# Week 4 chapter notes

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 society’s 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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## Document Summary

Chapter 8 economic growth ii: technology, empirics, and policy notes. N with these definitions, the equation showing the evolution of k over time becomes k = sf(k) ( + n + g)k. Steady-state growth rates in the solow model with technological progress. Symbol k = k / (e l) y = y / (e l) = f(k) N 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. N the most direct way in which the government affects national saving is through public saving the difference between what the government receives in tax revenue and what it spends. 8. 4 beyond the solow model: endogenous growth theory. The model can explain much of what we see in the data, such as balanced growth and conditional convergence.