This seems to be an improvement over the development accounting exercise in the

# This seems to be an improvement over the development

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to di/er by a factor of 8. This seems to be an improvement over the development accounting exercise in the lecture. The key is that the ratio in investment rate are raised to the power ° 1 ± ° ± ± and ± 1 ± ° ± ± : The appearance of ² in the denominator increases the power. (d) The speed of convergence is (1 ° ± ° ² ) ( n + ° + g ) . If ± = ² = 1 = 3 ; then ± + ² = 2 = 3 : So the half-life in this model is twice that of the Solow model without human capital (where the speed of convergence is (1 ° ± ) ( n + ° + g )) . The intuition is similar to the one given in Class Exercise 1. 3
(e) Given g = 0 ; the growth rate of Y=L is the same as the growth rate of y: As in part (a), it can be shown that Y; H; K all grow at the same rate along the balanced growth path and H K = s h s k From the production function Y = K ° H 1 ± ° = K ° H K ± 1 ± ° = K ° s h s k ± 1 ± ° so the model is reduced to a "AK" model with ´ s h s k µ 1 ± ° taking the role of "A". There is endogenous growth because of the nondecreasing return to the set of reproducible capital ( K and H ) . The common growth rate is _ y y = _ k k = _ h h = s ° k s 1 ± ° h ° ° ° n Thus, the growth rate depends on the investment rates. Higher s k and s h also imply higher growth rate in the long run. Math : The speed of convergence can be computed as below. Note ³ y ± _ y y = d ln y dt First order Taylor expansion around the steady state y ° d ln y dt ² ° ² (ln y ° ln y ° ) (7) where ² = ° y d (ln y ) j y ° is the rate of convergence for y near the steady state. From the production function, _ y y = ± _ k k + ² _ h h = ) d ln y dt = ± d ln k dt + ² d ln h dt (8) First order Taylor expansion around the steady state ( k ° ; h ° ) ; ³ k = d ln k dt ² ° k @ ln k ± (ln k ° ln k ° ) + ° k @ ln h ± (ln h ° ln h ° ) ³ h = d ln h dt ² ° h @ ln k ± (ln k ° ln k ° ) + ° h @ ln h ± (ln h ° ln h ° ) Given ³ k = _ k k = s k k ° ± 1 h ± ° ^ ° ³ h = _ h h = s h k ° h ± ± 1 ° ^ ° 4
so, k @ ln k = k @k @k @ ln k = s k ( ± ° 1) k ° ± 1 h ±

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• Winter '19
• NGAI
• Mankiw

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