Assignment 1.docx

t+h t ( ( r= CHENG Fangyuan ITSC ID:fcheng Student ID:20369816 Assignment 1 1. Since Y =Y er*h , so r=ln( + )/h (1) instantaneous rate: 1.000172% r=ln 2011 1981 )/30 =ln( 7.0716 5.2385 )/30 =0.01000172 (2) discrete rate: 1.005190% according to the discrete model, R=exp(r)-1 r= ln 2011 1981 )/30 =ln( 7.0716 5.2385 )/30 =0.01000172 R=e0.01000172-1 =0.01005190 (3) central rate: 0.9927349% + - h*(+) 2 7.0716-5.2385 = 30*(7.0716+5.2385)/2 =0.009927349 These three rates are not much different. Y =Y e ( t+h T ( ( Doubling time r*h t+h T , so h=ln( + )/r 2 h= =69.3 0.01000172 The doubling time implied by the 1981 2011 growth rate is 70 years. Times that HKs population reaches a size of 10 million h=ln( + )/r =ln( 10 7.0716 )/ 0.01000172 =34.64 In 2046 HKs population will reach 10 million. Growth rate to reach 10million r=ln + )/h =ln( 2030 2011 )/19 10 = ln( )/19 7.0716 =0.018236754 1.82% is high enough for HK population to grown to 10million by 2030. 2. According to the instantaneous growth rate model Y =Y er*h , the population growth rate r= ln + )/h, the population doubling time h= ln + 2 )/r= r 662 1950-1960: r= ln( 2 )/10=0.018171750, h= = 2 =38.14 552 r 0.018171750 830 1960-1970: r= ln( )/10=0.022616014, h= 2 =30.6485 662 0.022616014 987 1970-1980: r= ln( )/10=0.017324434, h= 2 =48.39 830 0.017324434 1143 1980-1990: r= ln( )/10=0.014674162, h= 2 =47.24 987 0.014674162 1250 1990-2000: r= ln( )/10=0.008948717, h= 2 =77.46 1143 0.008948717 Decades Growth Rate(%) Doubling Time(years) 1950-1960 1.82% 39 1960-1970 2.26% 31 1970-1980 1.73% 49 1980-1990 1.47% 48 1990-2000 0.89% 78 2000-2010 0.62% 112 ( Y =Y e Y =Y *e ( 1330 2000-2010: r= ln( )/10=0.006203539, h= 2 =111.73 1250 0.006203539 (1) According to continuous time model, r= ln + )/h 830 1960-1970: r= ln( 662 )/10=0.022616014 r*h t+h t 0.0022616014*50 2010 1960 =662* e0.0022616014*50 =2050.97 The population will reach 2050.97 million in 2010. (2) h= ln + )/r 1500 =ln( 1330 )/0.006203539 =19.39 2015+h 2015+h 1. ) > 2028 2025 In 2030 the population will reach 1.5billion. 3.(1) India: Y =1.26*e0.012*h China: Y =1.37*e0.005*h 0.012* 0.005* > 1.37 1.26 ln (1.37 h > 26 0.007 h > 11.957 In 2027, India will overtake China as the most populous country. (2) Assuming n is the time that Chinas GDO overtake Americas GDP, according to the GDP growth model, China:10.866*(1+0.069)n USA: 17.947*(1+0.026)n 10.866*(1+0.069)n > 17.947*(1+0.026)n (1+0.069) 17.947 1+0.026 10.866 1.0419103n > 17.94710.866 17.947 n > log( ) 10.866 n >12.22 In 2028, China will overtake USA as the largest economy. China: Population size: Y =Y er*h =1.37*e0.005*13 =1.462 billion 13 13 GDP: G2028=G2015*(1+0.069) = 10.866*(1+0.069) =25.869 trillion GDP per capita: India: 2028 2028 25.869*1012 = 1.462*109 =17694.169 r*h 0.012*13 Population size: Y2028=Y2025 e =1.26*e =1.473 billion 13 13 GDP: G2028=G2015*(1+0.078) = 2.074*(1+0.078) =5.506 trillion GDP per capita: USA: 2028 2028 5.506*1012 = 1.473*109 =3737.950 r*h 0.007*13 Population size: Y2028=Y2025 e =0.32*e =0.350 billion 13 13 GDP: G2028=G2015*(1+0.026) = 17.947*(1+0.026) =25.056 trillion GDP per capita: 2028 2028 25.056*1012 = 0.350*109 =71588.571