Question

A newly wedded couple is in the process of making fertility decisions. The table shown below illustrates the costs and benefits of different numbers of children.

Number of children	Total benefit	Additional cost
1	600	120
2	780	120
3	901	120
4	975	120
5	1040	120
6	1070	120
7	1080	120
8	1080	120

1. a) What is the optimal number of children that they should have?

2. b) Suppose the couple could convince one of their parents to help in taking care of their children without having to pay for their services. Assume that this would lower their total cost of raising children by 40%. How many children will the couple have?

3. c) Discuss the economic significance of your finding in part (b).

Answer 1

Additional Benefit = (Total Benefit)_n - (Total Benefit)_n-1
Additional Benefit:
0: -
1: 600
2: 780 - 600 = 180
3: 901 - 780 = 121
​​​​​​​4: 975- 901 = 74
​​​​​​​5: 1040- 975= 65
​​​​​​​6: 1070- 1040= 30
​​​​​​​7: 1080- 1070= 10
​​​​​​​8: 1080- 1080= 0

a)
Additional cost = 120
Parents should have children up to the point where Additional benefit > Additional Cost
As we can see from the tables that till 3 children Additional Benefit > Additional Cost
Therefore, optimal number of children = 3

b)
Additional cost has decreased by 40%
Additional cost = 120 * (1 - 0.4) = 72
As now Additional cost has decreases to 72, therefore Additional Benefit > Additional Cost till 4 number of children
Therefore, optimal number of children = 4

c)
Economic significance:
As the cost of production of a product decrease, producers find it profitable to produce more quantity compared to the scenario which has more cost of production.