ECON311HW4Solutions

# ECON311HW4Solutions - PS4 Answer key Exercise 1 a The key...

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PS4 Answer key: Exercise 1 a.) The key equation in the Solow model is ∆g1863 =g1871g1877−(g2012+g1866)g1863 In SS, ∆g1863 =0g1436 g1871g1877 =(g2012+g1866)g1863 0.3(3g1863 g2868.g2873 )=0.1g1863 0.9=0.1 g1863 g1863 g2868.g2873 g1863 =81 SS output per worker is: g1877 =3(g1863 ) g2868.g2873 =27 SS consumption per worker: g1855 =(1−g1871)g1877 g1855 =(1−0.3)27=18.9 b.) ss k : 0.4(3g1863 g2868.g2873 )=0.1g1863 g1863 =144 ss y: g1877 =3(g1863 ) g2868.g2873 =36 ss c: g1855 =(1−0.4)36=21.6 The higher is the saving rate, the higher the ss value for the ss k * and y * . On the other hand, increasing the saving rate has two effects on c: First, since y * is higher, g1855 should also be higher since g1855 =(1−g1871)g1877 Second, a higher s, decreases g1855 because of the first term on the right of the previous equation. The level of s that makes consumption the highest possible in SS is given by the golden rule. c.) ss k : 0.4(3g1863 g2868.g2871 )=0.1g1863 g1863 =34.8 ss y: g1877 =3(g1863 ) g2868.g2873 =8.7 ss c: g1855 =(1−0.4)36=21.6

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Exercise 2 a.) g1877 g2868 g3002 =4(g1863 g2868 g3002 ) g2868.g2873 =15.5 g1855 g2868 g3002 =(1−0.3)g1877 g2868 g3002 =10.8 g1877 g2868 g3003 =4(g1863 g2868 g3003 ) g2868.g2873 =17.8 g1855 g2868 g3003 =(1−0.25)g1877 g2868 g3003 =13.4
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