QUANTITATIVE ANALYSIS OF TECHNOLOGICAL DEVELOPMENT

QUANTITATIVE ANALYSIS OF TECHNOLOGICAL DEVELOPMENT

Indicators of technological progress

Technological progress

Technological progress is a process that leads to:– creation of new or improved methods of production that

provide savings,– introduction of new and improved products and services, – improvement of organization and production management.

Technological progress can be observed globally and /or partially.

Technological progress

At company level we consider 10 basic components of technological progress:

– product– equipment, – materials, – energy, – R & D, – investment, – human resources, – environmental protection, – organization – management.

Product

Global productivity Bp- gross production Tr- labor costs Tos- costs of fixed and

working assets

Global productivity

2000. 2001. 2002. 2003.

Bp·106 2695 2134 2787 2980

Tr ·105 953 841 904 810

Tos ·106 1153 1475 1171 1226

Equipment

Technical equipment per employee

Vos- Value of fixed assets

N- Number of employees.

Technical equipment per employee

Vos ·106 N

2000 50 250

2001 50 350

2002 60 350

Equipment

Factor of technological level of equipment

P- net product Z- number of employees Po- the average annual fees

for employees K- invested funds k- interest that would be

received on borrowed funds Q- production increase, as a

result of improved capacity utilization

Factor of technological level of equipment

Pi·107 Zi·103 pi·103 k Ki·107 Q·106

2000 55 60 30 0.07 20 -

2001 60 60 40 0.07 25 10

2002 90 70 50 0.08 30 20

2003 95 75 60 0.08 35 20

Energy

Electricity consumption per employee

Pe- overall electricity consumption

N - number of employees

Electricity consumption per employee

Pe ·103 N

2000 1488 13

2001 1184 14

2002 1440 11

R & D

Indicator of R & D ratio of income and expenses for R&D

P - total income TIR total costs for R&D

activities

Indicator of R & D

UP·106 TIR·102

2000 4000 450

2001 4000 490

2002 4500 600

Investments

Intensity of investments

IS- overall investments N- total number of

employees

Intensity of investments

IS·106 N

2000 1154 16

2001 1235 19

2002 1120 10

Human resources

Level of qualifications and qualification structure

n- number of employees at appropriate level of expertise

N- total number of employees

Qualification structure

Production workers

KV VK PK NK TOTAL

2000 6 20 4 2 32

2001 5 17 7 4 33

2002 8 39 10 3 60

2003. 5 29 1 2 37

Qualification structure

Production workers

% KV % VK. % PK % NK.

2000 18,75 62,5 12,5 6,25

2001. 15,15 51,52 21,21 12,12

2002. 13,33 65 16,67 5

2003. 13,51 78,38 2,70 5,41

Qualification structure

18.7515.15 13.33 13.51

62.5

51.52

65

78.38

12.5

21.2116.67

2.76.25

12.12

5 5.410

102030405060708090

100

2000 2001 2002 2003

(KV/UK)100

(VK/UK)100

(PK/UK)100

(NK/UK)100

Production function

Production function is a model that shows a maximum level of output that could be achieved with specific input

Global production function Particular production function

Cobb-Douglas

Cobb-Douglas form of production function is widely used to represent the relationship of an output to inputs

Q=ALα Kβ

– Q - total production (the monetary value of all goods produced in a year) – L – labor input - labor production factor– K – capital input - capital production factor– A – factor in proportion to production growth and depended on

technological progress– α – elasticity of production volume in relation to labor production factor – β - elasticity of production volume in relation to capital production factor

Rate of technological progress

A = emt

o e – constanto t – timeo m – rate of technological progress

Q= emtLα Kβ

lnQ = mt + αlnL + βlnK ΔQ/Q = m + α ΔL/L + β ΔK/K

m = ΔQ/Q - α ΔL/L - β ΔK/K

Exercise

Q(106) L(105) Q(106)

2000 2588 810 1301

2001 2932 905 1399

Exercise

Ratio of factor L to production growth Ratio of factor K to production growth Ratio of factor m to production growth