1. Use the following goalposts in calculating the HDI. "GOALPOSTS" 0% Progress $100 20 0 0 [Hint: You may want to use Excel to speed the following calculations, since the question involves re-calculating several times with different numbers. But, it is still necessary to show work from all key steps.] a. Calculate the HDI (Human Development Index) for a country with PPP income of $15,000, average education of 9 years, expected education of 11 years, and life expectancy of 65. What is the interpretation, or scale, of the HDI? Income Life Expectancy Average Education Expected Education 100% Progress $75,000 85 15 18 b. What would the country's HDI be if their income improved to $35,000 and all other numbers stayed the same? What is the percentage increase in the HDI as compared to part a.? c. Return to the original data of part a. To what level would life expectancy need to increase in order to increase the HDI by the same amount that the $20,000 increase (or more to the point, 133% increase) in income
1. Use the following goalposts in calculating the HDI. "GOALPOSTS" 0% Progress $100 20 0 0 [Hint: You may want to use Excel to speed the following calculations, since the question involves re-calculating several times with different numbers. But, it is still necessary to show work from all key steps.] a. Calculate the HDI (Human Development Index) for a country with PPP income of $15,000, average education of 9 years, expected education of 11 years, and life expectancy of 65. What is the interpretation, or scale, of the HDI? Income Life Expectancy Average Education Expected Education 100% Progress $75,000 85 15 18 b. What would the country's HDI be if their income improved to $35,000 and all other numbers stayed the same? What is the percentage increase in the HDI as compared to part a.? c. Return to the original data of part a. To what level would life expectancy need to increase in order to increase the HDI by the same amount that the $20,000 increase (or more to the point, 133% increase) in income
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Question
![1. Use the following goalposts in calculating the HDI.
"GOALPOSTS"
0% Progress
$100
20
0
0
Income
Life Expectancy
Average Education
Expected Education
100% Progress
$75,000
85
15
18
[Hint: You may want to use Excel to speed the following calculations, since the question involves re-calculating
several times with different numbers. But, it is still necessary to show work from all key steps.]
a. Calculate the HDI (Human Development Index) for a country with PPP income of $15,000, average
education of 9 years, expected education of 11 years, and life expectancy of 65. What is the interpretation, or
scale, of the HDI?
b. What would the country's HDI be if their income improved to $35,000 and all other numbers stayed the
same? What is the percentage increase in the HDI as compared to part a.?
c. Return to the original data of part a. To what level would life expectancy need to increase in order to
increase the HDI by the same amount that the $20,000 increase (or more to the point, 133% increase) in income
would (calculated in part b.)?
d. One might think the goalpost of $75,000 is somewhat arbitrary. Change this income goalpost to $125,000
and re-calculate the HDI for parts a. and b. What happens to the percentage increase in the HDI (from part a. to
part b) under the new goalpost (i.e. is it higher or lower than under the original goalpost)?
e. What level of income represents 50% progress from $100 to $75,000, according to the HDI income
subindex?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F144161ac-559f-4b1a-80a0-0fffa7827db1%2F82d5735b-69c3-40ca-823d-e5d24a6ebf61%2F8s0fhjb_processed.png&w=3840&q=75)
Transcribed Image Text:1. Use the following goalposts in calculating the HDI.
"GOALPOSTS"
0% Progress
$100
20
0
0
Income
Life Expectancy
Average Education
Expected Education
100% Progress
$75,000
85
15
18
[Hint: You may want to use Excel to speed the following calculations, since the question involves re-calculating
several times with different numbers. But, it is still necessary to show work from all key steps.]
a. Calculate the HDI (Human Development Index) for a country with PPP income of $15,000, average
education of 9 years, expected education of 11 years, and life expectancy of 65. What is the interpretation, or
scale, of the HDI?
b. What would the country's HDI be if their income improved to $35,000 and all other numbers stayed the
same? What is the percentage increase in the HDI as compared to part a.?
c. Return to the original data of part a. To what level would life expectancy need to increase in order to
increase the HDI by the same amount that the $20,000 increase (or more to the point, 133% increase) in income
would (calculated in part b.)?
d. One might think the goalpost of $75,000 is somewhat arbitrary. Change this income goalpost to $125,000
and re-calculate the HDI for parts a. and b. What happens to the percentage increase in the HDI (from part a. to
part b) under the new goalpost (i.e. is it higher or lower than under the original goalpost)?
e. What level of income represents 50% progress from $100 to $75,000, according to the HDI income
subindex?
Expert Solution
Introduction
HDI = (Life expectancy index * education index * income index)^(1/3)
Life Expectancy Index = (Life Expectancy - 20) / (85 - 20)
Education Index = (Mean years of schooling index + Expected years of schooling index) / 2
ncome index = (ln(income per capita) - ln(100)) / (ln(75000) - ln(100))
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