Question

1. Consider an economy in which the population grows at the rate 5% per year. It has the following production function Y = KL1-9 where is given by the last two digits of your student number divided by 100 (e.g. if your student number is SB6-1234-5, then the value of is 45/100 = 0.45). The depreciation rate of capital is 5% per year. Let us assume that the economy is in the steady state now. Suddenly, at year 0, an earthquake happens and it destroys 50% of the steady state value of the economy's capital stock per capita, k*. As standard, y = Y/L, K = K/L and C = C/L. a) Calculate the values of k and y at year 0 (the year when the earthquake happens) and year 1 (one year after the earthquake happens). b) What is the economy's economic growth rate (i.e. Ay/y) from year 0 to year 1 ? c) What is the economy's economic growth rate (i.e. Ay/y) from year 1 to year 2 ? d) Please use separate diagrams to describe the dynamic changes of the following variables due to this event: i) capital stock per capita (i.e. k), ii) output per capita (i.e. y). In your diagrams, x-axis is time.

please assume that the saving rate is 0.2 (i.e. s = 0.2) and the theta is 0.11

Answer 1

n=0.05 S=02 Y = KO LITO , 020111 , 8=0.05 Qu - per capita terms y = f(k)= Kolla ko u steady state , kas . ftn. = 2. 0.2 ol k = 0.2 Rooostoos k 1-0 =2 R=2to, o=0:11 k=2-173 y = ko = 109 At year o, 501 of k is destroyed, K*2173 - 1 (2.193) = (2.183) = 1:09. yo = ko = 1.0095ų 1.01 Qu year ! RH = (1-8-n) kt t s fllet). ki = (1-8-n) kots tro) = (1 -0.11.09 + 02 (101) = 1.183) y = f(ki) = kion = 1.018. u 1.02. ON

i. Ri= Yi= 1.183 rorg. 1.02 Economice growth rate >> AY - Yo-yo = 1 yo = 102-.01 1018 tot 1.04 0.01 lol I we know ki= 1.183 11 = 1:02. for year 2, k2= (-8-n) lei - Sfler) = 0.9 (1:18) - 0. 221.02) k2= 1.266 ņ 1:27 y2 = f(R2) = (1-27) x 1.03 Growth rate from year 2 to year! 9= AY = 42-Y) = 1.03-1.02 102 - 0.01. We can see the growth rate of y Counuts is more or less unstaut whereas growth rate of capital per talf capela is rectius declinin Also the grown rate of both Ray are neglit negligible ie almost o

Date DELTA Pg No Output her worker Grown effects. constant a rown I rate 2 . capital per worker i Grown effects. k - debring + destiny declining grown rate . 109 - the lines are flat (since grown is negligible).