Theories of the Demographic Transition (DT)
A. The rise in income in the process of industrialization triggered DT
Suppose that parents generate utility from consumption, c, and children, n.
Their utility function is
u = n!c1!!.
Parents are endowed with one unit of time. They optimally allocate this unittime endowment between work and raising children. If they work full time their
wage income is w. The time cost of raising a child is a fraction ! of parental
time and consequently the opportunity cost of raising n children is w!n. The
cost of consumption is normalized to 1. Parental’s budget constraint is therefore
w!n + c ! w.
1. Find the optimal level of consumption, c, and the optimal number of children,
n. (You may use the fact that when preferences are homothetic the share of
income allocated to consumption is given by the exponent that is associated with
consumption in the utility function, 1 ” “, and the share of income allocated to
children is the exponent associated with children, “).
2. Could a rise in wage income generate a decline in fertility in this economy?
Why?
3. What changes in the utility function will permit a rise in income to generate
a decline in fertility?
4. What are the testable predictions of the Beckerian theory?
5. Evidence suggests that countries that are similar in their sociopolitical environment, but di§er in income, experienced the DT in the same time period.
How does it reflect on the Beckerian theory?
6. Evidence suggests that in some society (e.g. England) richer individuals had
a larger number of surviving children in the pre-demographic transition era.
How does it reflect on the Beckerian theory?
Sample Solution
