QUANTITATIVE ANALYSIS OF TECHNOLOGICAL DEVELOPMENT
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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