Question

Using the procedure outlined in the appendix at the end of the chapter for geometric average growth rates​ (in the section titled​ "Calculating Average​ (Compound) Growth​ Rates," reproduce the​ "Implied (Average) Annual​ Growth" figures​ (for the following​ countries: France,​ Singapore, Botswana,​ India, and Kenya. GDP values are​ PPP-adjusted 2005 constant dollars.

Fill in the table below with the geometric average growth rates as a percentage.

​(Round

your responses to two decimal

places​.)

	GDP per Capita		Implied​ (Average) Annual Growth​ (%)
	1960	2010
France	10,212	31,299	_________
Singapore	4,383	55,862	_________
Botswana	674	9,675	_________
India	720	3,477	_________
Kenya	1,020	1,247	_________

Using the procedure outlined in the appendix for finding arithmetic average growth​ rates, calculate the arithmetic average growth rate for the five countries.  

Fill in the table below with the arithmetic average growth rates as a percentage.

​(Round

your responses to two decimal

places​.)

	GDP per Capita		Implied​ (Average) Annual Growth​ (%)
	1960	2010
France	10,212	31,299	_________
Singapore	4,383	55,862	_________
Botswana	674	9,675	_________
India	720	3,477	_________
Kenya	1,020	1,247	_________

Compare the geometric and arithmetic average growth rates.  

The arithmetic average

overstates, or neither understates nor overstates, or understates. choose one of the three.

the actual growth rate.

Answer 1

	GDP Per Capita		Implied (Average) Annual Growth (%)
	1960	2010
France	10212	31299	2.20
Singapore	4383	55862	5.22
Botswana	674	9675	5.47
India	720	3477	3.19
Kenya	1020	1247	0.40

Geometric Average Annual Growth rate (%) = {(GDP per capita in 2010/GDP per capita in 1960)^{(1/(2010-1960))} -1 } *100

	GDP Per Capita		Implied (Average) Annual Growth (%)
	1960	2010
France	10212	31299	206.49
Singapore	4383	55862	1174.51
Botswana	674	9675	1335.45
India	720	3477	382.91
Kenya	1020	1247	22.25

Average Annual Growth Rate = (GDP per capital in 2010-GDP per capita in 1960)/GDP per Capita in 1960*100

From comparing both tables, we see arithmetic annual growth rate(%) is very high than geometric Average annual growth rate(%). Therefore, Arithmetic average annual growth rate(%) overstates.