2. Population and Fertility Choice 2.1. True or False? [4 points] State whether the statement is true or false, and briey explain why. (a) If country A has a population growth rate that is lower than country B, then the average woman in country A has fewer children than her counterpart in country B. (b) Total population levels in a country should be lower at the end of a demographic transition than they were at the beginning. 2.2. This is a question on joint families, extemalities, and fertility choice. Suppose that Jose and Maria are the heads of a nuclear family, making their fertility decisions. For simplicity, suppose there is no gender bias and no infant or child mortality. The following table details the costs and benets (in dollars, say) of different numbers of children. [6 points] (a) Based on the information in the table, how many children would Jose and Maria have in order to maximize their net benet? # of children Total benet ($) Additional cost per additional child ($) One 500 100 Two 75 0 100 Three 840 100 Four 890 100 Five 930 100 Six 950 100 Seven 960 100 Eight 960 100 (b) Now consider two identical nuclear families: Jose and Maria (as above), and Jorge and Rosa. Jose and Jorge are brothers and the two couples form a joint family. Both couples have exactly the same costs and benets of having children as in the table. Now suppose that 50% of the upbringing costs of each child (e.g., child care) can be passed on to the other family. Each couple makes independent decisions, taking only its own welfare into account. Now how many children will each couple have? (c) Explain the reason for this seemingly paradoxical result, using the concept of extemalities, and try to understand why larger families (either integrated across generations or between siblings in the same generation) will tend to have a larger number of children per couple