# ECO433 Assignment 3

*Optimal marital sorting on traits: 40 points*Suppose that happiness*H*of a marital partnership between*f*and*m*depends only on the wealth*W*of the two partners. Consider the following two martial output functions:

- (20) Show whether, in (i) and (ii) respectively, the wealth of the man and the wealth of the woman are substitutes or complements in marital production (or “happiness”).
- (10) For a model in which wealth is the only trait that determines marital happiness, which functional form makes more sense to you and why?
- (10) Suggest a trait or pair of traits (e.g.
*W*could be wealth in stocks and_{m }*W*could be wealth in bonds) that would make the other functional form (the one you didn’t choose in (b)) a more realistic representation of the the marital output function of those traits._{f }

*Quantity and quality and the demand for children: 40 points*- (20 points) Explain, from a
*technical*point of view, why quantity and quality of children cannot be too close (or “perfect”) substitutes in order for the quantity/quality theory of demand for children to work. - (20 points) Explain, from an
*intuitive*point of view, why quantity and quality of children are not likely to be very close substitutes (put another way: are likely to be fairly complementary) in the production of parental happiness.

- (20 points) Explain, from a
*Parental investments in children: 20 points*

Using the notes from chapter 6, use equations (1) and (2) on slide 3 to derive “family income” *S *and the parents’ budget constraint at time *t *in terms of *Z *and *I _{t}*

_{+1 }(equation (*)). Interpret (∗) and explain how it differs from equation (1).