Graphing and Quantitative Exercises Introductory



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Title

Graphing and Quantitative Exercises

Introductory
Text






Question 1

Type:
Essay



Assume there are two countries, Oldsville and Youngsville, with populations of 500 people each with the same fertility rates among the young and the same mortality rates among the old in each country. Assume that in each country mortality rates are 13 percent and fertility rates are 3.7. Youngsville has 86 percent young and 14 percent old whereas Oldsville has 32 percent young and 68 percent old. Fill out the following table:

Age Group Per Country

Initial Age Distribution Per Country

Fertility Rate

Mortality Rate (%)

Population Second Period

Young in Youngsville

 

 

 

 

Old in Youngsville

 

 

 

 

Young in Oldsville

 

 

 

 

Old in Oldsville

 

 

 

 




Hint:

 

Feedback:

Answer:
a.

Age Group Per Country

Initial Age Distribution Per Country

Fertility Rate

Mortality Rate (%)

Population Second Period

Young in Youngsville

86

3.7

13

159.1

Old in Youngsville

14

0

100

74.82

Young in Oldsville

32

3.7

13

59.2

Old in Oldsville

68

0

100

27.84









Question 2

Type:
Essay



Use the information in Question 1 to answer the following questions.
a. What is the total population in the second period in each country? Show your calculations.
b. What are the population outcomes in each country given their differences in the initial age distribution? Explain.

Hint:

 

Feedback:

Answer:
a.
Youngsville-Calculations for the second period:
Young people= (86/2) * 3.7 = 159.1
Old people= 86 * 0.13 = 11.18 die in the first period so 86 – 11.18 = 74.82 old remain for the second period.
Total population in the second period= 159.1 + 74.82 = 233.92

Oldsville-Calculations for the second period:
Young people = (32/2) * 3.7 = 59.2
Old people = 32 * 0.13 = 4.16 die in the first period so 32 – 4.16 = 27.84 old remain for the second period.
Total population in the second period = 59.2 + 27.84 = 87.04

b. Both countries, Youngsville and Oldsville, have identical fertility and mortality rates but Youngsville is younger than Oldsville. The population grows by 133.92 % in Youngsville while it decreases by 12.96% in Oldsville.








Question 3

Type:
Essay



Using a system of indifference curves and a budget constraint, graphically show the effects of an increase in the cost of consumer goods. That is, determine changes, if at all, in the budget line, the fertility choice, and the level of consumption of goods. Label everything.

Hint:

 

Feedback:

Answer:
Students need to label the vertical axis Consumer Goods and the horizontal axis Number of Children. The budget constraint will rotate inwards on the consumer goods axis. That is, families can afford less consumer goods due to their price increase. If the income effect dominates over the substitution effect, families can afford less children as well. The new budget line tangent to a new indifference curve shows a fertility choice point that indicates a lower n. In other words, the increase in the cost of consumer goods acts like a decrease in income for both goods. Being able to afford less consumer goods also makes consumers demand less number of children. If the substitution effect dominated, the more expensive consumer goods will be substituted for more children. The new tangent between the budget line and the indifference curve would be at a point of lower consumer goods and a higher n, number of children.







Question 4

Type:
Essay



Provide two economic reasons (other than the inferior good explanation) why parents choose to have fewer children when income rises.

Hint:

 

Feedback:

Answer: Students may choose to refer to the following factors: first, raising children increases the opportunity cost of time for parents. Second, parents may want to invest more time and money in each child which, in turn, translates to being able to afford only fewer children.






Question 5

Type:
Essay



Draw an indifference curve-budget line diagram in which you show the effects of religious beliefs in choosing the number of children in a family. Explain your reasoning and label your graph.

Hint:

 

Feedback:

Answer: Religious beliefs relates to preferences in the sense that it alters a couple’s choice about the number of children to have. Religious beliefs that encourage fertility lead to an increase in the demand for children and a decrease in the demand for consumer goods. The indifference curve would move towards the right on the budget line, where n is greater.







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