List of sources used

Test

Option number 8

Task 8. According to the plan, the volume of production in the reporting year should increase by 2.5% against the previous year. The output plan was exceeded by 3.0%.

Exercise:

1. Determine the actual output in the reporting year, if it is known that the volume of production last year amounted to 25,300 thousand rubles.

Decision:

Plan excess:

25300 * (100% + 2.5%) u003d 25933 thousand rubles.

Exceeding the plan actual:

25933 * (100% + 3.0%) = 26710 thousand rubles.

Task 18. A small sample was taken from a batch of light bulbs to determine the duration of their service life. The results are presented in table. thirteen.

Table 13

Bulb No.
Burning time, hour 1450 1400 1 370 1430 1400 1 380 1 270

Exercise:

Determine the values of structural averages – mode and median.

Decision:
Data are ranked to determine the mode and median.
Ranked row: 1270, 1370, 1380, 1400, 1400, 1400, 1420, 1430, 1450.
Mode – M o – 1400 hours (1400 is the value of the feature, occurring three times).
The place of the median = = 5
Me = 1400 h (1400 is the value of the trait, which is in 5th place in the ranked series).

Problem 28

There are the following reporting data on the freight motor transport enterprise (table 1.1).

Table 1.1 – Reporting data for a freight motor transport enterprise

Indicator years
Cargo transported, thousand tons

Exercise:

Calculate the interval forecast of traffic volume for 2015 with a probability of 0.997.

Decision:

General view of the regression equation:

y = a + bx

Here x – years, y – cargo transported, thousand tons.

System of normal equations in general form:

Here’s a spreadsheet

System of normal equations with calculated coefficients:

8a + 36b = 3460

36a + 204b = 16441

System Solution

a = 9497/28

b = 871/42

a = 339.18; b = 20.74

The constructed regression equation:

yx u003d 339.18 + 20.74x

Let’s fulfill the forecast for 2015 (serial number – 9)

y x = 339.18 + 20.74*9 = 525.84 thousand tons

Thus, we can conclude that the constructed trend reflects an upward trend in the transported cargo, and in 2015 there is a similarity between the trend and the initial dependence.

Problem 38

The number of manufactured products in the reporting period increased by 8.0% compared to the base period, while the total cost of production decreased by 5.0%.

Exercise:

Determine how the average selling prices for products have changed.

Decision:

The individual cost index of a unit of production shows the change in the cost of a unit of production in the current period compared to the base one:

i q u003d q 1 / q 0 individual index of the physical volume of production.

If 100% is subtracted from the index value, expressed as a percentage, i.e. (i-100), then the resulting difference will show how much the indexed value has increased (decreased).

So, if the number of manufactured products in the reporting period increased by 8.0% compared to the base period, therefore,

iq = 108%.

The total cost of production decreased by 5.0%.

The cost of production is the product of the quantity of production in physical terms q and the price of a unit of production p.

The ratio of the cost of production of the reporting period ∑q1p1 to the cost of production of the base period ∑q0p0 decreased by 5.0%.

Ipq = 95%.

The value of the general index Ipq depends on the change in two indexed values: prices p1,p0 and the quantity of goods (q1,q0 ) It characterizes the change in the volume of production in general, i.e. reflects the simultaneous influence of both factors – a change in the number of products and a change in the price level.

The relationship between the general index of trade turnover, the general index of the physical volume of trade turnover and the price index is expressed by the equality:

I pq u003d I q / I p .

95 u003d 108 / I p

I p u003d 1.14 or 114% (114% – 100% u003d 14%)

Selling prices for products increased by an average of 14%.

Task 48. The following data are available for the Russian Federation, thousand people:

Average annual population ……………………………………………………… …. 147 200

The arrival of the population in the Russian Federation ………………………………………. …………………………… 940

The population withdrew from the Russian Federation ………………………………………. …………………………… 420

Exercise:

1. Determine the overall migration intensity factor.

2. Determine the coefficient of intensity of migration turnover.

3. Determine the migration efficiency factor.

Decision:

1. general coefficient of migration intensity.

K p-v = = 3.53%

2. coefficient of intensity of migration turnover.

K p+v = = 9.24%

3. migration efficiency ratio

K ef = = = 38.2%

Problem 58

There are the following indicators:

1. Output of goods and services at basic prices …………………………………………………. .2805.4

2. Intermediate consumption ……………………………………….. …………….. 1312.4

3. Taxes on products and imports ………………………………………….. ……………….. 196.4

4. Subsidies for products and imports (-) ………………………………………. …………….. 59.4

5. Remuneration of employees …………………………………………………….. ……….. 707.8

6. Taxes on production and imports ………………………………………. ………….. 245.4

7. Subsidies for production and imports (-) ………………………………………. ………. 59.6

8. Property income received from the “rest of the world” …………… 18.2

9. Property income transferred to the “rest of the world” ………………………… 32.2

10. Current transfers received from the “rest of the world” ……………………………………………. 3.5

11. Current transfers – transferred to the “rest of the world” ………………………………………. 2.7

12. Final consumption expenditure ……………………………………………………… ………. 1102.1

13, Gross Saving ……………………………………………………… ………………………….. 517.4

14. Gross capital formation ……………………………………….. ………………………….. 382.8

15. Import of goods and services……………………………………….. ………………………. 362.6

16. Export of goods and services ……………………………………….. ……………………. 428.1

17. Statistical difference ……………………………………………………… ………………. 79.6

18. Gross fixed capital formation……………………………………………………… .329.4

19. Change in inventories ………………………………………. 53.4

20. Capital transfers received from the “rest of the world” …………… 14.2

21. Capital transfers given to the “rest of the world” ……………………………. 15.8

Exercise:

Build and fill in the production account (at current prices), trln. rub.

Decision:

The production method GDP is calculated as follows:

output at basic prices plus taxes on products and imports

minus subsidies on products and imports minus intermediate consumption

GDP at market prices, calculated by the production method, is equal to:

2805, 4 +196, 4 – 59, 4 – 1312, 4 = 1630 trillion. rub .

GDP is defined by the apportionment method as the sum of primary incomes: the gross profit of the economy, wages of employees paid by residents to residents and non-residents, net taxes on production and imports (taxes minus subsidies). In this case, gross profit and mixed income are determined according to the following scheme:

GDP calculated by the production method

minus wages of employees paid by residents

minus taxes on production and imports

plus subsidies for production and imports

Gross profit and mixed income are: 1630 – 707.9 – 245.4 + 59.6 = 736.3 trillion. rub .

Consequently, the GDP calculated by the distribution method is: 736.3 + 707.9 + 245.4 – 59.6 = 1630 trillion. rub .

GDP by the end use method is calculated according to the following scheme:

final consumption

plus gross capital formation

plus export

minus imports

GDP by the end use method is equal to:

1102, 1 + 382.8 + 428, 1 – 362.6 = 1550.4 trillion. rub .

The statistical discrepancy is defined as the difference between GDP calculated by the production method (1630) and GDP calculated by the final use method (1550, 4). In our example, it is 79.6 trillion. rub .

Net profit is defined as the difference between gross profit and consumption of fixed capital: 736.3 – 413.7 = 322.6 trillion. rub .

Gross national income (GNI) can be calculated as follows: , where

– the balance of wages of employees paid by residents to non-residents and received by residents from non-residents: 0.7 – 2.0 = – 1.3 trillion. rub . ;

– balance of income from property transferred to the rest of the world and received from it: 18.2 – 32.2 u003d – 14 trillion. rub .

Therefore, GNI = 1630 + ( – 1.3) + ( – 14) = 1614.7 trillion. rub .

GNI can be calculated as the sum of primary income received by residents from residents and non-residents:

736.3 + (707.9 + 0.7 – 2.0) + (18.2 – 32.2) + (245.4 – 59.6) = 1614.7 trillion. rub .

Gross national disposable income (GNDI) is calculated as the sum of gross national income and the balance of current transfers received from and transferred to the rest of the world ().

GDPR u003d 1614.7 + 3.5-2.7 u003d 1615.5 trillion. rub

National saving is calculated as the difference between gross national disposable income (GNDI) and final consumption (CF):

NA u003d 1615.5 – 1102.1 u003d 513.4 trillion. rub

Net lending or borrowing is defined as follows:

national saving (NS)

plus balance of capital transfers ()

minus gross capital formation (GR)

VHF u003d 513.4 + 14.2 – 15.8 – 382.8 u003d 129 trillion. rub .

Let’s make the following accounts (in current prices; trillion rubles):

Production account

Usage Resources
Intermediate consumption 1312.4 Output of goods and services at basic prices 2805 4
GDP at market prices 1630 Taxes on products and imports 196.4
Subsidies on products and imports (-) 59, 4
Total: 2942.4 Total: 2942.4

Income generation account

Usage Resources
Salary 707.9 GDP at market prices 1630
Production and import taxes 245.4
Subsidies for production and imports 59.6
Gross profit and mixed income 736.3
Total: 1630 Total: 1630

Primary income distribution account

Usage Resources
Property income transferred to the rest of the world 32.2 Gross profit and mixed income 736.3
Gross national income 1614.7 Salary 706.6
Net taxes on production and imports 185.8
Property income received from the rest of the world 18.2
Total: 1646.9 Total: 1646.9

In contrast to the income generation account, the income distribution account in the “Resources” section reflects the wages received by residents from residents and non-residents: 707.9 + 0.7 – 2.0 = 706.6 trillion. rub .

Secondary distribution of income account

Usage Resources
Current transfers to the rest of the world 2.7 Gross national income 1614.7
Gross national disposable income 1615.5 Current transfers received from the rest of the world 3.5
Total: 1618.2 Total: 1618.2

Disposable income account

Usage Resources
Final consumption 1102.1 Gross national disposable income 1615.5
National savings 513.4
Total: 1615.5 Total: 1615.5

Capital account

Usage Resources
Gross capital formation 382.8 National savings 513.4
Net lending or borrowing 129 Capital transfers received from the rest of the world 14.2
Capital transfers to the rest of the world (-) 15.8
Total: 511.8 Total: 511.8

Goods and services account

Usage Resources
Intermediate consumption 1312.4 Output of goods and services at basic prices 2805 4
Final consumption 1102.1 Import of goods and services 362.6
Gross capital formation 382.8 Taxes on products and imports 196.4
Export of goods and services 428.1 Subsidies on products and imports (-) 59.4
Statistical discrepancy 79.6
Total: 3305 Total: 3305

Problem 68

The following data are available for one of the regions of the country. The full initial cost of fixed assets at the beginning of the year amounted to 120 million rubles. During the year, new funds were introduced in the amount of 40 million rubles. Retired for the year fixed assets at a cost minus depreciation in the amount of 5 million rubles. (their initial cost was 24 million rubles). Depreciation of fixed assets at the beginning of the year amounted to 18%.

Exercise

1. Determine the full historical cost of fixed assets and their value minus depreciation at the end of the year.

2. Determine the coefficients of movement and the state of fixed assets.

Solution :

On the basis of the given data, we will construct the balance sheets of fixed assets, thousand rubles.

Indicators Full value of fixed assets Residual value of fixed assets Depreciation of fixed assets
Availability of fixed assets at the beginning of the year 98.4 21.6
Entered fixed assets for the year +40 +40
Disposal of fixed assets for the year -24 -nineteen -5
Availability of fixed assets at the end of the year 119.4 16.6

The condition of fixed assets is characterized by the following indicators, which can be determined at the beginning and end of the year:

1. The depreciation coefficient of fixed assets is calculated as the ratio of the amount of depreciation of fixed assets on the date to the full initial cost of fixed assets on the same date:

– at the beginning of the year Kizn = 21.6 / 120 = 0.18 or 18%

– at the end of the year Kizn = 16.6 / 136 = 0.12 or 12%

2. The coefficient of validity is calculated as the ratio of the residual value of fixed assets on the date to their full initial cost on the same date:

at the beginning of the year Kgodn u003d 98.4 / 120 u003d 0.82 or 82%

at the end of the year Kgodn u003d 119.4 / 136 u003d 0.88 or 88%

The relationship between wear and service life coefficients:

Kizn + Kgodn = 1 (100%).

The indicators characterizing the movement of fixed assets include:

1. The coefficient of renewal of fixed assets is calculated as the ratio of the cost of fixed assets put into operation to the full initial cost of fixed assets at the end of the year.

Kobn u003d 40 / 136 u003d 0.29 or 29%

2. The coefficient of retirement of fixed assets is calculated as the ratio of the total initial cost of retired fixed assets to the total initial cost of fixed assets at the beginning of the year.

Ksp = 24 / 120 = 0.20 or 20%

List of sources used

1. Ayvazyan S.A., Mkhitaryan V.S. Applied Statistics and Fundamentals of Econometrics: Textbook. – M.: UNITI, 1998.

2. Dubrov A.M., Mkhitaryan V.S., Troshin L.I. Multivariate Statistical Methods: Textbook. – M .: Finance and statistics, 2000,

3. Eliseeva I.I., Yuzbashev M.M. General theory of statistics. Textbook. – M.: INFRA-M, 1998.

4. Efimova M.R., Petrova E.V., Rumyantsev V.N. General theory of statistics: Textbook, – M .: INFRA-M, I99S.

5. Kalinina V.N., Pankin V.N. Mathematical Statistics: Textbook – M .: Higher School, 1998.

6. Kremer N.Sh. Probability Theory and Mathematical Statistics: Textbook. – M.: UNITI, 2000.

7. General theory of statistics / Ed. O.E. Bashina, A.A. Spirin. – M.: Finance and statistics, 1999.

8. Workshop on the theory of statistics / Ed. prof. R.A. Shmoylova. – M .: finance and statistics, 1998.

9. Theory of Statistics: Textbook / Ed. prof. G.L. Gromyko – M.: INFRA-M, 2000.

10. Theory of Statistics: Textbook / Ed. prof. R.A. Shmoylova. – M.: Finance and statistics, 1999.

11. Tyurin Yu.N. Math statistics. – M.: Knowledge, 1976.

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