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Lecture 4

Week 4 chapter notes

3 Pages
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Department
Economics for Management Studies
Course Code
MGEB06H3
Professor
Jack Parkinson

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Chapter 8 Economic Growth II: Technology, Empirics, and Policy Notes
8.1 Technological Progress in the Solow Model
The Efficiency of Labour
x the production function is now written as: Y = F(K, L × E) where E is a new variable called the efficiency of labour
x efficiency of labour Æ variable in Solow growth model that measures health, education, skills, and knowledge of labour force
x the efficiency of labour is meant to reflect societys knowledge about production methods: as the available technology improves,
the efficiency of labour rises, and each hour of work contributes more to the production of goods and services
x the term L × E can be interpreted as measuring the effective number of workers
x it takes into account the number of actual workers L and the efficiency of each worker E; in other words, L measures the number
of workers in the labour force, whereas L × E measures both the workers and the technology with which the worker is equipped
x this new production function states that total output Y depends on K and on the effective number of workers, L × E
x the essence of this approach to modelling technological progress is that increases in E are analogous to increases in L
x the simplest assumption about technological progress is that it causes the efficiency of labour E to grow at some constant rate g
x this form of technological progress is called labour augmenting, and g is called rate of labour-augmenting technological progress
x labour-augmenting technological progress Æ advances in productive capability that raise the efficiency of labour
x because the labour force L is growing at rate n, and the efficiency of each unit of labour E is growing at a rate g, the effective
number of workers L × E is growing at rate n + g
The Steady State with Technological Progress
x although technological progress does not cause the actual number of workers to increase, each worker in effect comes with more
units of labour over time; thus, technological progress causes the effective number of workers to increase
x now let k = K / (L × E) stand capital per effective worker, and y = Y / (L × E) stand for output per effective worker
x with these definitions, the equation showing the evolution of k over time becomes ûk = sf(k) – (/ + n + g)k
x as before, change in capital stock ûk equals investment sf(k) minus breakeven investment (/ + n + g)k; but, because k = K / EL,
break-even investment includes 3 terms: to keep k constant, /k is needed to replace depreciating capital, nk is needed to provide
capital for new workers, and gk is needed to provide capital for the new “effective workers” created by technological progress
x there is one level of k denoted k*, at which capital per effective worker and output per effective worker are constant
x as before, this steady state represents the long-run equilibrium of the economy
The Effects of Technological Progress
Steady-State Growth Rates in the Solow Model with Technological Progress
Variable Symbol Steady-State Growth Rate
Capital per effective worker k = K / (E × L) 0
Output per effective worker y = Y / (E × L) = f(k) 0
Output per worker Y / L = y × E g
x according to the Solow model, only technological progress can explain sustained growth and persistently rising living standards
x the Golden Rule level of capital is now defined as the steady state that maximizes consumption per effective worker
x the steady-state consumption per effective worker is c* = f(k*) – (/ + n + g)k*
x steady-state consumption is maximized if MPK = / + n + g or MPK – / = n + g
x that is, at Golden Rule level of capital, net marginal product of capital, MPK – /, equals rate of growth of total output, n + g
8.2 From Growth Theory to Growth Empirics
Balanced Growth
x according to the Solow model, technological progress causes the values of many variables to rise together in the steady state
x the capital-output ratio has remained approximately constant over time
x technological progress also affects factor prices; however, the real rental price of capital is predicted to stay constant over time
Convergence
x the Solow model makes clear predictions about when convergence should occur
x according to the model, whether two economies will converge depends on why they differ in the first place
x on the one hand, if two economies have similar steady states, perhaps because the economies have similar rates of saving, then
convergence should be expected; on the other hand, if two economies have different steady states, perhaps because the
economies have different rates of saving, then convergence should not be accepted
x the economies of the world exhibit conditional convergence: they appear to be converging to their own steady states, which in
turn are determined by such variables as saving, population growth, and human capital
Factor Accumulation versus Production Efficiency
x as a matter of accounting, international differences in income per person can be attributed to either (1) differences in the FOPs,
such as the quantities of physical and human capital, or (2) differences in the efficiency with which economies use their FOPs
x workers in poor country may be poor because they lack tools and skills (TAS) or because TAS they have are not put to best use
x to describe the issue in terms of the Solow model, the question is whether the large gap between rich and poor is explained by
differences in capital accumulation (including human capital) or differences in the production function
x a common finding is that factor accumulation and production efficiency are positively correlated: nations with higher levels of
physical and human capital also tend to use those factors efficiently
x one hypothesis is that an efficient economy may encourage capital accumulation
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Description
Chapter 8 Economic Growth II: Technology, Empirics, and Policy Notes 8.1 Technological Progress in the Solow Model The Efficiency of Labour N the production function is now written as: Y = F(K, L E) where E is a new variable called the efficiency of labour N efficiency of labour variable in Solow growth model that measures health, education, skills, and knowledge of labour force N the efficiency of labour is meant to reflect societys knowledge about production methods: as the available technology improves, the efficiency of labour rises, and each hour of work contributes more to the production of goods and services N the term L E can be interpreted as measuring the effective number of workers N it takes into account the number of actual workers L and the efficiency of each worker E; in other words, L measures the number of workers in the labour force, whereas L E measures both the workers and the technology with which the worker is equipped N this new production function states that total output Y depends on K and on the effective number of workers, L E N the essence of this approach to modelling technological progress is that increases in E are analogous to increases in L N the simplest assumption about technological progress is that it causes the efficiency of labour E to grow at some constant rate g N this form of technological progress is called labour augmenting, and g is called rate of labour-augmenting technological progress N labour-augmenting technological progress advances in productive capability that raise the efficiency of labour N because the labour force L is growing at rate n, and the efficiency of each unit of labour E is growing at a rate g, the effective number of workers L E is growing at rate n + g The Steady State with Technological Progress N although technological progress does not cause the actual number of workers to increase, each worker in effect comes with more units of labour over time; thus, technological progress causes the effective number of workers to increase N now let k = K (L E) stand capital per effective worker, and y = Y (L E) stand for output per effective worker N with these definitions, the equation showing the evolution of k over time becomek = sf(k) ( + n + g)k N as before, change in capital stock k equals investment sf(k) minus breakeven investment ( + n + g)k; but, because k = K EL, break-even investment includes 3 terms: to keep k constant, k is needed to replace depreciating capital, nk is needed to provide capital for new workers, and gk is needed to provide capital for the new effective workers created by technological progress N there is one level of k denoted k*, at which capital per effective worker and output per effective worker are constant N as before, this steady state represents the long-run equilibrium of the economy The Effects of Technological Progress Steady-State Growth Rates in the Solow Model with Technological Progress
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