the average annual growth rate.

2. Select the "growth rate" variable. To do this, divide both sides of the formula by the "initial value", then raise both sides to the power 1/n, and then subtract 1.

   • As a result of algebraic operations you will get the formula: growth rate = (Final value/Initial value) 1/n - 1.

3. Calculate the growth rate. Substitute the start and end values, as well as the number of time intervals. Perform calculations according to the basic principles of algebra, the order of calculations, and so on.

   • In our example, the initial value is 205, the final value is 310, the number of time periods is 10 (that is, we calculate the growth rate for 10 years). In this case, the average annual growth rate will be equal to (310/205) 1/10 - 1 = 0,0422
   • 0,0422 * 100 = 4,22% . Thus, the average growth rate was 4.22% per year.

If you have ever dealt with the analysis of time series, then you have probably heard a lot about such statistical indicators as growth rate and growth rate. But if the growth rate is a fairly simple concept, then the growth rate often raises many questions, including the formula for calculating it. This article will be useful both for those for whom these concepts are not new, but slightly forgotten, and for those who hear these terms for the first time. Next, we will explain the concepts of growth rate and gain for you and tell you how to find the growth rate.

Growth rate and growth rate: what's the difference?

The growth rate is an indicator that is necessary to determine how much one value of a series occupies in another. As the latter, as a rule, they use the previous value, or the basic one, that is, the one that is at the beginning of the series under study. If the result of calculating the growth rate is more than one hundred percent, then this indicates that there is an increase in the indicator being studied. And vice versa, if the result is less than one hundred percent, this means that the indicator under study is decreasing. Calculating the growth rate is quite simple: you need to find the ratio of the value for the reporting period to the value of the base or previous time period. Unlike the growth rate, the growth rate allows us to calculate how much the value we are studying has changed. During calculations, the resulting positive value may indicate the presence of a growth rate, while at the same time, a negative value indicates that there is a rate of decline in the value relative to the previous or base period. How is the growth rate calculated? To do this calculation, you must first find the ratio of the indicator to the previous one, and then subtract one from the result obtained and multiply the resulting amount by one hundred. By multiplying the number by one hundred you can get the total as a percentage. This method of calculation is used more often than others, but it also happens that only the value of the absolute increase is known, and we do not know the actual value of the indicator that we are analyzing. Is it possible to calculate the growth rate in this case? It is possible, but the standard formula will no longer help us with this; we need to apply an alternative formula. Its essence is to find the percentage of absolute growth to a certain level in comparison with which it was calculated.

How to find absolute growth

To calculate the growth rate, you need to know such a thing as absolute growth. In addition, you need to be able to calculate it, which is extremely easy to do. To determine absolute growth, it is necessary to calculate the difference between the latest and previous economic indicators. For clarity, let's give a simple example. Let’s say that in the reporting period the selected indicator is Z rubles, and in the previous period it is R rubles. To calculate the absolute increase, we just need to create the formula AP=Z-R. Thus, the absolute increase is equal to Z-R rubles. It is important that absolute growth can be both positive and negative. Having learned this information, you can determine whether the selected indicator increases or decreases over a certain period.

How to calculate growth rate

Since the growth rate is a relative value, it is calculated in shares or percentages, and acts as a growth coefficient. If we are faced with the question of how to determine the growth rate, we need to divide the absolute growth for the selected period by the indicator for the initial period and multiply the total by one hundred to get a percentage figure. For clarity, consider an example. Let's say we have the following conditions:

• Revenue for the reporting period is Z rubles;
• Revenue for the previous period is R rubles.

We can already calculate that the absolute increase will be equal to Z-R under such conditions. Next, we calculate the growth rate for the entire selected period. To do this, it is necessary to determine the initial level (let's say this will be the year the enterprise was founded). In this case, the absolute increase is calculated as the difference between the indicators of the last and first year. Then we calculate the growth rate for the entire period by dividing this difference by the indicator for the first year.

Calculation of growth rate on a calculator

Of course, the growth rate formula is not at all complicated, but even with such calculations difficulties can sometimes arise. With the latest technologies, of course, we can find ways that will make our lives easier and help us with calculations even of such complexity. Nowadays you can find special calculators on the Internet designed to calculate analytical indicators of statistical time series. Now, knowledge of complex formulas is not at all necessary in order to find out the rate of growth or increase; it is enough to enter the available data into the appropriate fields of the calculator and it will do all the calculations itself. After we have dotted all the i’s and found out what formulas can be used to find out the rate of growth and increase, it is important to note that in order to give the only correct assessment of the phenomenon under study, it is not enough to have information about only one indicator. For example, a case may arise when at an enterprise the absolute increase in profit gradually increases, but at the same time development slows down. This suggests that any signs of dynamics require a comprehensive analysis.

The growth rate is one of the dynamic, that is, changing indicators of the economic system. To calculate dynamics indicators, you need to set a base level - that is, the one with which all further indicators will be compared.

In economics, the variable base principle is often used. This means that each subsequent indicator is compared with the previous one. To understand how to calculate the growth rate, you need to be able to calculate basic indicators.

Quick navigation through the article

Absolute increase

First of all, we need such a concept as absolute growth. Calculating absolute growth is quite simple: to do this, calculate the difference between the latest economic indicators and the previous ones.

For example, if the selected indicator in the reporting period amounted to X rubles, and in the previous reporting period Y rubles, then the absolute increase will be X-Y rubles.

Absolute growth can be positive or negative. Using this indicator, you can immediately see the increase or decrease of the selected indicator for the selected period.

Rate of increase

The growth rate indicates relative growth. This is a relative value and is calculated as a percentage or fraction, as a growth factor. In order to calculate the growth rate for a selected indicator, you need to divide the absolute growth for the selected period by the indicator for the initial period. We multiply the resulting value by 100 to obtain a percentage.

Let's look at the example already given:

• For the reporting period, revenue is X rubles, and for the previous one - Y rubles.
• The absolute increase is X-Y.
• The growth rate can now be calculated from the available data: (X-Y)/Y *100. This indicator can also be positive or negative.

To calculate the growth rate for the entire period, you need to select an initial, base level (for example, the year the company was founded). Then the absolute increase is calculated as the difference between the indicators of the last year and the first year. By dividing this difference by the indicator for the first year, you can calculate the growth rate for the entire period.

Dynamic indicators of the economic system show its viability and profitability. One of these indicators is the growth rate, which shows the percentage of growth in indicators.

(Tr) is an indicator of the intensity of changes in the level of a series, which is expressed as a percentage, and the growth coefficient (Kr) is expressed in shares. Kr is defined as the ratio of the subsequent level to the previous one or to the indicator taken as the basis of comparison. It determines how many times the level has increased compared to the base level, and in the case of a decrease, what part of the base level is being compared.

We calculate the growth rate, multiply by 100 and get the growth rate

Can be calculated using the formulas:

Also, the growth rate can be determined as follows:

The growth rate is always positive. There is a certain relationship between the chain and base growth rates: the product of the chain growth coefficients is equal to the base growth rate for the entire period, and the quotient of dividing the subsequent base growth rate by the previous one is equal to the chain growth rate.

Absolute increase

Absolute increase characterizes the increase (decrease) in the level of the series over a certain period of time. It is determined by the formula:

where уi is the level of the period being compared;

Уi-1 - Level of the previous period;

Y0 is the level of the base period.

Chain and basic absolute increases are related each other in this way: the sum of successive chain absolute increases is equal to the base, i.e., the total increase for the entire period of time:

Absolute increase can be a positive or negative sign. It shows how much the level of the current period is higher (lower) than the base one, and thus measures the absolute rate of growth or decline in the level.

(Tpr) shows the relative magnitude of the increase and shows by what percentage the compared level is greater or less than the level taken as the basis of comparison. It can be either positive or negative or equal to zero, it is expressed in percentages and shares (growth rates); is calculated as the ratio of absolute growth to the absolute level taken as the base:

The growth rate can be obtained from the growth rate:

The growth rate can be obtained as follows:

Absolute value of 1% increase

The absolute value of 1% growth (A%) is the ratio of absolute growth to the growth rate, expressed as a percentage and shows the significance of each percentage of growth over the same period of time:

Absolute value of one percent increase equal to one hundredth of the previous or base level. It shows what absolute value is hidden behind the relative indicator - one percent increase.

Examples of calculations of dynamics indicators

Before studying the theory on the topic of dynamics indicators, you can look at examples of problems on finding: growth rate, growth rate, absolute growth, average dynamics

About dynamics indicators

When studying the dynamics of social phenomena, the difficulty arises in describing the intensity of change and calculating the average indicators of dynamics that are asked to students.

Analysis of the intensity of change over time occurs using indicators that are obtained by comparing levels. These indicators include: growth rate, absolute growth, absolute value of one percent growth. To generalize the dynamics of the phenomena under study, the following are determined: the average levels of the series and the average indicators of changes in the levels of the series. Dynamics analysis indicators can be determined using constant and variable comparison bases. Here it is customary to call the comparable level the reporting level, and the level from which the comparison is made is the base level.

For calculation dynamics indicators on a permanent basis, you need to compare each level of the series with the same basic level. As a base level, only the initial level in the dynamics series or the level from which a new stage in the development of a phenomenon begins is used. The indicators that are calculated in this case are called basic. To calculate dynamics analysis indicators on a variable basis, you need to compare each subsequent level of the series with the previous one. The calculated dynamics analysis indicators will be called chain indicators.