# L3 - Within and beyond the Solow model Chapters 4-5 book 1...

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Within and beyond the Solow model Chapters 4-5, book 1 Within the Solow model Technological progress (increasing A t ) Effects of s , A , L 0 , and n A side point: The Malthus model The model predictions and data Beyond the Solow model Long run growth without technological progress: AK model Long run growth with endogenous technological progress 1

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Technological progress: increasing A t Recall that k t +1 = s · A t · ( k t ) β 1 + n + (1 - δ ) · k t 1 + n . The case of interest: A t = (1 + γ ) t · A 0 and γ 0 γ = 0 , no technological progress (the numerical example in L2). γ > 0 , constant but positive technological progress. 2
For this case, the economy is in a steady state at t if y t +1 /y t = k t +1 /k t . Because y t = A t k β t and y t +1 = A t +1 k β t +1 and A t +1 /A t = 1 + γ , y t +1 /y t = k t +1 /k t implies (1 + γ ) k β t +1 k β t = k t +1 k t , and so k t +1 k t = (1 + γ ) 1 1 - β . (If γ = 0 , then k t +1 = k t . So this new definition of steady state encompasses the definition in L2.) To solve the steady-state value of k t , use k t +1 /k t = (1 + γ ) 1 1 - β and (1 + n ) k t +1 = (1 - δ ) k t + sA t k β t . 3

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Effects of s, A, n and L 0 First consider γ = 0 . An important equation: k * = ( sA n + δ ) 1 1 - β . 4
Two economies: s 1 < s 2 , same k 0 and else. Outside steady states, economy 2 has higher growth rates of k and y .

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