Question

Suppose that the current (first) generation consists of 1 million people, half of whom are women. Assume the total fertility rate is 1.3 and the only way people die is of old age.

Instructions: In parts a and b, enter your answers as whole numbers. In part c, round your answer to 2 decimal places.

a. How big will the fourth generation (the great-grandchildren) be? .

b. How much smaller (in percentage terms) is each generation than the previous generation?  percent.

c. How much smaller (in percentage terms) is the fourth generation than the first generation?  percent.

d. Are you surprised by how quickly the population declines?

	Yes, because a fertility rate of 1 would cause each successive generation to double in size, so a fertility rate of 1.3 should lead to a relatively large increase in population.
	Yes, because a fertility rate of 1 would cause each successive generation to double in size, so a fertility rate of 1.3 should lead to a relatively small decline in population.
	No, because a fertility rate of 1 would cut each successive generation in half, so a fertility rate of 1.3 should lead to a relatively large decline in population.

Answer 1

Answer

50% of the first generation (the women) will have 1.3 children per person.  Another way to say this is that 100% of the population will be 65% of the previous.

1st gen 1,000,000
2nd gen 650,000
3rd gen 422,500
4th gen 274,625

each generation is 65% smaller than the previous generation.

The 4th generation is 27.56% of the first.

the population decline is quite shocking. since each couple in the economy is having only one child, it is not even replacing their own parents and hence world will be empty soon.