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Answer 17 questions of Economic Development including economic maths

Development Economics

Problem Set 1

Sherif Khalifa

1. (a) What is the usual indicator of living standards?

(b) How is this indicator of living standards calculated ?

(c) What are the problems with this indicator?

2.Consider a country whose national income is $750 Million and whose population is 12.5
million. Assume in this country that the rich are 20% of the population and own 85% of the

nation’s income.

(a) The income per capita of the nation =

(b) The income per capita of the rich =

(c) The income per capita of the poor =

(d) If the total income of the rich increases by 50%, the new nation’s income =

(e) If the total income of the rich increases by 50%, the new nation’s income per capita =

(f) The growth rate of the nation’s income per capita =

(g) Can we conclude that the living standards have improved in this country? Why?

1

3.Assume the growth rate of income is 10% and the growth rate of population is 5.83%?
(a) The doubling time of income =

(b) The doubling time of population =

(c) The doubling time of income per capita =

4. Consider the following information about a developing country:

Income per capita $1037

Life expectancy 43 years

Adult literacy 53%

Gross enrollment 46%

(a) Income index =

(b) Life Expectancy index =

(c) Education index =

(d) Human Development index =

2

5. Consider the Harrod-Domar model:
(a) If capital output ratio is 3, and the saving rate is 27%. The growth rate of income =

(b) To increase the growth rate of income, what do we need to do?

(c) if you want your country to grow at 5%, and the capital output ratio is 2. The nation

should save what percentage of the nation’s income =

(d) What are the criticisms to the Harrod-Domar model?

6. Consider the Lewis Theory of structural change. What are the assumptions that are
considered unrealistic in this model?

3

7. Consider the following table with individuals in a country and their incomes:

Individuals Income Deciles Quintiles

1 1

2 3

3 5

4 8

5 10

6 12

7 13

8 15

9 16

10 17

Total 100 100 100

(a) Calculate the deciles and quintiles.

(b) The Kuznets’ratio =

(c) The Palma ratio=

(d) The Quintile ratio=

4

8. Consider the following table with individuals in a country and their incomes. Fill in
the following table:

Individuals Income % of income recipients % of Income

1 $4 10%

2 $8 20%

3 $16 30%

4 $20 40%

5 $28 50%

6 $40 60%

7 $44 70%

8 $60 80%

9 $80 90%

10 $100 100% 100%

Total $400

Draw the Lorenz curve for this country:

10% 20% 30% 40% 50% 60% 70% 80% 90% 100%0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

% of income recipients

% of income

5

9. Consider the following Lorenz curves for countries A and B:

A

B

(a) Which country has a higher income inequality?

(b) Which country has a higher Gini coeffi cient?

(c) What is bad about income inequality?

10. Consider the following graph for the labor market in a developing country:

Supply

Demand

500
Employment

Wage

300

650

(a) Total income =

6

(b) Total wages =

(c) Total profits =

(d) The share of workers out of the nation’s income =

(e) The share of capitalists out of the nation’s income =

11. Consider the following table of annual incomes of individuals in a country. Assume
the poverty line is at $1 per day:

Individual Income

1 465

2 215

3 505

4 325

5 275

6 400

7 175

8 265

9 105

10 65

(a) The headcount index =

(b) The total poverty gap =

(c) The average poverty gap =

(d) The average income shortfall =

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12. If a country has a birth rate of 25 per 1000 of the population, and a death rate of 15
per 1000 of the population, and no net migration. What is the population growth rate?

13. Consider the Malthusian model:

Income per capita

Growth rates
Income growth rate

Population growth rate

15,4391,685

2.3

0.56

5,674

Forecast the population growth rate, income growth rate, and income per capita for a

country with the following initial income per capita:

Initial Final Final Final

Income per capita Population Growth Income Growth Income per capita

$16,000

$15,439

$7,891

5,674

$4,367

$1,685

$981

8

14. Consider the household theory of fertility. If the income of the household is $250,
and the price of a child=$25, while the price of goods=$5:

Children

Goods

0 X

Y

(a) X =

(b) Y =

If the equilibrium number of children and goods is always determined by dividing the

income equally between them.

(c) The initial equilibrium number of children =

(d) The initial equilibrium number of goods =

(e) Start from the initial equilibrium in the following graph. If the cost of children declines

to $12.5 only, draw the new household’s budget line and the new household’s equilibrium?

Children

Goods

0 X

Y

9

(f) Start from the initial equilibrium again. If the income of the household doubles because

men got better paying jobs, draw the new household’s budget line and the new household’s

equilibrium?

Children

Goods

0 X

Y

(g) Start from the initial equilibrium again. If the income of the household doubles because

women are working and contributing to the income of the household, which increases the

opportunity cost and the price of children to $50, and the price of goods=$5. Draw the new

household’s budget line and the new household’s equilibrium?

Children

Goods

0 X

Y

10

15. Consider the Harris-Todaro model:
Agriculture

Wage
Manufacturing

Wage

70

0 1000375 525 875

66

4

14

Assume full employment and flexible wages:

(a) Manufacturing wage =

(b) Agriculture wage =

(c) Manufacturing employment =

(d) Agriculture employment =

If the labor union increases the manufacturing wage to $70, and assuming full employment:

(a) Manufacturing wage =

(b) Agriculture wage =

(c) Manufacturing employment =

(d) Agriculture employment =

If the labor union increases the manufacturing wage to $70, and assuming unemployment:

(a) Manufacturing wage =

(b) Agriculture wage =

(c) Manufacturing employment =

(d) Agriculture employment =

(e) Total Unemployment =

(f) Unemployment rate in urban areas =

(g) Unemployment rate in the country =

(h) Expected Wage in Manufacturing =

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16. Consider the child labor model of multiple equilibria:

14,961
Employment

Wage

123

187

10,485

154

12,376

Forecast the wage and the level of child labor and adult labor in a country with the

following initial wages:

Initial Final Final Final

Wage Wage Adult Labor Child Labor

$115

$123

$130

$154

$160

$187

$190

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17. Consider the following graph for a 13 years old who is deciding whether to attend a
secondary school or dropout from school after primary education.

Age

Earnings

retirement13 18

Secondary

Primary
49.75

23.67

24.98

Describe the decision of this person and its determinants?

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