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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