The essence and purpose of the method of relative differences. Scope of its application. Algorithm for calculating the influence of factors in this way

The method of relative differences, like the previous one, is used to measure the influence of factors on the growth of a performance indicator only in multiplicative models and combined types Y = (a - b)c. It is much simpler than chain substitutions, which makes it very effective under certain circumstances. This primarily applies to those cases when the source data contains previously determined relative deviations of factor indicators in percentages or coefficients.

Let us consider the methodology for calculating the influence of factors in this way for multiplicative models of type.

;
;
.

The deviation of the effective indicator due to each factor is determined as follows.

 To calculate the influence of the first factor, it is necessary to multiply the basic (planned) value of the effective indicator by the relative increase of the first factor, expressed as a percentage, and divide the result by 100:

.

To calculate the influence of the second factor, you need to add the change in it due to the first factor to the planned value of the effective indicator and then multiply the resulting amount by the relative increase in the second factor as a percentage and divide the result by 100:

.

The influence of the third factor is determined in a similar way: to the planned value of the effective indicator, it is necessary to add its increase due to the first and second factors and multiply the resulting amount by the relative increase of the third factor, etc.:

.

Let us consolidate the considered methodology using the example given in Table 7.1:

As you can see, the calculation results are the same as when using the previous methods

The method of relative differences is convenient to use in cases where it is necessary to calculate the influence of a large set of factors (8-10 or more). Unlike previous methods, the number of calculations is significantly reduced.

Methods of proportional division and equity participation.

Essence, purpose and scope of application of methods of proportional division and equity participation, procedure and calculation algorithms

In a number of cases, to determine the magnitude of the influence of factors on the growth of a performance indicator, it can be used proportional division method . This applies to cases where we are dealing with additive Y type models =
And mixed type
.

IN first In the case when we have a single-level model of type Y=a+b+c, the calculation is carried out as follows:

;
;
.

For example, the level of profitability (R) decreased by 8% due to an increase in the enterprise’s capital by 200 thousand rubles. At the same time, the value of fixed capital (a) increased by 250 thousand rubles, and working capital (b) decreased by 50 thousand rubles. This means that, due to the first factor, the level of profitability decreased, and due to the second, it increased:

Calculation method for mixed models somewhat more complicated. The relationship of factors in the combined model is shown in Fig. 7.1.

Performance indicator

First level factors

Second level factors

Fig 7.1 Scheme of interaction of factors

When known
and
, then to determine
,
,
, you can use the method of proportional division" which is based on the proportional distribution of the increase in the effective indicator Y due to a change in factor B between the second level factors D, N and M according to their value. The proportionality of this distribution is achieved by determining a constant for all factors proportionality coefficient (K ) which shows the amount of change in the effective indicator Y due to a change in factor B by one.

The value of the proportionality coefficient (K ) is defined as follows:

.

By multiplying this coefficient by the absolute deviation B due to the corresponding factor, we find the deviations of the effective indicator:

;
;
.

For example, the cost of 1 t/km due to a decrease in the average annual production of a car (C ) increased by 180 rubles. At the same time, it is known that the average annual production of a vehicle (GV) has decreased due to:

A) above-planned machine downtime -5000 t/km;

B) above-plan idle runs -4000 t/km;

B) incomplete use of carrying capacity -3000 t/km

Total -12000 t/km

From here you can determine the change in cost under the influence of second-level factors:

Total:+180rub

To solve this type of problem you can also use equity participation method (Table 7.3) .

Table.7.3

Calculation of the influence of factors on the performance indicator using the equity method

 WITHAt the beginning, the share of each factor in the total amount of their increases is determined, which is then multiplied by the total increase in the effective indicator:

;

;

.

Absolute difference method

It is used in multiplicative and multiplicative-additive models and consists in calculating the magnitude of the influence of factors by multiplying the absolute increase in the factor under study by the base value of the factor located to the right of it and by the actual value of the factors located to the left. For example, for a multiplicative factor model like Y = a-b-s-y the change in the magnitude of the influence of each factor on the performance indicator is determined from the expressions:

where /> th, sat, ¿4- values ​​of indicators in the base period; jaf,bf, sf - the same in the reporting period (i.e. actual); Aa = bf - Ob, AB = bf - b6, Ac = sf - sb; Asi = b?f - A.

Relative difference method

The method of relative differences, like the method of absolute differences, is used only in multiplicative and multiplicative-additive models to measure the influence of factors on the growth of a performance indicator. It consists in calculating the relative deviations of the values ​​of factor indicators with the subsequent calculation of the change in the effective indicator Uf due to each factor relative to the base Uf. For example, for a multiplicative factor model like

Y = abc the change in the magnitude of the influence of each factor on the performance indicator is determined as follows:

The method of relative differences, having a high level of clarity, provides the same results as the method of absolute differences with a smaller amount of calculations, which is quite convenient when there are a large number of factors in the models.

Method of proportional division (equity participation)

Applicable for additive Y = a + b + c and multiple models like Y= a/(b + c + d), including multi-level ones. This method consists of proportional distribution of the increase in the effective indicator U by changing each of the factors between them. For example, for an additive model of type Y = a + b + c influence is calculated as

We will assume that Y is the cost of production; a, b, c - costs for materials, labor and depreciation, respectively. Let the level of overall profitability of the enterprise decrease by 10% due to an increase in production costs by 200 thousand rubles. At the same time, costs for materials decreased by 60 thousand rubles, labor costs increased by 250 thousand rubles, and depreciation costs increased by 10 thousand rubles. Then due to the first factor (A) profitability level has increased:

Due to the second (b) and the third (c) factors, the level of profitability decreased:

Differential calculus method

Assumes that the total increment of a function is divided into terms, where the value of each of them is determined as the product of the corresponding partial derivative and the increment of the variable by which this derivative is calculated.

Consider a function of two variables: g=/(x, y). If this function is differentiable, then its increment can be represented as

Where Ag = (2(- 2о)- change of function; Oh = ("Г] - ,г0) - change in the first factor; Ау = (у^ - r/()) - change in the second factor.

Sum (dg/dh)Ah + (dg/du)Ay - the main part of the increment of the differentiable function (which is taken into account in the method of differential calculus); 0Ud~r ^+d7/ - an indecomposable remainder, which is an infinitesimal value for sufficiently small changes in the factors x and u. This component is not taken into account in the differential calculus method under consideration. However, with significant changes in factors (Oh And Ay) Significant errors may occur in assessing the influence of factors.

Example 16.1. Function G looks like z = x-y, for which the initial and final values ​​of the influencing factors and the resulting indicator are known (x&y0, r0,X,y, 2). Then the influence of influencing factors on the value of the resulting indicator is determined by the expressions

Let us calculate the value of the residual term as the difference between the value of the total change in the function Dg = X ■ y - x0 o g/o and the sum of the influences of influencing factors g. + Dg(/ = y0-Ax + xn■ &y:

Thus, in the method of differential calculus, the indecomposable remainder is simply discarded (logical

error of the differentiation method). This approximation of the considered method is a disadvantage for economic calculations, where an exact balance of changes in the resulting indicator and the sum of the influence of influencing factors is required.

(to contents)

Example 1. Create a factor system for the volume of gross output that is functionally dependent on the following indicators:

· number of days worked by one employee per year (D);

· average hourly output per worker (AC);

· average working day (P);

· average daily production per worker (DV);

· average annual production per worker (GW);

· average annual number of workers (UA).

Solution:

Factor model of gross output volume:

VP = CR*GV or VP = CR*D*DV or VP = CR*D*P*CHV.

Example 2. Based on the initial data of Table 14 (in italics), determine the absolute and relative change in sales revenue and the magnitude of the influence of the volume and price of products sold on this indicator using the following methods:

· chain substitutions;

· absolute differences;

· relative differences;

· integral;

· logarithms

based on model:

B =VRP * C,

where B is revenue from sales of products,

VRP – volume of products sold,

P – price of sold products.

Table 14

Indicators	Base	Report	Changes
			abs.	rel.
1	2	3	4=3-2	5=4/2*100%
1.Volume of products sold, thousand units.	10	12
2.Price of products sold, thousand rubles.	7	10		42,8
3. Revenue (2*3), million rubles.		120		71,4

Solution:

1. Chain substitution method

We calculate the value of revenue by sequentially replacing the basic values ​​of factor indicators with the values ​​of the reporting period:

B 0 =VRP 0 * C 0 = 10 * 7 = 70 million rubles.

In condition1 =VRP 1 * C 0 = 12 * 7 = 84 million rubles.

B 1 =VRP 1 * C 1 = 12 * 10 = 120 million rubles.

Let's evaluate the influence of each factor separately:

∆V V RP = In condition1 - In 0 =84 - 70 = 14 million rubles.

∆V C = V 1 – V condition1 =120 - 84 = 36 million rubles.

Examination:

∆V= V 1 -V 0 =∆V V RP +∆V C =120-70=14+36=50 million rub.

2. Absolute difference method

∆V V RP = ∆ VRP *C 0 = 2*7 = 14 million rubles.

∆V C =VRP 1 * ∆C = 12 * 3 = 36 million rubles.

Examination:

3. Relative difference method

∆V V RP = V 0 *(∆VRP/VRP 0)= 70*(2/10)=14 million rubles.

∆V C =(V 0 +∆V V RP ) *(∆C/C 0)= 84*(3/7) = 36 million rubles.

Examination:

∆B= 120-70=14+36=50 million rubles.

4. Integral method

∆V V RP = 0,5*∆ VRP *(C 0 + C 1) = 0.5*2*(7+10) = 17 million rubles.

∆V C = 0.5*∆C*(VRP 0 +VRP 1) =0.5*3*(10+12) = 33 million rubles.

Examination:

5. Logarithm method

∆V V RP = ∆V*lg( VRP 1 /VRP 0)/lg(B 1 / B 0) = 50*(0.079/0.23) = 17 million rubles.

∆V C =∆V*lg(C 1 /C 0)/lg(B 1 / B 0) = 50*(0.15/0.23) = 33 million rubles.

Examination:

∆B= 120-70=17+33=50 million rubles.

Conclusion: calculations showed that the greatest impact on the increase in sales revenue had an increase in product prices. Three out of five methods gave the same results on the magnitude of the factorial influence on the performance indicator. The use of the integral method and the logarithm method made it possible to take into account the interaction of factor indicators with each other and, as a result, more accurately determine their influence on the effective indicator, in particular, to identify a stronger influence of the volume factor.

Example 3. Based on the initial data (in italics) given in Table 15, determine the absolute and relative change in gross profit from product sales and the magnitude of the influence of factors on gross profit by the method of proportional division and the equity method, using the model:

where Pr is the gross profit from product sales,

B – revenue from sales of products,

C – cost of goods sold.

Table 15

Indicators	Basic year	Reporting year	Changes
			abs.	rel.
			4=3-2	5=4/2*100%
1.Revenue, thousand rubles.	56 377	62 849	6472	11,48
2. Cost, thousand rubles.	46 496	57 738	11242	24,18
3.Gross profit (1-2), thousand rubles.	9881	5111	4770	48,27

Solution:

1. Proportional division method

thousand. rub.

thousand. rub.

Examination :

thousand. rub.

2. Method share participation

thousand. rub.

thousand. rub.

Examination :

thousand. rub.

Conclusion: gross profit from product sales in the reporting period decreased by 4,770 thousand rubles. or by 48.27% compared to the base period due to the rapid growth of product costs over the growth of sales revenue. The share of the negative impact of cost growth on the decrease in gross profit amounted to 63.46% (3027.23/4770*100%).

Example 4. Based on the data in Table 16, determine the existence of a relationship between sales revenue and advertising costs, calculate the correlation coefficients, determination coefficients and determine the correlation ratio.

Table 16

Solution: Let's calculate the derivatives for analysis in Table 17:

Table 17

			X*Y	X 2	Y2	Y x
			2800	1600	4900
			3024	1764	5184	71,2
			2584	1444	4624	68,8
			2990	2116	4225	73,6
			3520	1936	6400	72,4
			3600	2304	5625	74,8
			3900	2500	6084
Total	308	508	22418	13664	37042	506,8

Based on the table, we build a system of equations

from here

The relationship equation describing the dependence of sales revenue on advertising costs received the following expression:

Y x =46+ 0,6 x

Let's calculate the correlation coefficient:

Let's calculatecoefficientdetermination:

Conclusion: in this case, the relationship between the indicators is insignificant, the value of the coefficient of determination indicates that revenue from product sales depends by 22% on advertising costs, and other factors account for 78% of the change in its level.

Task 2.1. Convert the analytical formula using the expansion method:

where GW is annual output (labor productivity);

CR – average number of personnel,

in such a way that it reflects the dependence of labor productivity on capital productivity and capital-labor ratio.

Task 2.2. Using the reduction method, transform the analytical formula:

where FO is the capital productivity of fixed production assets;

VP – gross output for the year;

OPF – average annual cost of fixed production assets,

in such a way that it reflects the relationship between the average annual output of one worker and the capital-labor ratio.

Problem 2.3. Using the extension method, transform the analytical formula:

where ME is the material intensity of products;

MR – costs of material resources;

B – revenue,

in such a way that it reflects the relationship between the material intensity of raw materials and materials, fuel intensity, energy intensity, material intensity of other costs.

Problem 2.4. Systematize the factors that determine the amount of profit from product sales:

- revenue (B);

- volume of sales (VRP);

- total costs (Z);

- unit price (P);

- structureproducts ();

- unit cost (C)

and write down the factor model of profit.

Problem 2.5. Transform the analytical formula using the expansion method so that it reflects the dependence of return on assets on the value of return on sales and asset turnover.

Problem 2.6. Create a factor model, where the factor indicators are the volume of gross output and the average annual cost of fixed production assets. Using the method of chain substitution, determine the quantitative influence of factors on the performance indicator if:

· gross output for the reporting period increased compared to the plan from 78,000 to 82,000 rubles;

· the average annual cost of fixed production assets decreased from 72,000 to 70,000 rubles.

Problem 2.7. Based on the data in Table 18, create a factor model of profit from product sales and calculate the influence of factors on the change in its amount in all possible ways.

Table 18

Index	Base year	Reporting year
Product sales volume, pcs.	8 000	8 400
Sales price, thousand rubles.
Product cost, thousand rubles.

Problem 2.8. Based on the data in Table 19, create a factor model of the dependence of the volume of production on the average annual cost of fixed assets and capital productivity and, using the integral method and the method of absolute differences, determine the magnitude of the influenceI factor indicators on effective.Volume of production, million rubles.

21409

22287

Average annual cost of fixed assets, million rubles.

23000

23447

Problem 2.9. Using the data in Table 20, create a factor model of a multiple-additive type and, using the equity method, determine the impact of changes in sales profit, average annual cost of fixed assets and the amount of working capital on changes in production profitability.

Table 20

Index	Base year	Reporting year
Profit, thousand rubles	55,25	65,16
Average annual cost, thousand rubles: fixed assets working capital	500 350	520 385

Problem 2.10. The duration of capital turnover decreased by 25 days. Calculate the influence of factors on changes in the duration of capital turnover using the method of proportional divisiontaking into account changes in factor indicators given in table 21.

Table 21

	Change in average balances, thousand rubles.
Stocks of raw materials and supplies	+2700
WIP balances	+1300
Finished products	- 800
Accounts receivable	+2000
Cash	- 200

Problem 2.11. The relationship between the costs of production and its volume is described by a linear relationship . Based on the data in Table 22, determine the relationship equation coefficients, correlation and determination coefficients, and explain their economic meaning.

No.

Production costs, thousand rubles.

Production volume, thousand rubles.

1

120

62

7

200

70

2

130

63

8

270

77

3

150

65

9

280

78

4

140

64

10

250

75

5

180

68

11

200

71

6

200

70

12

180

67

19. Method of relative differences

used in deterministic factor analysis to assess the influence of each individual factor on the growth of the performance indicator. The advantage of this method is its simplicity. The relative difference method can only be used for multiplicative and multiplicative-additive factor models.

This method is based on the elimination method. Elimination (from English. eliminate) means eliminating the influence of all other factors (except one), that is, all other factors remain static. The method is based on the fact that all factors change independently of each other. First, the basic value changes to the reporting value for one factor with the other factors remaining unchanged, static, then for two, three, and so on.

To calculate the influence of the first factor on the effective indicator, you should multiply the base value of the effective indicator by the relative increase in the first factor in percentage and divide by 100.

To calculate the influence of the second factor, you should multiply the sum of the base value of the effective indicator and its increase due to the first factor by the relative increase of the second factor.

To calculate the influence of the third factor, you should multiply the sum of the basic value of the effective indicator, the influence of the first and second factors by the relative deviation of the third factor. And so on.

When using this method, the order of arrangement of factors in the factor model and, accordingly, the sequence of changes in factor values ​​is of great importance, since the quantitative assessment of the influence of each factor depends on this.

For For the method of relative differences, a correctly constructed deterministic factor model must be used, and a certain order in the arrangement of factors must be observed.

If the factor model contains quantitative and qualitative factors, then the replacement of factors should begin with the quantitative factor.

Quantitative factors reflect the quantitative certainty of phenomena. Quantitative factors can be expressed in both cost and physical terms. For example, quantitative factors characterize the volume of production and sales of products, and the value of these factors can be expressed both in rubles and in pieces, meters, etc.

Qualitative factors characterize the internal properties, features and attributes of the objects being studied. For example, a qualitative factor is the fat content of milk, labor productivity, product quality, etc.

If there are several quantitative and several qualitative indicators, then you should first change the value of the factors of the first level of subordination, and then the lower one.

According to the hierarchy, factors are divided into factors of the first, second, third level etc. First-level factors are factors that directly affect the performance indicator. Factors that influence the performance indicator indirectly, through factors of the first level, are factors of a lower level (second, third, etc.).

The algorithm for calculating the method of relative differences for a two-factor multiplicative model is as follows:

X = A* B;

Δ rel A-((A 1 -A 0 )/A 0 *100;

Δ rel B-((B 1 -B 0 )/B 0 *100;

Δ HA= X plan* Δ rel A;

ΔХ B = (X plan +ΔХ(а)) Δ rel B.

The sum of these quantities (ΔHa And ΔХb) must be identical to the difference between X 1 and X 0

Let's consider the calculation algorithm using a specific example.

The annual production volume of the enterprise depends on the average annual number of workers (H) and average annual output per worker (IN). A two-factor multiplicative model is compiled, where the number of workers is a quantitative factor, and therefore it comes first in the model, and production is a qualitative factor, and it comes after the quantitative one.

OP=H*V.

The data we will use is included in table 6.

Table 6. Data for factor analysis

So on first tag we need to calculate the relative increases of the factors.

Δ rel H=((H fact -H plan)/H plan)* 100= ((27 - 25)/25) 100 = 8;

Δ rel B=((B fact -B plan)/B plan)*100= ((230-200)/200)*100=15.

The relative change in the average annual number of workers was 8%, and the relative change in the average annual output was 15 %.

Second step. We find the influence of the first factor on the value of the effective indicator. In our case, how will the volume of production change if the number of workers increases by two people. We must multiply the planned output by the relative increase in the number of workers and divide the resulting number by 100.

ΔOP(H) = OP plan * Δ rel H;

Δ OP(H) = 5000 8/100 = 400.

Conclusion: an increase in the average annual number of workers by 2 people led to an increase in production volume by 400 thousand rubles.

Third step. We continue to consider the factors in our model one by one. Now we find the influence of the second factor on the value of the effective indicator. In our example, how the volume of production will change if the average annual output of one worker increases (by 30 thousand rubles). We must multiply the sum of the planned value of the effective indicator (production volume) and the influence of the first factor (average annual number of workers) by the relative increase in the second factor (average annual output per worker) and divide the resulting figure by 100:

ΔOP (V)= ((OP plan + ΔOP(H)) * Δ rel V)/100;

ΔOP (V)= ((5000+400) 15)/100 = 810.

Conclusion: an increase in the average annual output of one worker led to an increase in production volume by 810 thousand rubles.

Fourth step. Examination. The algebraic sum of the influence of factors when using this method must necessarily be equal to the total increase in the effective indicator. The absence of such equality indicates errors in the calculations.

OP fact - OP plan = 6210-5000=1210;

ΔOP(H) + ΔOP(V) = 400 + 810 = 1210.

Our calculations are correct.

Calculations are carried out similarly for other acceptable types of models.

The disadvantage of the method is the formation of an indecomposable residue, which is added to the magnitude of the influence of the last factor. This leads to a decrease in the accuracy of calculations. This can be avoided by using the integral method of factor analysis.

Topic 3. Characteristics of traditional techniques of factor economic analysis

Chain substitution method

This method is used in cases where two or more factors are included in the model for calculating a generalizing (resultative) indicator and the relationship between them is functional in nature.

The essence of the chain substitution method:

1) Consistently replace the basic factors with actual ones and recalculate the general indicator after each substitution. The first substitution is always basic, and the last is always factual. Therefore, the number of substitutions is always one more than the number of factors included in the model for calculating the general indicator.

2) In order to quantify the influence of a factor, it is necessary to subtract the general indicator obtained in the previous calculation from the general indicator obtained in the subsequent calculation.

The disadvantage of the chain substitution method is that the quantitative assessment of the influence of factors strongly depends on the sequence of substitutions.

In order to avoid this drawback it is necessary:

First replace quantitative (extensive) factors, and then qualitative (intensive);

If there are several quantitative factors, then those that are least dependent on the subsequent ones are replaced first.

Example. Assess the influence of labor factors on changes in production volume at an industrial enterprise.

Table 2 - Assessment of the influence of the main factors on changes in product output in an industrial enterprise

Indicators	Last year	Reporting year	Changes (+/-)	Substitutions	Quantitative assessment of the influence of factors
1.Volume of production (thousand rubles)	157,1	144,2	- 12,9	157,1	103,15	104,4	110,2	144,2	-12,9
2. Average number of workers			-1						-53,95
3.Average number of days worked by one worker per year									+ 1,25
4.Average number of hours. worked by 1 worker per day	7,2	7,6	0,4	7,2	7,2	7,2	7,6	7,6	+5,8
5. Product output per 1 man-hour worked (item 1/item 2*item 3*item 4), thousand rubles.	0,029	0,038	0,009	0,029	0,029	0,029	0,029	0,038	+34

The data presented in Table 2 show that the volume of production in the reporting year compared to the previous year decreased by 12.9 thousand rubles. This is mainly due to a decrease in the number of employees per person, so due to the influence of this factor, production output decreased by 53.95 thousand rubles.

Due to an increase in the number of working days by 3 days, product output increased by 1.25 thousand rubles, and due to an increase in the duration of the working day by 0.4 hours, the volume of production increased by 5.8 thousand rubles. Due to more efficient use of labor resources, product output increased by 34 thousand rubles.

Thus, the main factor in reducing production output at an industrial enterprise is the lack of personnel.

Absolute difference method

This method is derived from the method of chain substitutions and is used in cases where only two factors (or several) are included in the model for calculating the general indicator and the relationship between them is necessarily multiplicative. If two factors are included in the model for calculating a general indicator, one of these factors must be qualitative and the other quantitative.

The essence of the absolute difference method:

1). In order to assess the influence of a quantitative factor on the change in the general indicator, it is necessary to multiply the change in the quantitative factor by the basic qualitative factor;

2). In order to assess the influence of a qualitative factor on the change in the general indicator, it is necessary to multiply the change in the qualitative factor by the actual quantitative factor.

Example. Based on the data presented, it is necessary to determine the influence of the main factors on the change in the wage fund.

The data presented in Table 3 show that the total wage fund increased in the reporting year compared to the previous year by 3.4 thousand rubles.

Table 3 - Assessment of the influence of the main factors on the change in the wage fund of an industrial enterprise

This increase is mainly due to an increase in the average annual salary of one employee by 2.32 thousand rubles; due to the influence of this factor, the total wage fund increased by 13.92 thousand rubles.

By reducing the number of personnel per person, the wage fund. fees decreased by 10.4 thousand rubles.

The method of absolute differences can also be used if there are several factors included in the model for calculating the general indicator, but the relationship between them is necessarily multiplicative.

Let us evaluate the influence of labor factors on changes in production volume (Table 3) using the method of absolute differences.

Change in product output due to reduction in personnel numbers:

∆VP ∆h = (-1) *247 * 7.2 * 0.029 = -51.57 thousand rub.

Change in output due to an increase in the number of working days worked by one worker per year:

∆VP ∆d = 2 * (+3) * 7.2 * 0.029 = +1.25 thousand rub.

Change in output due to an increase in the number of hours. worked by 1 worker per day:

∆VP ∆hour = 2 * 250 * (+0.4) * 0.029 = +5.8 thousand rub.

Change in product output due to increased efficiency in the use of labor resources:

∆VP ∆pr = 2 * 250 * 7.6 * (+0.009) = +34.2 thousand rub.

Relative difference method

The method of relative differences, like the method of absolute differences, is used to measure the influence of factors on the growth of an effective indicator only in multiplicative models and combined types

y = (a-b) c.

It is much simpler than chain substitutions, which makes it very effective under certain circumstances. This applies, first of all, to those cases when the source data contains previously determined relative deviations of factor indicators in percentages or coefficients.

Let us consider the methodology for calculating the influence of factors in this way for multiplicative models such as y = a b c. First you need to calculate the relative deviations of factor indicators:

Then the deviation of the effective indicator due to each factor is determined as follows:

According to this rule, to calculate the influence of the first factor, it is necessary to multiply the basic value of the effective indicator by the relative increase in the first factor, expressed as a percentage, and divide the result by 100.

To calculate the influence of the second factor, you need to add to the basic value of the effective indicator the change due to the first factor and then multiply the resulting amount by the relative increase in the second factor in percentage and divide the result by 100. The influence of the third factor is determined in the same way: you need to add to the basic value of the effective indicator its increase due to the first and second factors and the resulting amount multiplied by the relative increase of the third factor, etc.

The advantage of this method is that when using it it is not necessary to calculate the value of factor indicators. It is enough to have data on the growth rates (percentage of plan fulfillment) of factors for the analyzed period.

Thus, the results of calculations obtained using this method are the same as when using the chain substitution and absolute difference methods, but the number of computational procedures is reduced. This makes it convenient to use the method of relative differences in cases where it is necessary to calculate the influence of a large set of factors.

Example. Assess the influence of average wages and average number of personnel on changes in the wage fund of the enterprise under study

Table 4 - Quantitative assessment of the influence of the main factors on the change in the wage fund of the enterprise under study

To determine the influence of each factor, the relative deviations of factor indicators are first calculated as follows:

The change in the general indicator due to each factor is determined as follows:

The data in Table 4 shows that the wage fund changed by 3.5 thousand rubles compared to last year, which is due to the influence of the following factors:

Due to an increase in wages by 2.32 thousand rubles. the wage fund increased by 16.24 thousand rubles;

The reduction in the number of personnel per person led to a decrease in the wage fund by 12.72 thousand rubles.

Index method

Along with the considered methods of chain substitution, absolute differences and relative differences index method is based on elimination, that is, excluding the impact on the value of the performance indicator of all factors except one. This method is used in cases where it is necessary to determine the influence of prices, rates and tariffs on changes in the general indicator.

Indices are an effective tool for comparative economic analysis. An index is a statistical indicator representing the ratio of two states of a characteristic. Using indices, comparisons are made with the plan, in dynamics, in space. An index is called simple (particular, individual) if the characteristic under study is taken without taking into account its connection with other characteristics of the phenomena being studied. A simple index looks like:

Where p 0 and p 1- compared states of the characteristic.

The index is called analytical (general, aggregate), if the characteristic under study is not taken in isolation, but in connection with other characteristics. An analytical index always consists of two components: the indexed attribute p (the one whose dynamics are being studied) and the weight attribute q. Using weights, the dynamics of a complex economic phenomenon, the individual elements of which are incommensurable, are measured.

Where q 0 u q 1- weight sign.

Simple and analytical indices complement each other.

The index method is one of the most powerful, informative and widespread tools of economic analysis in all its aspects: from analysis of the activities of individual economic units to macroeconomic studies of national economies.

Example. Determine the impact of price and changes in the quantity of goods sold on sales volume in a trading organization.

1. In order to determine the impact of price on changes in total sales volume, it is necessary to subtract the sales volume in comparable prices from the sales volume in the reporting year.

This follows from the calculation of the general price index:

I p = ∑p 1 q 1 / ∑p 0 q 1 = ∑p 1 q 1 / (∑p 1 q 1 /i p); i p = p 1 /p 0 – individual. price index.

Change in total sales volume due to the price factor: ∆О ∆ p = ∑p 1 q 1 - ∑p 1 q 1 /i p.

2. In order to assess the impact of the physical volume of goods sold on changes in total sales volume, it is necessary to subtract the base sales volume from the sales volume at comparable prices.