Answer
a) Please see the first graph.
b) Please see the second graph.
c) The fact is consistent with the model. If fewer children are born, then the substitution effect must be larger than the income effect.
Work Step by Step
a) The budget constraint curve is $BC_{1}$, and the two indifference curves are $I_{1}$ and $I_{2}$. One possible optimum choice is $(2, 160000)$.
b) The budget constraint curve now is $BC_{2}$. Under the income effect, if both wages and children are normal goods, the increase in the wage will increase the total wages (consumption) and the number of children. Under the substitution effect, there will be an increase in total wages (consumption) and a decrease in the number of children.
