LSP 120: Quantitative Reasoning and Technological Literacy Section 903
QUANTITATIVE ANALYSIS OF TECHNOLOGICAL DEVELOPMENT
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Transcript of QUANTITATIVE ANALYSIS OF TECHNOLOGICAL DEVELOPMENT
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QUANTITATIVE ANALYSIS OF TECHNOLOGICAL DEVELOPMENT
Indicators of technological progress
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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.
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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.
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Product
Global productivity Bp- gross production Tr- labor costs Tos- costs of fixed and
working assets
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Global productivity
2000. 2001. 2002. 2003.
Bp·106 2695 2134 2787 2980
Tr ·105 953 841 904 810
Tos ·106 1153 1475 1171 1226
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Equipment
Technical equipment per employee
Vos- Value of fixed assets
N- Number of employees.
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Technical equipment per employee
Vos ·106 N
2000 50 250
2001 50 350
2002 60 350
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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
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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
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Energy
Electricity consumption per employee
Pe- overall electricity consumption
N - number of employees
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Electricity consumption per employee
Pe ·103 N
2000 1488 13
2001 1184 14
2002 1440 11
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R & D
Indicator of R & D ratio of income and expenses for R&D
P - total income TIR total costs for R&D
activities
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Indicator of R & D
UP·106 TIR·102
2000 4000 450
2001 4000 490
2002 4500 600
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Investments
Intensity of investments
IS- overall investments N- total number of
employees
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Intensity of investments
IS·106 N
2000 1154 16
2001 1235 19
2002 1120 10
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Human resources
Level of qualifications and qualification structure
n- number of employees at appropriate level of expertise
N- total number of employees
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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
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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
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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
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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
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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
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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
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Exercise
Q(106) L(105) Q(106)
2000 2588 810 1301
2001 2932 905 1399
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Exercise
Ratio of factor L to production growth Ratio of factor K to production growth Ratio of factor m to production growth