Question

The table below contains real GDP per capita for selected years in the U.S., in 2011 U.S. dollars, from the Maddison data base. The variable yt denotes real GDP per capita in period t. Year GDP pc 1800y1800, - 1,980 91929 = 10, 543 1930 |y1930-9,490 1931y19318,864 1932|| y1932 7,525 1933 -7,270 1945 y1945-15,992 1948 y1948 14,559 U2007 = 50, 902 V2008-50,276 V2009-48,453 312010 49, 267 V2016 - 53,015 1933 y 2008y

Answer 1

Let the growth rate between 1800 and 2016 in g_t therefore (1 + g_t)^216 times y_1800 = y_2016 therefore (1 + g_t)^216 = y_2016/y_1800 or, (1 + g_t)^216 = 53015/1980 = 26.775 or, 216 ln(1 + g_t) = ln(26.775) or, ln(1 + g_t) = 3.288/216 = 0.0152 or, 1 + g_t = 1.0153 therefore g_t = 0.0153 = 1.53% Let the growth rate between 1948 and 2016 is g_1 therefore (1 + g_1)^68 = y_2016/y_1948 or (1 + g_1)^68 = 53015/14559 or, (1 + g_1)^68 = 3.64 or, 68 ln(1 + g_1) = ln(3.64) or, ln(1 + g_1 = 1.2924/68 = 0.019 or, 1 + g_1 = 1.01919 therefore g_1 = 1.92% Let the RGDP in 1800 be y_1800: therefore (1 + g_t)^216 times y_1800 = 53015 or, (1.01)^216 times y_1800 = 53015 therefore y_1800 = 6179.91 \r\n Let in t years the yearly RGDP per capita would have been $ 365. Then with 1% growth rate till 2016