Lecture 8 - 11/9/2009 ECONOMICGROWTH:TECHNOLOGICAL

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11/9/2009 1 ECONOMIC GROWTH TECHNOLOGICAL ECONOMIC GROWTH: TECHNOLOGICAL PROGRESS AND EMPIRICAL APPLICATIONS EC205.01 FALL 2009 ALPER 1 Outline y Solow model with technological progress y Policies to promote growth y Empirics: Theory vs. facts y Endogenous growth models y One sector y Two sector EC205.01 FALL 2009 ALPER 2 The Solow Model y … does not incorporate technological progress in its standard version y Implication: Per capita income is constant at the steady state y Is this realistic? y Examples: y U.S. real per capita income growth: 2% annually on average between 1904–2004 y Turkish real per capita income growth: 2% annually on average between 1969 – 2008 y The real price of computer power has fallen by 30% in the last 3 decades EC205.01 FALL 2009 ALPER 3
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11/9/2009 2 TECHNOLOGICAL PROGRESS IN THE SOLOW MODEL y Define E = labor efficiency y Assume: y Technological progress is labor augmenting y it increases labor efficiency at the exogenous rate g E g Δ y We now write the production function as: where L × E = the number of effective workers. y Increases in labor efficiency have the same effect on output as increases in the labor force. EC205.01 FALL 2009 ALPER 4 = (, ) Y FKL E Notation y Notation: y = Y/LE = output per effective worker k = K/LE = capital per effective worker y Production function per effective worker: y = f ( k ) y Saving and investment per effective worker: sy = sf ( k ) y “Per effective worker” y a mathematical device to make the model tractable… EC205.01 FALL 2009 ALPER 5 Break even investment ( δ + n + g ) k = break even investment: the amount of investment necessary to keep k constant. Consists of: y k to replace depreciating capital y n k to provide capital for new workers y gk to provide capital for the new “effective” workers created by technological progress y Technological progress increases the number of effective workers at rate , y capital per effective worker to fall at rate y Investment equal to would prevent this. EC205.01 FALL 2009 ALPER 6
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11/9/2009 3 Technological progress in the Solow model Investment, break even investment sf(k) ( δ + n + g ) k Δ = s f ( ) ( + n + ) EC205.01 FALL 2009 ALPER 7 Capital per effective worker, * Steady state growth rates 0 k = K / ( L × E ) Capital per effective worker Steady state growth rate Symbol Variable EC205.01 FALL 2009 ALPER n + g Y = y × E × L Total output g ( Y / L ) = y × E Output per worker 0 y = Y / ( L × E ) Output per effective worker The Golden Rule To find the Golden Rule capital stock, express c * in terms of k * : c * = y * i * = f k * + n + g k * In the Golden Rule steady state, the marginal EC205.01 FALL 2009 ALPER 9 f ( k ) ( n g ) k c * is maximized when MPK = + n + g or equivalently, MPK = n + g product of capital net of depreciation equals the pop. growth rate plus the rate of tech progress.
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11/9/2009 4 Balanced Growth y Solow model’s steady state exhibits balanced growth many variables grow at the same rate.
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Lecture 8 - 11/9/2009 ECONOMICGROWTH:TECHNOLOGICAL

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