Consider the following data on real gdp per capita in the united states:
year us real gdp per capita
1950 $14,432
1960 $17,335
1970 $23,236
1980 $28,472
1990 $36,005
2000 $44,503
2010 $47,790
2011 $48,186
2012 $48,884
2013 $49,247
2014 $50,051
(a) calculate the percentage growth rates in real gdp per capita in each of the years 2011 through 2014, from the previous year.
(b) now, instead of calculating the annual percentage growth rates in the years 2011 through 2014 directly, use as an approximation 100 x (in yt - in yt-1), where y, is real per capita gdp in year t. how close does this approximation come to the actual growth rates you calculated in part (a)?
(c) repeat parts (a) and (b), but now calculate the percentage rates of growth in real per capita gdp from 1950 to 1960, from 1960 to 1970, from 1970 to 1980, from 1980 to 1990, from 1990 to 2000, and from 2000 to 2010. in this case, how large an error do you make by approximating the growth rate by the change in the natural log? why is there a difference here relative to parts (a) and (b)?