2500+ words Essay

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SESS0042 Economics of Family

30th September 2019

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Family economics…  Why this will be fun, maybe?

 It’s about relationships, dating, childbearing  But with an econ twist (no-nonsense and to the

point)  Questions of interest:

 Who marries/dates whom and why?  Why hasn’t he called?  Should we cohabit or tie the knot?  When is polygamy efficient?  Are we getting more sex than our ancestors?  What makes relationships unstable and has the

instability increased over time?

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My rap sheet  I would recommend going to every lecture, as even skipping one can lead to confusion. Same goes for the

office hours.  Slides are well organized and he is able to expand on the slides in great detail. His material was

interesting and he provided all sorts of credible references that backed up what he was teaching the class.  Could you please add more notes to the slides which display tables from papers; it is very difficult to

understand what is going on in those tables and graphs sometimes. 3-5 Bullet points explaining the graph would be amazing, especially when you want to go over to graphs after the lecture or during revision.

 It was probably the first course over three years of studying for which I attended all 10 lectures despite the fact that they were taught in the early morning on Mondays.

 I got only 9s and 10s at homework, but I've worked a lot (maybe 20-25h on average / homework). It's a bit too much, considering that we are in the 3rd year (dissertation, grad scheme applications, part time jobs, other subjects, etc) and we have only from Mon to Thu to solve the exercises. The worst part is that you actually have to find a way to solve them, cause there are so complicated compared to what we have in the lectures. This was the first module / subject in my entire schooling which required me to actually "invent" ways of solving the problems, so I found it quite interesting.

 I was very skeptical at first since "economics of the family" doesn't exactly sound useful for anything, really. Nonetheless, Tomas' amazing lectures quickly convinced me otherwise. Not only is this module fun, but it actually has got me thinking about my own life goals and relationships. I'd even go so far to say that Tomas would probably be a fun dad. In short, Econ of Family has become one of my favorite modules and I will recommend it to any second year that I see.

 Spend more time to explain difficult theories/graphs & maybe have some practice questions throughout the lecture to test understanding of difficult material before moving on

 Accommodative in terms of coming to office hours. His appointments are booked as far in advance as possible but you can always ask him and he does the best he can to help you.

 Please consider bringing the selfie competition into this module.

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Men and Women: What motivates them?

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Salient features of families

 Men and women form them (mostly)  Ubiquitous across cultures and epochs

 They form them voluntarily  There must be some net gain

 They are the primary context for child rearing  Evolutionary advantage over other

contexts?  They involve some division of labor

 Comparative advantage of some kind is involved

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Difference in mean

some variable

f(x)

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How are men and women different?

 At the mean:  Height, weight  Brain size and weight  Voice frequency  Physical strength  Endurance  Pain tolerance  …  Child-bearing prospects

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Reproductive potential

 Women: fertile in age 15 – 50 (at most)  9 mos of pregnancy + some neonatal

care = at least 1 yr per child  Maximum capacity = way less than 50

children  Men: fertile age 13 – †

 Reproduction takes 5 minutes & is fun  Sperm is cheap because plentiful  Maximum capacity = 000’s?

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Meet Mulay Ismail ibn Sharif

 The ruler of Morocco, 1672 – 1727

 Recorded to have sired 888 children

 Estimated 4.8 sexual partners per day for 40 yrs (most of them involuntary)

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How are men and women different?

 Women bear most of the cost of childbearing /childrearing  Death due to childbirth (maternal

mortality)  7.1 per 100K women today  600+ per 100K women in 1915-1920 (HSUS)  Even higher (presumably) before that

 Loss of income and career prospects  250K for college women by some estimates

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Implications for partner search

 Women incur large costs and risk a lot; men can have lots of children w/ little bio risk  Women should be “reluctant buyers” =

high reservation value (of singlehood)  Men can afford to be indiscriminate

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Differences in variance - graph

Applies to: Height, weight Physical strength Brain size Crime rate # sexual partners # children sired Certain aptitudes

f(x)

What happens at the high end?

B ACDE

grades

f(x)

What happens at the high end?

B ACDE

grades

f(x)

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What happens at the low end?

min. wage income

f(x)

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What produces the high variance?

 Nature partly: physical strength, voice  Our actions (i.e. how ♀ & ♂ respond to

incentives)  Our attitudes toward risk  Rewards and punishments

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How are men and women different?

 At the mean:  Height, weight  Brain size and weight  Voice frequency  Physical strength  Stamina  Pain tolerance  …  Important: Attitude toward risk!

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Concept of risk aversion

 Tendency of consumers to refuse fair games  Fair game is one where the expected

VALUE is equal to the cost of the game  The consumers refuse because their

expected UTILITY is lower than the utility from their current income which is certain

 Graphically, risk aversion is conveyed in the CONCAVITY of the utility function

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Playing with the concept I

$$$

U

“poor” gambler

“rich” gambler

U0>E U

Neither will play at p = 0.5 but if p is increased, the rich gambler will step in at lower p.

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Playing with the concept II

$$$

U How much is one willing to pay to avoid

risk?

UL

UW U0

M*

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Playing with the concept III - Insurance

$$$

U How much is one willing to pay to avoid

risk?

Uinjury

Uregular EU

IregularIinjury insuranc

e premium

certainty equivalent

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Men vs Women: Risk aversion

$$$

U

los s

win

U0 Neither will play at p = 0.5 but if p is increased, men will step in at lower p.

EUp=0.5

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Men vs Women: Risk aversion

$$$

U

los s

win

U0 Women will willingly pay more to avoid the risky situation.

EUp=0.5

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Men vs Women: Risk aversion

Number of offspring

U

los s

winF

U0

Biologically, males can reap potentially higher rewards.

winM

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Implications for theory

 On average:  Men will take more risks than women  Men will willingly face worse odds than

women would choose to face  Whatever initial inequality among men,

the outcomes of risky situations will exacerbate it

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Croson & Gneezy (2009)

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Croson & Gneezy (2009) cont.

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Men have…

 Higher variance in certain characteristics

 Higher variance in certain rewards and penalties (possible outcomes)

 … higher variance in actions taken (effort)

… which all leads to …  higher variance of actual outcomes

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Implications for partner search

 Women incur large costs and risk a lot; men can have lots of children w/ little bio risk  Women should be “reluctant buyers” (high

reservation value)  Men can afford to be indiscriminate

 Men will vary significantly  Women can be comparison shoppers  Men will want to stand out

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Should you date out of your league?

 Depends on what you’re looking for:  Short-term fun?  Long-term commitment?  Power in the relationship?

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Who ends up with whom & why?

 High degree of homogamy:  Age  Education  Ethnicity  Parental wealth  Religion/Culture?

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Matching algorithm of Gale & Shapley (1962)

 Assume many singles, men and women

 Assume everyone can rank the opposite sex in terms of desirability (not necessarily identically)

 All preferences are strict (i.e. >, not ≥)  Men move first, women respond

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Gale-Shapley (1962) algorithm

Abby Barbar a

Carrie Dana

Jake 1, 2 3, 1 2, 2 4, 3

Kyle 2, 1 1, 3 4, 4 3, 4

Len 4, 3 1, 2 2, 3 3, 1

Martin 2, 4 3, 4 4, 1 1, 2

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Why is this arrangement stable?

 Len and Martin got their first choice, so they cannot improve their situation

 Jake and Kyle got their second choice after their first choices found someone better, so they cannot improve their situation

 Stability (def.): when there exists no pair who want to change matches from their current partners to each other

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If women move first…

Abby Barbar a

Carrie Dana

Jake 1, 2 3, 1 2, 2 4, 3

Kyle 2, 1 1, 3 4, 4 3, 4

Len 4, 3 1, 2 2, 3 3, 1

Martin 2, 4 3, 4 4, 1 1, 2

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What has changed and what hasn’t?

 This is also a stable equilibrium:  All women got their first choice, no need to

change  However, it is a DIFFERENT equilibrium

 When men moved first, they all got their 1st or 2nd choices; not when women moved first

 When women moved first, all women got their first choices (net improvement over first time)

 There IS such as thing as first-mover advantage!

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Other examples of G-S process

 Choosing a dance partner  Polygamous marriage market  College applications  Job search  …

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Uniqueness of equilibrium

 Assume common rankings  General agreement on “who’s hot & who’s

not”  All other assumptions stay in place

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Universally shared preferences

Abby Barbar a

Carrie Dana

Jake 1, 2 2, 2 3, 2 4, 2

Kyle 1, 1 2, 1 3, 1 4, 1

Len 1, 3 2, 3 3, 3 4, 3

Martin 1, 4 2, 4 3, 4 4, 4

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Women differ; men move first

Abby Barbar a

Carrie Dana

Jake 1, 2 2, 1 3, 3 4, 4

Kyle 1, 1 2, 2 3, 1 4, 1

Len 1, 3 2, 4 3, 4 4, 3

Martin 1, 4 2, 3 3, 2 4, 2

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Women differ; women move first

Abby Barbar a

Carrie Dana

Jake 1, 2 2, 1 3, 3 4, 4

Kyle 1, 1 2, 2 3, 1 4, 1

Len 1, 3 2, 4 3, 4 4, 3

Martin 1, 4 2, 3 3, 2 4, 2

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Uniqueness of equilibrium  Even if only one side has common

preferences, the matching will be unique  The matching will reflect the preferences

of the non-common side  Is it a realistic assumption, that men

may agree while women may disagree?  If so, then men’s first-mover advantage goes

away (even if they ever had one)

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Becker-Shapley-Shubik matching

 What is behind the rankings?  Men and women get some

enjoyment/utility out of the relationships/ matches

 So far, we have assumed the rankings fixed

 But men & women may sway each other’s rankings by sharing the good

 This idea is based on Becker (1973), Part I and on Shubik and Shapley (1972)

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Gale-Shapley (1962) algorithm (the original matching example)

Abby Barbar a

Carrie Dana

Jake 1, 2 3, 1 2, 2 4, 3

Kyle 2, 1 1, 3 4, 4 3, 4

Len 4, 3 1, 2 2, 3 3, 1

Martin 2, 4 3, 4 4, 1 1, 2

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Replace rankings with utilities

Abby Barbar a

Carrie Dana

Jake 8, 7 3, 8 5, 7 1, 2

Kyle 2, 8 9, 5 0, 2 1, 1

Len 2, 6 5, 6 4, 5 3, 7

Martin 7, 5 5, 3 1, 9 9, 4

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Transferable utility = endogenous division of spoils

Abby Barbar a

Carrie Dana

Jake 15 11 12 3

Kyle 10 14 2 4

Len 8 11 9 10

Martin 12 8 10 13

Are these matches stable with transferable utility?

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Transferable utility = endogenous division of spoils

Abby Barbar a

Carrie Dana

Jake 15 11 12 3

Kyle 10 14 2 4

Len 8 11 9 10

Martin 12 8 10 13

Are these matches stable with transferable utility?

Kyle: Hey B, wt r u getting out of that r-ship? Barbara: x utils. Kyle: U kidding? So Len gets 11-x? Barbara: Yes. U? Kyle: Abby keeps 10-y utils, I get y. … Kyle: U know wt Im thinking? Barbara: Wt? Kyle: Right now, the 2 of us get x+y; u & me 2gethr, we’d have 14>x+y. Barbara: Wt r u saying? Kyle: Dump him 4 me. He can have Abby. Barbara: OK. I luv u.

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Transferable utility = endogenous division of spoils

Abby Barbar a

Carrie Dana

Jake 15 11 12 3

Kyle 10 14 2 4

Len 8 11 9 10

Martin 12 8 10 13

Are these matches stable with transferable utility?

Kyle: Hey B, wt r u getting out of that r-ship? Barbara: x utils. Kyle: U kidding? So Len gets 11-x? Barbara: Yes. U? Kyle: Abby keeps 10-y utils, I get y. Barbara: Sounds like both of us get sweet deals. Kyle: Yep. Don’t mess w/ the good thing. 14<x+y. … … Len: Hey Abby, wt r u getting out of that r-ship? Abby: 10-y utils.

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Formal analysis  Barbara + Len = x + 11-x = 11  Kyle + Abby = y + 10-y = 10  x+y 21-x-y 21  Either: x + y < 14 => Len + Abby = 21 – x –y

> 7  Then Kyle & Barbara will get together &

have 14  14 is enough to increase both people’s

utility  Or: x + y > 14 => Len + Abby = 21 – x –y <

7  Then Len & Abby will get together & have 8  8>7, so again, both can be made better off

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Transferable utility = endogenous division of spoils

Abby Barbar a

Carrie Dana

Jake 15 11 12 3

Kyle 10 14 2 4

Len 8 11 9 10

Martin 12 8 10 13

These matches are NOT stable: break-ups will follow.

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Results of Shapley-Shubik  If realignment can bring about higher total

utility, it will happen  The dating-market equilibrium will be where Σu across all couples is maximized

 Inside-couple negotiation about who gets what is endogenous  This is because people can now make offers about

the division to entice others to date them  Still, even though the matches are stable and

unique, the actual divisions are not unique

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Assortative mating  What is behind the relationship utility?

 It will depend on individual characteristics of the 2 people

 Some personal traits go well together, some not  So, let x be a personal trait, standing for “being

entertaining”  Assume being with fun person is better than

being with a dull person  i.e. U(fun, fun) > U(fun, dull) > U(dull, dull)

 Assume supermodularity:  i.e. U(fun, fun) + U(dull, dull) > U(fun, dull) + U(dull,

fun)  In short, have, for example, U = xfxm

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Relationship utility, as it depends on personal trait

Name (fun)

Abby (4)

Barbara (3)

Carrie (2)

Dana (1)

Jake (4) 16 12 8 4

Kyle (3) 12 9 6 3

Len (2) 8 6 4 2

Martin (1)

4 3 2 1

Following Shapley-Shubik, stable matches max Σu.

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Results

 Personal traits will be strongly correlated  Fours marry fours, threes marry threes…

 This is called positive assortative mating

 If instead of supermodularity, the u-fn is submodular (i.e. “opposites attract”), then we get negative assortative mating

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Theory: summary  As long as men and women can rank each other,

there exists a stable matching (Gale & Shapley, 1962)

 If M or F all rank the other sex exactly the same way, there will be stable & unique matching (Eeckhout, 2000)

 If partners can bargain over the gains from relationship (transferable utility), the matching will maximize total utility across all couples – (Shapley & Shubik, 1972; Becker, 1973)

 This means it is globally optimal  If the utility fn is supermodular, the unique stable

matching will also be positively assortative (i.e. “likes attract”) as partners seek complements to each other (Becker, 1973)

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Conclusions

 Matches on the dating/marriage market are not random

 The way the market operates produces predictable results  Ignore the market forces at your peril

 Still, dating out of your league may lead to short-term success

 So, it depends on what you’re looking for