In: Economics

Consider the following data on real GDP per capita in:

Year |
Per Capita Real GDP |

1950 |
14 339 |

1960 |
17 351 |

1970 |
23 790 |

1980 |
30 732 |

1990 |
35 868 |

2000 |
43 288 |

2010 |
46 406 |

2011 |
47 554 |

2012 |
47 741 |

2013 |
48 066 |

2014 |
48 780 |

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×*log*y**t**-*log*y**t-1*

where *y**t* is real per capita GDP in year
*t*. How close does this approximation come to the actual
growth rates you calculated in part (a)?

a)

The annual percentage growth rates in real GDP per capita is given by [(Yt - Yt-1)/Yt-1]*100%

Thus, the annual percentage growth rates in real GDP per capita for each of the years 2011 through 2014, from the previous year is:

Year | Per Capita Real GDP | The percentage growth rates in real GDP per capita |

1950 | 14339 | |

1960 | 17351 | |

1970 | 23790 | |

1980 | 30732 | |

1990 | 35868 | |

2000 | 43288 | |

2010 | 46406 | |

2011 | 47554 | 2.47% |

2012 | 47741 | 0.39% |

2013 | 48066 | 0.68% |

2014 | 48780 | 1.49% |

b)

Using as an approximation
*100×*log*y**t**-*log*y**t-1*,
where *y**t* is real per capita GDP in year
*t*, the result is:

Year | Per Capita Real GDP (Yt) | The percentage growth rates in real GDP per capita | Per Capita Real GDP (Yt-1) | 100×logyt-logyt-1 |

1950 | 14339 | |||

1960 | 17351 | 14339 | ||

1970 | 23790 | 17351 | ||

1980 | 30732 | 23790 | ||

1990 | 35868 | 30732 | ||

2000 | 43288 | 35868 | ||

2010 | 46406 | 43288 | ||

2011 | 47554 | 2.47 | 46406 | 1.06 |

2012 | 47741 | 0.39 | 47554 | 0.17 |

2013 | 48066 | 0.68 | 47741 | 0.29 |

2014 | 48780 | 1.49 | 48066 | 0.64 |

It shall be noted that when
*100×*log*y**t**-*log*y**t-1*
is used as an approximation, the result is not close to the annual
percentage growth rates in real GDP per capita. This is because,
the approximation uses log, which is log to the base of 10.

It shall be noted that instead natural log, that is log to the base of e if used, the approximation would take the form

*100×*ln*y**t**-*ln*y**t-1*

The result is:

Year | Per Capita Real GDP (Yt) | The percentage growth rates in real GDP per capita | Per Capita Real GDP (Yt-1) | 100×logyt-logyt-1 | 100×lnyt-lnyt-1 |

1950 | 14339 | ||||

1960 | 17351 | 14339 | |||

1970 | 23790 | 17351 | |||

1980 | 30732 | 23790 | |||

1990 | 35868 | 30732 | |||

2000 | 43288 | 35868 | |||

2010 | 46406 | 43288 | |||

2011 | 47554 | 2.47 | 46406 | 1.06 | 2.44 |

2012 | 47741 | 0.39 | 47554 | 0.17 | 0.39 |

2013 | 48066 | 0.68 | 47741 | 0.29 | 0.68 |

2014 | 48780 | 1.49 | 48066 | 0.64 | 1.47 |

It shall be noted that excel function log(yt) would provide the value of log to the base of 10, whereas Ln(yt) would provide the value of log to the base of e

Thus, the approximation
*100×*ln*y**t**-*ln*y**t-1*
provides an estimate that is close to the annual percentage growth
rates in real GDP per capita

Consider the following data for the country below.
Real GDP per Capita$60,000, Year 1 Population 300 ,Year 1 and
Year 2(Millions) Inflation Rate(%) 3 Growth Rate Real GDP (%),Year
1 to Year 2 8
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a. What is real GDP per capita in year 2? $
b. What is real GDP in year 2? $ trillion

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