Chapter 3: Marriage

• Why look at marriage first?  1) different impact for women:

identity; like occupation.• 2)  important economic

institution: major determinant of income distribution.

• 3) marriage as “economics as choice”: even if key determinant is love.

• 4) family like a miniature economy

Overview of Marriage and Family Structure

• Different ways to describe– What is a family?– What if uncle lives with you?

• Changing family structure over time:– Cohabitation– Single parenthood– Rising divorce rates– Rising rates of re-marriage

Changing Marital StatusOver Time

• 2000: 51% married

25% never married

12.6% divorced/separated

•  1950: 67% married

19% never married

2.4% divorced/separated

• See Table 1 in text

Marriage Patterns

• See Figure 1 in text:– Key: age at first marriage rising over

time; still most individuals do marry.

•  Median age at first marriage:– 1960 = 20.3 years

– 2000 = 25

•  To note: median versus mean (average).

• Predicted proportion of marriages that will end in divorce: over 50%.

Marriage by Age and Education Level

• See Table 2.

•  Biggest drop % married for individuals with less than HS education.

• Young adults also have big decline marriage.

“New” Family Structures

• POSSLQs: Persons of opposite sex sharing living quarters: relatively new phenomenon; so precise data new too.

• Since 1977: this % has quadrupled (now 7.5% of # of married couples)

• Same-sex couples: hard to identify in data: approx. 3% to 10% of # of married couples

• Data issues.

Family Structure

• Biggest change in family structure: HH w/kids.– 1960: over 90% kids in 2-parent HHs.

– 2000: about 67% kids in 2- parent HHs.

• Definitions: – Family HH: 2+ persons sharing

household that are related by marriage,blood,adoption.

– Non-family HH: 1+ unrelated (like college students living together).

– Householder: single adult heading a HH.

Marriage Theory:Background

• Recall stats: still most marry eventually but:– Marriages don’t last as long and– Individuals spend more of adult life not

married.

•  Theory: must explain its underlying strength as well general decline in importance.

•  Three different approaches:– Marriage like a little factory

(emphasize production): traditional economics approach.

– Marriage like little city (public goods).– Marriage like two persons bargaining.

Gains from Marriage • Only marry if expect to be better off

than if stay single.• Use model from international trade:

benefits of specialization and trade.• Economic model: based on man and

woman with different productivity in home and paid labor market. Show gains from “trade” and show how these gains are over time as productivity differences decline.

• Focus on productivity while single versus joint productivity while married; similar to focus on utility.

• Model of traditional marriage; less appropriate in current times.

Marriage Theory: continued

• Key: only have gain to marriage if there IS a difference in productivity between the two individuals.

• So: gains to marriage derive from the relative differences in market and non-market productivity; I.e., because they have differences in productivity, they gain from being able to specialize in one of the two activities then “trading” with one another.

• This is like a difference in relative prices of their time in the two different activities.

Numerical Example• Two activities:

– paid work (w); – home work (H)..

• Two people: – Example 1: John and Jane.– Example 2: Dave and Diane.

• Each has own “prices” that show productivity in each activity (or, value of time in each activity). w = value of paid work. H = value of home work.

• Interpret: w = what earn per hour in market; represents

value of market goods can produce with 1 work hour.

H = value of home cooked meal also prepared in one hour; proxy for “home wage rate.”

Two Types of Productivity Advantage

• Some advantage required for there to be gains from trade.

• Absolute advantage: One type of comparative advantage: – Jane is more productive in one activity and

John more productive in the other activity.

• Comparative advantage: a relative advantage.– Compare relative productivities using

the relative productivity inequality. Ex.: Dave has lower H and w than Diane,

but his w relative to his H is Diane’s wage relative to her H so pays for him to specialize in market work.

Dave(w)/Dave(H) Diane(w)/Diane(H).

Absolute and Comparative Advantage

• Absolute Advantage:– John: w = $10; H = $5.– Jane: w = $5; H = $10.– John has AA in market work and Jane has

AA in home work.

• Comparative Advantage: – Dave: w = $10; H = $5.– Diane: w = $15; H = $15.– Diane has AA in both but CA in home

work.; Dave has CA in mkt work.– Dave(w)/Dave(H) = 10/5– Diane(w)/Diane(H) = 15/15– Dave’s Diane’s so Dave CA: mkt.– If reverse and put H in numerators, see it

shows Diane’s CA in home work.

Opportunity Cost: Absolute Advantage

• Every hour spent in home production is 1 hr NOT spent in market work.

• OC of 1 hour market work is the value of the 1 hour of lost home time.

• Absolute Advantage:– To compare, use $10 of mkt goods- can be

divided evenly by 10 and 5.– John’s OC of gaining $10 in mkt goods (1

hr) is the foregone $5 meal.– Jane’s OC of gaining $10 in mkt goods (2

hrs) is $20 in meals – Key: calculating OC for each for $10 in

mkt goods; this is one hour for John but two hours for Jane.

– OC of mkt work is lower for John.

Opportunity Cost and Comparative Advantage

• Comparative Advantage:– To compare, use $30 value of mkt goods

(since can be divided evenly for both 10 and 15).

– Diane’s OC of gaining $30 in mkt goods (2 hours) is 2*15 = 30.

– Dave’s OC of gaining $30 in mkt goods (3 hours) is 3*5 = 15.

– Dave has lower OC for mkt goods so he will work in market while Diane will work in home.

• Theory of Comparative Advantage: Spouse will choose the activity for which he/she has the lower opportunity cost or the greater relative productivity.

Exercise

• Given: Paul: w = $9; H = $6.• Sara: w = $6; H = $3.• Paul and Sara choose to get married

and specialize according to their comparative advantages.

• As a married couple, what is Paul’s CA and what is Sara’s CA?– 1. Show using the relative productivity

inequality for each person.

– 2. Show using the opportunity cost method for each person.

• Hint: Use $36 in market goods to compare.

Specialization

• Question: Do women really have advantage in home production and why?

• This model implies that specialization is efficient and therefore a good thing.

• Criticism: NOT clear if specialization is “good” choice and in reality, individuals differ in preferences too so perhaps won’t see full specialization.

Downside to Specialization

Life-cycle changes: advantage changes as individual ages (kids grow up), etc.

Specialization divorce even under extreme circumstances (e.g. domestic violence).

When gives up one activity entirely, then productivity in given up sector will fall.

• I.e., if I stay home with the kids for 10 years, when I re-enter the paid workforce, my earnings potential will have fallen.

– This is risky given high probability of divorce.

– Reduces incentives to specialize.

– Both occur simultaneously:

divorce specialization;

specialization divorce.

Other Economic Benefits to Marriage

• Principal-Agent Issues: Best way to explain: plant owner and manager:– Principal: Owner wants to max profits; – Agent: Manager may have other explicit

goals, like max output, min injuries, etc.– So principal can only get what he wants

if he knows all about manager’s job and can monitor properly

•  2 ways to get HH produced goods: – 1) Could hire out: but employee might

not do good job and hard to monitor.– 2) Could marry: now “worker”(really a

partner now) has personal stake in quality of work. Works best when marriage based on love, trust, etc.

Economies of Scale

• Essentially: costs less per person if two people live together: lowers per-person (avg.) housing cost, food cost

• Avg. cost as # persons . • So, need one fridge if one person or

5 people.• Example: Official poverty

threshold incorporates this idea:– Threshold for 2 people is NOT twice

the threshold for one person.

More Benefits

• Risk-sharing: lowers cost of job loss if two people share expenses.– Good example of how cohabiting

college students differ from “partners.”

• Public goods:type of good that can be consumed by 1 person without utility from consumption.– Watching a TV program.

• Institutional advantages: • Tax benefits

• Access to spouse’s health coverage.

Marriage Market: S & D

• Uses Becker Model: uses productivity as proxy for utility.– How marital status choice is made;– How gains of trade are divided between

husband and wife?

• Need basics (M=male; F=female):– Output: Z (Happiness, Love, etc.)

• For single person: ZM and ZF

• For married-couple HH: ZMF

• Z: productivity/utility//happiness; like a single composite good.

– Share of Output: S• Amount of ZMF to husband = SM

• Amount of ZMF to wife: = SF

Further Details: Marriage Market

• Note: SM + SF = ZMF.• Marriage “rule”:

– Marry if expect to be better off:– Man: marry if SM ZM.– Female: marry if SF ZF.

• Implies that for married couple:– SM + SF ZM + ZF.– So: ZMF ZM + ZF:

• NOT assuming that SM = SF.– Gains to marriage for most

individuals.

Basics of S & D Model

• Price term: SF:– What a woman must receive to be willing to

marry and what a man is willing to pay to be married.

• Quantity term:# men, # women• Restate marriage “rule” and resulting

shape of S curve:– Marry only if SF ZF.– SF ranges from very low to very high; when SF

low, very few women willing to marry.– When SF very high: all women willing to

marry; curve becomes vertical since no more single women.

– Shows positive relationship between price and quantity supplied (w/Zf fixed)

• Law of Supply

Marriage Model(continued)

• To complete model, need demand curve (of men) FOR wives.

• Need SAME price: – Know: When SF high, SM very low.I.,e.,

when pay a lot to wife via SF, portion left over for husband via SM is small.

– So man prefers low SF (and so high SM).

• Yields negative relationship between man’s willingness to marry and price of marriage (I.e., amount of productivity within marriage that must go to wife).

• Consistent with Law of Demand.– See Figure 3.10.

Marriage Market Equilibrium

• Horizontal axis: # men or women willing to marry.

• Vertical axis: price (SF): what woman gets; what man pays.

• Equilibrium: – not determined by negotiations within each

single marriage; – general terms set by market (like social

norms); – interpret: “..this is what married life is like

for men and women.”

• NOT showing how pick specific partner, rather, shows: – general decisions regarding marriage.– how men/women treated within marriage.

More on Equilibrium

• Marriage market equilibrium: – unique price SF* that sets S = D.

• Explain equilibrating process as with any market:– If price too low as at SFL:

• Qd Qs: more men looking than women willing to marry;

• shortage; • so men bid up price.

– If price too high as at SFH : Qs Qd.

• At equilibrium: – See N* – # unmarried men– # unmarried women.

Exercise

• 1. Sketch and label completely a S and D model for marriage.

• 2. Using the Law of Supply, explain the slope of the S curve.

• 3. Moving down to the right on the demand curve, at some point, as the price falls further, the demand does not change. Why?

• 4. What is the marriage rule? (Hint: use the terms ZF and SF.in your answer)

• 5. List one ceteris paribus factor for the supply curve.

• 6. Where/How does love enter this model?

Effect of Changes in S & D

• Comparative statics examples: – 1) change in sex ratio – 2) women’s improved L mkt

opportunities – 3) Effect of birth control, etc.

• Change in sex ratio: – See Table 3.3 in text;– Shows differences by age and race.– Also: differences by education.– Effect of in sex ratio:

# women w/no # men• Shift vertical part over to right• See slope (same % in #women ; smaller

# at low SF; larger # at high SF).• See Figure 3.12.

Other Changes in S & D

• Increase in women’s wages:– Will ZF (well-being while single).

– Shifts S upwards: • each woman now willing to marry at higher

value of SF than before.

• see Figure 3.13;

• no change vertical point.

• More effective birth control: ZF and ZM

– See Figure 3.14: • start with S2 and D2

• AIDS has opposite effect.