The multiplicative model is expressed in the following formula. Analysis and diagnostics of financial and economic activities

They are used in cases where the effective indicator is an algebraic sum of several factor indicators.

2. Multiplicative models

Y=
.

This type of model is used when the performance indicator is a product of several factors.

3. Multiples models

Y= .

They are used when the effective indicator is obtained by dividing one factor indicator by the value of another.

4. Mixed (combined) models are a combination in various combinations of previous models:

Y= ; Y= ; Y=(a+b)c .

Conversion factor systems

1. Conversion multiplicative factor systems are carried out by sequential division of the factors of the original system into factor factors.

For example, when studying the process of formation of production volume (see Fig. 6.1), you can use such deterministic models as

VP=KR GV; VP=KR D DV, VP=KR D P NE.

These models reflect the process of detailing the original factor system of a multiplicative form and expanding it by dividing complex factors into factors. The degree of detail and expansion of the model depends on the purpose of the study, as well as on the possibilities of detailing and formalizing indicators within the established rules.

2. Simulation is carried out in a similar way additive factor systems due to dividing one of the factor indicators into its constituent elements-components.

Example. As is known, the volume of product sales

VRP = VVP – VI,

where VVP is the volume of production;

VI – volume of on-farm use of products.

In an agricultural enterprise, grain products were used as seeds (S) and feed (K). Then the given initial model can be written as follows: VP = VVP - (C + K).

3. To class multiples models, the following methods of their transformation are used:

elongation;

formal decomposition;

extensions;

abbreviations.

First the method involves lengthening the numerator of the original model by replacing one or more factors with the sum of homogeneous indicators.

For example, the cost per unit of production can be represented as a function of two factors: the change in the amount of costs (3) and the volume of output (VVP). The initial model of this factor system will have the form

C= .

If the total amount of costs (3) is replaced by their individual elements, such as wages (W), raw materials and materials (SM), depreciation of fixed assets (A), overhead costs (OC), etc., then the deterministic factor model will have type of additive model with a new set of factors

C= +++=X +X +X +X ,

where X – labor intensity of products; X – material consumption of products; X – capital intensity of production; X – level of overhead costs

Formal decomposition method factor system provides lengthening the denominator of the original factor model by replacing one or more factors with the sum or product of homogeneous indicators.

If b=l+m+n+р, That

Y=
.

As a result, we obtained a final model of the same type as the original factor system (multiple model). In practice, such decomposition occurs quite often. For example, when analyzing the production profitability indicator (P):

P= ,

where /7 is the amount of profit from sales of products;

3 - the amount of costs for production and sales of products.

If the sum of costs is replaced by its individual elements, the final model as a result of the transformation will take on the following form:

P=
.

Cost of one ton-kilometer (C
) depends on the amount of costs for maintaining and operating the car (3) and on its average annual output (AG). The initial model of this system will have the form

WITH
=.

Considering that the average annual production of a car, in turn, depends on the number of days worked by one car per year (D), the duration of the shift (P) and the average hourly output (AS), we can significantly lengthen this model and decompose the increase in cost into a larger number of factors:

WITH
=
.

Extension method provides for the expansion of the original factor model due to multiplying the numerator and denominator of a fraction by one or more new indicators. For example, if the original model

introduce a new indicator c, then the model will take the form

.

The result was a final multiplicative model in the form of a product of a new set of factors.

This modeling method is very widely used in analysis. For example, the average annual production by one worker (labor productivity indicator) can be written as follows: GV = VP / KR. If we introduce such an indicator as the number of days worked by all employees (D), we obtain the following model of annual output:

GV=
,

where DV is the average daily output; D – number of days worked by one employee.

After introducing the indicator of the number of hours worked by all employees (T), we obtain a model with a new set of factors: average hourly output (AS), number of days worked by one employee (D) and length of the working day (P):

Reduction method represents the creation of a new factor model by dividing the numerator and denominator of a fraction by the same exponent:

.

In this case, the final model is of the same type as the original one, but with a different set of factors.

Another example. The economic return on assets of an enterprise (ROA) is calculated by dividing the amount of profit (P) by the average annual cost of the enterprise's fixed and working capital (A): ROA=P/A.

If we divide the numerator and denominator by the sales volume of products (S), we obtain a multiple model, but with a new set of factors: profitability of products sold and capital intensity of products:

 Performance indicators can be decomposed into their constituent elements (factors) in various ways and presented in the form of various types of deterministic models. The choice of modeling method depends on the object of study, the goal, as well as the professional knowledge and skills of the researcher. The process of modeling factor systems is a very complex and crucial moment in economic analysis. The final results of the analysis depend on how realistically and accurately the created models reflect the relationship between the indicators being studied..

Multiplicative model.

Example 2. Revenue from sales of products (product volume - V) can be expressed as the product of a set of factors: number of personnel (nr), the share of workers in the total number of personnel (dр); average annual output per worker (Vr)

V = Chp * dр * Вр

Ø Transformations of deterministic factor models

To model various situations in factor analysis, special methods for transforming standard factor models are used. They are all based on reception detail. Detailing– decomposition of more general factors into less general ones. Detailing allows, based on knowledge of economic theory, to streamline the analysis, promotes a comprehensive consideration of factors, and indicates the significance of each of them.

The development of a deterministic factor system is achieved, as a rule, by detailing complex factors. Elemental (simple) factors are not decomposed.

Example 1. Factors

Most of the traditional (special) techniques of deterministic factor analysis are based on elimination. Reception elimination used to identify an isolated factor by excluding the effects of all others. The starting premise of this technique is as follows: All factors change independently of each other: first one changes, and all the others remain unchanged, then two, three, etc. change. with the rest remaining unchanged. The elimination technique is, in turn, the basis for other techniques of deterministic factor analysis, chain substitutions, index, absolute and relative (percentage) differences.

Ø Acceptance of chain substitutions

Target.

Application area. All types of deterministic factor models.

Restricted use.

Application procedure. A number of adjusted values ​​of the performance indicator are calculated by sequentially replacing the basic values ​​of the factors with the actual ones.

It is advisable to calculate the influence of factors in an analytical table.

Original model: P = A x B x C x D

Ø Acceptance of absolute differences

Target. Measuring the isolated influence of factors on changes in performance indicators.

Application area. Deterministic factor models; including:

1. Multiplicative

2. Mixed (combined)

type Y = (A-B)C and Y = A(B-C)

Restrictions on use.Factors in the model should be sequentially arranged: from quantitative to qualitative, from more general to more specific.

Application procedure. The magnitude of the influence of an individual factor on the change in the performance indicator is determined by multiplying the absolute increase in the factor under study by the basic (planned) value of the factors that are located to the right of it in the model, and by the actual value of the factors located to the left.

In the case of the original multiplicative model P = A x B x C x D we obtain: change in the effective indicator

1. Due to factor A:

DP A = (A 1 – A 0) x B 0 x C 0 x D 0

2. Due to factor B:

DP B = A 1 x (B 1 - B 0) x C 0 x D 0

3. Due to factor C:

DP C = A 1 x B 1 x (C 1 - C 0) x D 0

4. Due to factor D:

DP D = A 1 x B 1 x C 1 x (D 1 - D 0)

5. General change (deviation) of the performance indicator (balance of deviations)

D P = D P a + D P in + D P c + D P d

The balance of deviations must be maintained (just as in the reception of chain substitutions).

Ø Acceptance of relative (percentage) differences

Target. Measuring the isolated influence of factors on changes in performance indicators.

Application area. Deterministic factor models including:

1) multiplicative;

2) combined type Y = (A – B) C,

It is advisable to use when the previously determined relative deviations of factor indicators in percentages or coefficients are known.

There are no requirements for the sequence of arrangement of factors in the model.

Original package. The resultant characteristic changes in proportion to the change in the factor characteristic.

Application procedure. The magnitude of the influence of an individual factor on the change in the effective indicator is determined by multiplying the basic (planned) value of the effective indicator by the relative increase in the factor characteristic.

Original model:

Change in performance indicator:

1. Due to factor A:

2. Due to factor C:

Balance of deviations. The total deviation of the performance indicator consists of deviations by factors:

D Y = Y 1 - Y 0 = D Y A + D Y B + D Y C

Ø Index method

Target. Measuring relative and absolute changes in economic indicators and the influence of various factors on it.

Application area.

1. Analysis of the dynamics of indicators, including aggregated (added) indicators.

2. Deterministic factor models; including multiplicative and multiple ones.

Application procedure. Absolute and relative changes in economic phenomena.

Aggregate index of product value (turnover)

I pq – characterizes the relative change in the cost of products in current prices (prices of the corresponding period)

The difference between the numerator and denominator (åp 1 q 1 - åp o q 0) – characterizes the absolute change in the cost of products in the reporting period compared to the base one.

Aggregate price index:

I p – characterizes the relative change in the average price for a set of types of products (goods).

The difference between the numerator and denominator (åp 1 q 1 - åp o q 1) – characterizes the absolute change in the cost of products due to changes in prices for certain types of products.

characterizes the relative change in production volume at fixed (comparable) prices.

åq 1 p 0 - åq 0 p 0 – the difference between the numerator and denominator characterizes the absolute change in the cost of products due to changes in the physical volumes of its various types.

Based on index models, it is carried out factor analysis.

Thus, a classic analytical task is to determine the influence of quantity factors (physical volume) and prices on the cost of products:

In absolute terms

å p 1 q 1 - å p 0 q 0 = (å q 1 p 0 - å q 0 p 0) + (å p 1 q 1 - å p 0 q 1).

Similarly, using the index model, it is possible to determine the influence on the total cost of production (zq) of the factors of its physical volume (q) and the cost of a unit of production of various types (z)

In absolute terms

å z 1 q 1 - å z 0 q 0 = (å q 1 z 0 - å q 0 z 0) + (å z 1 q 1 - å z 0 q 1)

Ø Integral method

Target. Measuring the isolated influence of factors on changes in performance indicators.

Application area. Deterministic factor models, including

· Multiplicative

· Multiples

Mixed type

Advantages. Compared to methods based on elimination, it gives more accurate results, since the additional increase in the effective indicator due to the interaction of factors is distributed in proportion to their isolated impact on the effective indicator.

Application procedure. The magnitude of the influence of an individual factor on the change in the performance indicator is determined on the basis of formulas for different factor models, derived using differentiation and integration in factor analysis.

Change in performance indicator due to factor x

D¦ x = D xy 0 + DxDу / 2

due to factor y

D¦ y = Dух 0 +DуDх / 2

Overall change in the effective indicator: D¦ = D¦ x + D¦ y

Balance of deviations

D¦ = ¦ 1 - ¦ 0 = D¦ x + D¦ y

Condition: determine the influence of the number of personnel, the number of shifts worked and output per shift per employee on the change in production volume (N p).

Draw a conclusion.

Solution algorithm:

The factor model describing the relationship between indicators has the form: N = h * cm * v

Initial data - factors and the resulting indicator are presented in the analytical table:

Methods of deterministic factor analysis used to solve three-factor models:

- chain substitution;

- absolute differences;

- weighted final differences;

- logarithmic;

- integral.

Application of various methods to solve a typical problem:

1. Chain substitution method. The use of this method involves the identification of quantitative and qualitative factor characteristics: here the quantitative factors are the number of personnel and the number of shifts worked; qualitative sign - production.

a) N 1 = h 0 * Cm 0 * IN 0 =5184 thousand units;

b) N 2 = h 1 * Cm 0 * IN 0 =25 * 144 * 1500 =5400 thousand units;

c) N (h) = 5400 – 5184 = 216 thousand units;

N 3 = h 1 * Cm 1 * IN 0 =25 * 146 * 1500 =5475 thousand pieces;

N(cm) = 5475 – 5400 = 75 thousand pieces;

N 4 = h 1 * Cm 1 * IN 1 =25 * 146 * 1505 =5493.25 thousand pieces;

N(B) = 5493.25 – 5475 = 18.25 thousand units;

N= N(h) + N(cm) + N (B) = 216 + 75 +18.25 = 309.25 thousand units.

4.2 . Absolute difference method also involves identifying quantitative and qualitative factors that determine the sequence of substitution:

A) N(h) = h*cm 0 * IN 0 = 1 * 14 * 1500 = 216 thousand units;

b) N(cm) = cm*h 1 * IN 0 = +2 * 25 * 1500 = 75 thousand units;

V) N(B)= B*h 1 * Cm 1 = +5 * 25 * 146 = 18.25 thousand pieces;

N= N(h) + N(cm) + N (B) = 309.25 thousand units.

Relative difference method

A) N(h) =
thousand pieces;

b) N(cm) = thousand. PC.;

V) N(B) thousand PC.;

General influence of factors: N= N(h) + N(cm) + N (B) = 309.3 thousand units.

4.4 . Weighted Finite Difference Method involves the use of all possible formulations based on the method of absolute differences.

Substitution 1 is performed in the sequence
the results are determined in the previous calculations:

N(h) = 216 thousand units;

N(cm) = 75 thousand pieces;

N (B) = 18.25 thousand pcs.

Substitution 2 is performed in the sequence
:

a)+1 * 1500 * 144 = 216 thousand units;

b) +5 * 25 * 11 = 18 thousand units;

c) +2 * 25 *1505 = 75.5 thousand units;

Substitution 3 is performed in the sequence
:

a) 2 * 24 * 1500 = 72 thousand units;

b) 1 * 146 * 1500 = 219 thousand units;

c) + 5 * 25 * 146 = 18.25 thousand pcs.

Substitution 4 is performed in the sequence
:

a) 2 * 1500 * 5 * 146 * 24 = 17.52 thousand units;

b) 5 * 146 * 24 = 17.52 thousand pieces;

c) 1 * 146 * 1515 = 219.73 thousand units;

Substitution 5 is performed in the sequence
:

a) 5 * 144 * 24 = 17.28 thousand pieces;

b) 2 * 1505 * 24 = 72.27 thousand units;

c) 1 * 146 * 1505 = 219.73 thousand pcs.

Substitution 6 is performed in the sequence
:

a) 5 * 24 * 144 = 17.28 thousand pieces;

b) 1 * 1505 * 144 = 216.72 thousand units;

c) 2 * 1505 * 25 = 75.25 thousand pcs.

Influence of factors on the resulting indicator

4.5. Logarithmic method assumes the distribution of the deviation of the resulting indicator in proportion to the share of each factor in the amount of deviation of the result

a) the share of influence of each factor is measured by the corresponding coefficients:

b) the influence of each factor on the resulting indicator is calculated as the product of the deviation of the result by the corresponding coefficient:

309,25*0,706 = 218,33;

309,25*0,2438 = 73,60;

309,25* 0,056 = 17,32.

4.6. Integral method involves the use of standard formulas to calculate the influence of each factor:

5. The calculation results of each of the listed methods are combined in a table of the cumulative influence of factors.

Cumulative influence of factors:

A comparison of the calculation results obtained by various methods (logarithmic, integral and weighted finite differences) shows their equality. It is convenient to replace cumbersome calculations using the method of weighted finite differences by using logarithmic and integral methods, which give more accurate results compared to the methods of chain substitution and absolute differences.

5. Conclusion: The volume of production increased by 309.25 thousand units.

Positive impact in the amount of 217.86 thousand units. had an increase in the number of personnel.

As a result of the increase in the number of shifts, the output volume increased by 73.6 thousand units.

Due to the increase in production, the volume of production increased by 17.76 thousand units.

Extensive factors had the strongest impact on the volume of production: an increase in the number of personnel and the number of shifts worked. The total influence of these factors was 94.26% (70.45 +23.81). The influence of the production factor accounts for 5.74% of the growth in output.

Note: The application of the considered techniques is similar in relation to multiplicative models of any number of factors. However, the use of the method of weighted finite differences to multifactor models is limited by the need to perform a large number of calculations, and this is inappropriate in the presence of other, simpler and more rational methods, for example, logarithmic.

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An example of a multiplicative model is a two-factor model of sales volume

where H is the average number of employees;

CB - average output per employee.

Multiple models:

An example of a multiple model is the indicator of the turnover period of goods (in days). TOB.T:

,

where ST is the average stock of goods; OR - one-day sales volume.

Mixed models are a combination of the above models and can be described using special expressions:

Examples of such models are cost indicators per 1 ruble. commercial products, profitability indicators, etc.

To study the relationship between indicators and quantitatively measure the many factors that influenced the performance indicator, we present general rules for transforming models to include new factor indicators.

To detail the generalizing factor indicator into its components, which are of interest for analytical calculations, the technique of lengthening the factor system is used.

If the original factor model

then the model will take the form

.

To identify a certain number of new factors and construct the factor indicators necessary for calculations, the technique of expanding factor models is used. In this case, the numerator and denominator are multiplied by the same number:

.

To construct new factor indicators, the technique of reducing factor models is used. When using this technique, the numerator and denominator are divided by the same number.

.

The detail of factor analysis is largely determined by the number of factors whose influence can be quantitatively assessed, therefore multifactorial multiplicative models are of great importance in the analysis. Their construction is based on the following principles: · the place of each factor in the model must correspond to its role in the formation of the effective indicator; · the model should be built from a two-factor complete model by sequentially dividing factors, usually qualitative, into components; · when writing a formula for a multifactor model, factors should be arranged from left to right in the order of their replacement.

Building a factor model is the first stage of deterministic analysis. Next, determine the method for assessing the influence of factors.

The method of chain substitutions consists in determining a number of intermediate values ​​of the generalizing indicator by sequentially replacing the basic values ​​of the factors with the reporting ones. This method is based on elimination. Eliminate means to eliminate, exclude the influence of all factors on the value of the effective indicator, except one. Moreover, based on the fact that all factors change independently of each other, i.e. First, one factor changes, and all the others remain unchanged. then two change while the others remain unchanged, etc.

In general, the application of the chain production method can be described as follows:

where a0, b0, c0 are the basic values ​​of factors influencing the general indicator y;

a1, b1, c1 - actual values ​​of factors;

ya, yb, are intermediate changes in the resulting indicator associated with changes in factors a, b, respectively.

The total change Dу=у1–у0 consists of the sum of changes in the resulting indicator due to changes in each factor with fixed values ​​of the other factors:

Let's look at an example:

table 2

Initial data for factor analysis

We will analyze the impact of the number of workers and their output on the volume of marketable output using the method described above based on the data in Table 2. The dependence of the volume of commercial products on these factors can be described using a multiplicative model:

Then the effect of a change in the number of employees on the general indicator can be calculated using the formula:

Thus, the change in the volume of marketable products was positively influenced by a change in the number of employees by 5 people, which caused an increase in production volume by 730 thousand rubles. and a negative impact was had by a decrease in output by 10 thousand rubles, which caused a decrease in volume by 250 thousand rubles. The combined influence of two factors led to an increase in production volume by 480 thousand rubles.

The advantages of this method: versatility of application, ease of calculations.

The disadvantage of the method is that, depending on the chosen order of factor replacement, the results of factor decomposition have different meanings. This is due to the fact that as a result of applying this method, a certain indecomposable residue is formed, which is added to the magnitude of the influence of the last factor. In practice, the accuracy of factor assessment is neglected, highlighting the relative importance of the influence of one or another factor. However, there are certain rules that determine the sequence of substitution: · if there are quantitative and qualitative indicators in the factor model, the change in quantitative factors is considered first; · if the model is represented by several quantitative and qualitative indicators, the substitution sequence is determined by logical analysis.

Deterministic factor analysis puts forward as a goal the study of the influence of factors on an effective indicator in cases of its functional dependence on a number of factor characteristics.

Functional dependence can be expressed by various models - additive; multiplicative; multiple; combined (mixed).

Additive the relationship can be represented as a mathematical control, reflecting the case when the effective indicator (y) is the algebraic sum of several factor characteristics:

Multiplicative the relationship reflects the direct proportional dependence of the general indicator under study on the factors:

where P is the generally accepted sign for the product of several factors.

Multiple The dependence of the effective indicator (y) on factors is mathematically reflected as a quotient of their division:

Combined (mixed) The relationship between effective and factor indicators is a combination in various combinations of additive, multiplicative and multiple dependence:

Where a, b, c etc. - variables.

There are a number of methods for modeling factor systems: the method of dissection; lengthening technique; the method of expansion and the method of contraction of the original multiple two-factor systems of the type: -. As a result of the modeling process, additive-multiple, multiplicative and multiplicative-multifactorial systems of the type are formed from a two-factor multiple model:

Methods for measuring the influence of factors in deterministic models

Widely used in analytical calculations chain substitution method due to the possibility of using it in deterministic models of all types. The essence of this technique is that to measure the influence of one of the factors, its base value is replaced by the actual one, while the values ​​of all other factors remain unchanged. Subsequent comparison of the performance indicators before and after replacing the analyzed factor makes it possible to calculate its influence on the change in the performance indicator. A mathematical description of the method of chain substitutions when used, for example, in three-factor multiplicative models is as follows.

Three-factor multiplicative system:

Consecutive substitutions:

Then, to calculate the influence of each factor, you need to perform the following steps:

Deviation balance:

We will consider the sequence of calculations using the method of chain substitutions using a specific numerical example, when the dependence of the effective indicator on the factor indicators can be represented by a four-factor multiplicative model.

The cost of products sold was chosen as the performance indicator. The goal is to study the change in this indicator under the influence of deviations from the comparison base of a number of labor factors - the number of workers, daily and intra-shift losses of working time and average hourly output. The initial information is given in table. 15.1.

Table 15.1

Information for factor analysis of changes in the value of goods sold

products

The original four-factor multiplicative model:

Chain substitutions:

Calculations of the impact of changes in factor indicators are given below.

1. Change in the average annual number of workers:

2. Change in the number of days worked by one worker:

3. Change in the average working day:

4. Change in average hourly output:

Deviation balance:

The results of calculations using the method of chain substitutions depend on the correct determination of the subordination of factors, on their classification into quantitative and qualitative. Changes in quantitative multipliers should be carried out earlier than qualitative ones.

Widely used in multiplicative and combined (mixed) models method of absolute differences, also based on the elimination technique and characterized by simplicity of analytical calculations. The rule for calculations using this method in multiplicative models is that the deviation (delta) for the analyzed factor indicator must be multiplied by the actual values ​​of the multipliers (factors) located to the left of it, and by the basic values ​​of those located to the right of the analyzed factor.

We will consider the order of factor analysis using the method of absolute differences for combined (mixed) models using a mathematical description. Initial baseline and actual models:

Algorithm for calculating the influence of factors using the absolute difference method:

Deviation balance:

Relative difference method is used, just like the method of absolute differences, only in multiplicative and combined (mixed) models.

For multiplicative models, the mathematical description of this technique will be as follows. Initial basic and actual four-factor multiplicative systems:

For factor analysis using the method of relative differences, it is first necessary to determine the relative deviations for each factor indicator. For example, for the first factor this will be the percentage of its change to the base:

Calculations are then made to determine the effect of changing each factor.

Let's consider the sequence of actions using a numerical example, the initial information for which is contained in table. 15.1.

In gr. 7 tables Table 15.1 shows the relative deviations for each factor indicator.

The results of the influence of changes in each factor on the deviation of the performance indicator from comparison will be as follows:

Balance of deviations: RP, -RP 0 =432,012-417,000 = +15,012 thousand rubles. (-9811.76) + 3854.62+ (-10,673.21) + 31,642.36 = 15,012.01 thousand rubles. Indices represent general indicators of comparison in time and space. They reflect the percentage change in the phenomenon being studied over a period of time compared to the base period. Such information makes it possible to compare changes in various factors and analyze their behavior.

In factor analysis index method used in multiplicative and multiple models.

Let's turn to its use for analyzing multiple models. Thus, the aggregate index of physical sales volume (Jg) has the form:

Where q- indexed quantity value; p 0- co-measurer (weight), price fixed at the level of the base period.

The difference between the numerator and denominator in this index reflects the change in trade turnover due to changes in its physical volume.

The Paasche aggregate price index (formula) is written as follows:

Using the information contained in table. 15.1, let us calculate the impact of changes in the index of the average number of workers and the index of average annual output per worker on the growth rate of sold products.

Labor productivity (LP) of one worker in the base year is equal to 245.29 million rubles, and in the reporting year - 260.25 million rubles. The growth index (/pt) will be 1.0610 (260.25: 245.29).

Growth indices of sold products (/rp) and the average annual number of workers (/nw) according to table. 15.1 - accordingly:

The relationship between the three indicated indices can be represented in the form of a two-factor multiplicative model:

Factor analysis using the absolute difference method gives the following results.

1. Impact of changes in the average number of workers index:

2. Impact of changes in the labor productivity index:

Balance of deviations: 1.0360 - 1.0 = +0.0360 or (-0.0235) + 0.0596 = + 0.0361 100 = 3.61%.

Integral method used in deterministic factor analysis in multiplicative, multiple and combined models.

This method allows you to decompose the additional increase in the effective indicator in connection with the interaction of factors between them.

The practical use of the integral method is based on specially developed working algorithms for the corresponding factor models. For example, for a two-factor multiplicative model (y = A V) the algorithm will be like this:

As an example, we use a two-factor dependence of sold products (RP) on changes in the average annual number of workers (NA) and their average annual output (AP):

Initial information is available in table. 15.1.

Impact of changes in average annual numbers:

Impact of changes in labor productivity (average annual output per worker):

Deviation balance:

In factor analysis in additive models of the combined (mixed) type, it can be used method of proportional division. Algorithm for calculating the influence of factors on the change in the effective indicator for an additive system of type y = a + b + c will be like this:

In combined models, the influence of second-level factors can be calculated by way of equity participation. First, the share of each factor in the total amount of their changes is calculated, and then this share is multiplied by the total deviation of the effective indicator. The calculation algorithm is as follows:

Let us systematize the considered methods for calculating the influence of individual factors in deterministic factor analysis using the scheme (Fig. 15.4).