"a retrospective of the development of ukraine`s economy based on the indicators of...

A RETROSPECTIVE OF THE DEVELOPMENT

OF UKRAINE`S ECONOMY BASED ON THE

INDICATORS OF THREE-SECTOR THEORY

AGENDA 1) Three-sector theory 2) Fixed assets 3) Employment 4) Capital-labor ratio 5) Deriving of iterative formula 6) Forecast of capital labor ratio of second sector 7) Dynamics of workforce quotas 8) Conclusions

1) Three-sector theory

Sector division of three-sector theorySector of economy

Description Economic activities

Primary Production of objects of labor: fuel, power, raw

materials.

Agriculture, forestry, fishing, mining, petrochemical industry, metallurgy,

industrial chemistry, freight transport, etc.

Secondary Production of means of labor:

machinery, equipment, industrial buildings.

Mechanical engineering, metalworking, industrial construction.

Tertiary Production of commodities and

providing of services.

Processing of agricultural products, light and food industry, household chemicals,

passenger transport, commodities trade, civil communications

ADVANTAGES OF THREE-SECTOR MODEL

We can measure intermediate product, which is ‘invisible’ in calculation of GDP

It is assumed that every sector has its own fixed assets, while labor and investments can move freely among sectors

2) Fixed assets*Fixed asset is an asset that is not consumed or

sold during the normal course of business.

DISTRIBUTION OF FIXED ASSETS BY SECTORK1 = (Mining) + (Agriculture, hunting and forestry)/2 + + (Production and distribution of electricity, gas and water).K2 = (Manufacturing) + (Construction).K3 = (Transport and Communications) + + (Agriculture, hunting and forestry)/2 +

+ (Trade, repair of motor vehicles, household goods and commodities) +

+ (Industry) - (Manufacturing) - (Mining).+

3) Employment

DISTRIBUTION OF EMPLOYEES BY SECTOR

L1 = (Agriculture, hunting and forestry and fishing)/2 + + (Industry)/3.L2 = (Construction) + (Industry)/3.L3 = (Transport and communication) + + (Trade, repair of motor vehicles, household goods and Commodities. Hotels and restaurants) ++ (Agriculture, hunting, forestry and fishing)/2 + + (Industry)/3.

4) Capital-labor ratio*

5) Deriving of iterative formula

*mathematical part

Assumptions of three-sector theory1 Constant technological level, defined by neoclassical linear homogeneous

production functions: 𝑿𝒊 = (𝑲𝒊, 𝑳𝒊), 𝒊 = 1, 2, 3. { 𝑿𝒊 – output, 𝑲𝒊 – fixed assets, 𝑳𝒊– number of employees in sectors }

2 The total number of employees in the economy 𝑳 change with constant growth rate ν. {sectoral allocation : 𝑳 = 𝑳1 +𝑳2 +𝑳3 }

3 Lag of investment is absent. 4 The coefficients of depreciation of fixed assets 𝝁𝒊 are constant.5 The economy is closed, foreign trade not considered directly. {imperfect

simplifying assumption}6 Time 𝒕 changes continuously {In this document this

imperfection is eliminated, because of discrete nature of economic data}

Annual change of fixed assets of ith sector consists of growth rate of gross investment (+ ) , and depreciation 𝑰𝒊(− ∗ ):𝝁𝒊 𝑲𝒊

𝑲𝒊( + ) − ( ) = − ∗ ( ) + ( ) ,𝒕 𝟏 𝑲𝒊 𝒕 𝝁𝒊 𝑲𝒊 𝒕 𝑰𝒊 𝒕or in continuous time:

𝑲𝒊(𝒕 + ∆𝒕) − 𝑲𝒊(𝒕) = (− 𝝁𝒊 ∗ 𝑲𝒊(𝒕) + 𝑰𝒊(𝒕)) ∗ ∆𝒕 .According to definition of derivative:

By dividing both sides of the equation on and 𝑳𝒊using equation of capital-labor ratio , we are getting:

*Growth rate of employment added to the formula to account for changes in the number of employees in the division on

For further transformations let me give new definitions of variables:

- workforce quotas, .

)-investment allocation, ( –investment in ith sector. , – sum of investments in all three sectors ).

Labor productivity of sector:

Macroeconomic productivity of sector:

Using previous formulas, and transformed expression:

we receive system of equations:

Using discrete approximation of derivative: ,

we receive recurrent relation (in the further parts of this paper only second sector will be considered):

Using Cobb-Douglass production function:

After substitution for both and : ,

we receive final iterative equality:

6) Forecast of capital-labor ratio of second

sector of Ukraine

DYNAMICS OF WORKFORCE QUOTAS

OF UKRAINE* WORKFORCE QUOTA IS PERCENT OF

EMPLOYEES, WORKING IN CERTAIN SECTOR

CONCLUSIONS

Formally, Ukraine still not belong to Tertiary civilizationTertiary sector is dominantMain contribution to growth of fixed assets of Ukraine led transport and

communication, which share in 2014 achieve 76% in overall structure Number of employees rapidly decreased over 2013 and in 2014 reach historical

minimum over period from 2000.

Thank you for attention!