Problem $1$

Consider a couple$$s decision about how many children to have. Assume that over a life time a couple has $200,000$ hours of time to either work or raise children. The wage is $$10$ per hour. Raising a child takes $20,000$ hours of time.

A$-$ draw the budget constraint showing the tradeoff between life time consumption and the number of children. $($Ignore the fact that children come only in whole numbers$).$ Show indifference curves and the optimum choice

$(5$ Marks$)$

B$-$ suppose the wage increases to $$12$ per hour. Show how the budget constraint shifts. Using income and substitution effects, discuss the impact of the change on number of children and on life time consumption

$(5$ Marks$)$

C$-$ we observe that, as societies get richer and wages rise, people typically have fewer children. Is this fact consistent with this model? Explain

$(5$ Marks$)$

$(15$ Marks in Total$)$