GROWTH, INSTITUTIONS AND BUSINESS: CHAPTER 7 NOTES: MEASURING PRODUCTIVITY
Productivity – the effectiveness with which factors of production are converted into output
7.1 PRODUCTIVITY IN THE PRODUCTION FUNCTION
(a) two countries have the same production function but country 1 has higher levels of factors of production
and therefore output
(b) two countries have the same quantities of factors of production but country 1 is more productive
(c) country 1 has both a better production function and more factors of production than country 2, difference
in output per worker results from both effects
7.2 DIFFERENCES IN THE LEVEL OF PRODUCTVITY AMONG COUNTRIES
Ø Comparing productivity among countries is problematic if the only information at our disposal is the
countries’ levels of output and factor accumulation.
Measuring Productivity Differences among countries: Ratio of productivity * ratio of factors
Factors of production = kah1-a of production
Output = productivity * factors of production
To compare two countries, we can use
Ratio of output per worker in
country 1 to output per worker
in country 2
, Ø When determining the productivity difference between two countries, we look at their levels of
output and levels of factors of accumulation
!"#$% %' %(#)(#
Ratio of productivity = !"#$% %' '"*#%!+ %' )!%,(*#$%-
Development accounting – technique for breaking down differences in income into the part that is accounted
for by differences in productivity and the part accounted for by differences in factor accumulation.
Ø However, if we do not measure factors of production well, then differences in productivity will also be
incorrect.
The contribution of Productivity to Income Differences among countries:
How much variation in productivity contributes to variation in income
Ø 47% of the variation in output per worker among countries is a result of factor accumulation, and 53%
is a result of productivity.
Mathematical analysis:
Ry = ratio of output
Rp = ratio of productivity
Rf = ratio of factor accumulation
Ry = Rp + Rf
Ln(Ry) = ln(Rp) + ln(Rf) à we can look across a large sample of countries and construct the variance
Var(ln(Ry)) = Var(ln(Rp )) + Var(ln(Rf)) + 2 Cov(ln(Rp ), ln(Rf))
."!/0-(2))456%7(0-(2) ),0-(2'))
Fraction of income variance due to productivity =
."!(0-(29))
7.3 DIFFERENCES IN THE GROWTH RATE OF PRODUCTIVTY AMONG COUNTRIES
Growth accounting - examining how much of a country’s income growth is accounted for by growth in
productivity and how much by growth in the quantity of factors of production.
Measuring Countries’ Productivity growth:
y = Ak ha 1-a à output = productivity * factors of production
Growth rate of output = growth rate of productivity + growth rate of factors of production
Growth rate of productivity = growth rate of output – growth rate of factors of production
à An= yn- akn- (1 - a)hn.
The Contribution of Productivity to growth differences among countries:
Ø The typical rich country has both higher productivity and higher factor accumulation than the typical
poor country, part of income differences explained by differences in productivity is a bit larger than
the part explained by the differences in factors of production
Ø productivity growth is a much more important source of differences in output growth rates than is
growth of factors of production.
Ø 68% of the variation in growth rates is the result of variation in productivity growth, whereas 32% of
the variation in growth rates is the result of variation in factor accumulation.
, CHAPTER 8 NOTES: THE ROLE OF TECHNOLOGY IN GROWTH
8.1 THE NATURE OF TECHNOLOGICAL PROGRESS
An improvement in technology will mean that given quantities of physical and human capital can be combined
to produce more output than was previously possible.
A crucial aspect of technological change is that it allows an economy to transcend the limitations imposed by
diminishing returns (as long as A gets bigger, income per capita can continue to grow)
Technology creation:
Ø Creating new technologies requires investments,
Ø In the case of capital creation, someone must use resources that could have been devoted to
something else to create, refine and put into practise a productive idea
Ø The most important way in which government aids R&D is by providing investors with legal protection
against the copying of their work, in the form of a patent
Transfer of technology:
Ø Conventional factors of production are objects, technologies are ideas lacking a concrete existence
Ø Technology is non-rival and non-excludable
Ø Excludability – degree to which an owner of something can prevent other from using it without
permission.
Determinants of R&D Spending:
Ø Most R&D spending is undertaken privately by firms.
Ø If we wish to understand the determinants of R&D spending, we should look at the problem facing a
firm that is deciding whether to do R&D and how much.
1. Profit Considerations:
à producing a new technology will raise firm’s profits, if it is successful
à in the best-case scenario, its invention will give it monopoly on the sale of some product, allowing
it to earn supernormal profits.
à the extra profits that arise from this competitive advantage are the incentive that makes the firm
do the research
à the amount a firm will want to spend on R&D will depend on how much of an advantage a new
invention will confer (patents)
à the larger the available market, the greater the profits that the new invention will earn
à the firm will take into account how long the advantage conferred by a new invention will last
à uncertainty and risk surrounding R&D will influence the firm’s spending.
2. Creative destruction:
àcreative destruction is the process by which new inventions create profits for firms, these profits
serve as the inventive to engage in research in the first place, and the new technologies so created
are eventually supplanted by yet newer technologies
à enthusiasm often ignores the dislocations suffered by firms and workers that the new technologies
displace.
Productivity – the effectiveness with which factors of production are converted into output
7.1 PRODUCTIVITY IN THE PRODUCTION FUNCTION
(a) two countries have the same production function but country 1 has higher levels of factors of production
and therefore output
(b) two countries have the same quantities of factors of production but country 1 is more productive
(c) country 1 has both a better production function and more factors of production than country 2, difference
in output per worker results from both effects
7.2 DIFFERENCES IN THE LEVEL OF PRODUCTVITY AMONG COUNTRIES
Ø Comparing productivity among countries is problematic if the only information at our disposal is the
countries’ levels of output and factor accumulation.
Measuring Productivity Differences among countries: Ratio of productivity * ratio of factors
Factors of production = kah1-a of production
Output = productivity * factors of production
To compare two countries, we can use
Ratio of output per worker in
country 1 to output per worker
in country 2
, Ø When determining the productivity difference between two countries, we look at their levels of
output and levels of factors of accumulation
!"#$% %' %(#)(#
Ratio of productivity = !"#$% %' '"*#%!+ %' )!%,(*#$%-
Development accounting – technique for breaking down differences in income into the part that is accounted
for by differences in productivity and the part accounted for by differences in factor accumulation.
Ø However, if we do not measure factors of production well, then differences in productivity will also be
incorrect.
The contribution of Productivity to Income Differences among countries:
How much variation in productivity contributes to variation in income
Ø 47% of the variation in output per worker among countries is a result of factor accumulation, and 53%
is a result of productivity.
Mathematical analysis:
Ry = ratio of output
Rp = ratio of productivity
Rf = ratio of factor accumulation
Ry = Rp + Rf
Ln(Ry) = ln(Rp) + ln(Rf) à we can look across a large sample of countries and construct the variance
Var(ln(Ry)) = Var(ln(Rp )) + Var(ln(Rf)) + 2 Cov(ln(Rp ), ln(Rf))
."!/0-(2))456%7(0-(2) ),0-(2'))
Fraction of income variance due to productivity =
."!(0-(29))
7.3 DIFFERENCES IN THE GROWTH RATE OF PRODUCTIVTY AMONG COUNTRIES
Growth accounting - examining how much of a country’s income growth is accounted for by growth in
productivity and how much by growth in the quantity of factors of production.
Measuring Countries’ Productivity growth:
y = Ak ha 1-a à output = productivity * factors of production
Growth rate of output = growth rate of productivity + growth rate of factors of production
Growth rate of productivity = growth rate of output – growth rate of factors of production
à An= yn- akn- (1 - a)hn.
The Contribution of Productivity to growth differences among countries:
Ø The typical rich country has both higher productivity and higher factor accumulation than the typical
poor country, part of income differences explained by differences in productivity is a bit larger than
the part explained by the differences in factors of production
Ø productivity growth is a much more important source of differences in output growth rates than is
growth of factors of production.
Ø 68% of the variation in growth rates is the result of variation in productivity growth, whereas 32% of
the variation in growth rates is the result of variation in factor accumulation.
, CHAPTER 8 NOTES: THE ROLE OF TECHNOLOGY IN GROWTH
8.1 THE NATURE OF TECHNOLOGICAL PROGRESS
An improvement in technology will mean that given quantities of physical and human capital can be combined
to produce more output than was previously possible.
A crucial aspect of technological change is that it allows an economy to transcend the limitations imposed by
diminishing returns (as long as A gets bigger, income per capita can continue to grow)
Technology creation:
Ø Creating new technologies requires investments,
Ø In the case of capital creation, someone must use resources that could have been devoted to
something else to create, refine and put into practise a productive idea
Ø The most important way in which government aids R&D is by providing investors with legal protection
against the copying of their work, in the form of a patent
Transfer of technology:
Ø Conventional factors of production are objects, technologies are ideas lacking a concrete existence
Ø Technology is non-rival and non-excludable
Ø Excludability – degree to which an owner of something can prevent other from using it without
permission.
Determinants of R&D Spending:
Ø Most R&D spending is undertaken privately by firms.
Ø If we wish to understand the determinants of R&D spending, we should look at the problem facing a
firm that is deciding whether to do R&D and how much.
1. Profit Considerations:
à producing a new technology will raise firm’s profits, if it is successful
à in the best-case scenario, its invention will give it monopoly on the sale of some product, allowing
it to earn supernormal profits.
à the extra profits that arise from this competitive advantage are the incentive that makes the firm
do the research
à the amount a firm will want to spend on R&D will depend on how much of an advantage a new
invention will confer (patents)
à the larger the available market, the greater the profits that the new invention will earn
à the firm will take into account how long the advantage conferred by a new invention will last
à uncertainty and risk surrounding R&D will influence the firm’s spending.
2. Creative destruction:
àcreative destruction is the process by which new inventions create profits for firms, these profits
serve as the inventive to engage in research in the first place, and the new technologies so created
are eventually supplanted by yet newer technologies
à enthusiasm often ignores the dislocations suffered by firms and workers that the new technologies
displace.
