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# lecture3 - Lecture 3 Implications of The Solow Model The...

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Lecture 3 Implications of The Solow Model

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ECN/APEC 6000/7230 III - 2 The Saving Rate Saving rate s is exogenous in Solow model. How can policy affect saving? Public consumption vs investment decision. Taxes on capital alter return on saving. Later, we will endogenize consumption-saving decision. For now, we consider how changes in s affect endogenous variables.
ECN/APEC 6000/7230 III - 3 Saving and Capital Suppose the saving rate increases from s 1 to s 2 . Steady state capital per effective labor increases from k * 1 to k * 2 . ( n + g + δ ) k s 1 f ( k ) s 2 f ( k ) k k * 1 k * 2

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ECN/APEC 6000/7230 III - 4 Transition to New Steady State The capital stock does not immediately jump to k * 2 . We have to solve the differential equation with the initial condition k (0) = k * 1 . Since dk (0)/ dt > 0, k will increase. As k increases, dk / dt will return to 0. ). ( ) ( )) ( ( ) ( t k n g t k sf dt t dk + + - = δ
ECN/APEC 6000/7230 III - 5 Saving and Per Capita Output Per capita output is Since f > 0, steady-state Y / L increases with s . A change in the saving rate has a level effect but not a growth effect on per capita output. The growth rate of Y / L initially jumps above g . – As k converges to k * 2 , the growth rate returns to g . The intercept of ln( Y ( t )/ L ( t )) increases but the long-term slope is unchanged.

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