In this chapter, we studied a model where a family wants one surviving child to provide old-age security. Let us say that the probability of any one child living to look after its parents in old age is 1/2 (i.e., 50–50). However, the family wants this security level to be higher, say a probability of q > 1/2.

(a) Describe the family’s fertility choices for different values of q, by first writing down a model that captures this story, and then examining the results for different values of q.

(b) Calculate the expected number of surviving children for this family, under various values of q.