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Econ 175 Cheat Sheet (DRAFT) by

Fertility Model(Time+QQ)

This is a draft cheat sheet. It is a work in progress and is not finished yet.

OC Fertility Model(app cost)

X: Goods (p=1)
p: cost/kid
w:salary
c:time/kid
N: # of kids
T: total time ( T=L+cN)
I:other income

Change variables

change I
change W(incr­ease)
Effect: 1.consume more X and N. 2. curve shift up 3. slope unchanged
Effect: 1.effect on N is ambiguous. 2. slope changes. 3. 2 effect evolve­d.(­1)i­ncome: more N.(more $ can spend on fixed cost of kids) 2. substi­tute: less N(OC cost of kids increase)

income VS substi­tution effect

a

Why marry? Who marry who?(L­ab10)

Odds ratio
1: neutral. no positive or negative sorting
(F[1,1]F[2,2]­)/(­F[1,2]F[2,1]
2. A value close to 0 : very negative sorting;
 
3. high values (10, 100+) , very positive sorting.
Why called the odds-r­atio:
The numerator is the odds of being in cell [1,1] compared to [1,2], and the
denomi­nator is odds of being in cell [2,1] compared to [2,2].
If there were no tendency to marry one sex rather than the other, the odds of
marrying a "­mal­e" would be the same for females and males and the
ratio would be 1.
  

Becker's QQ fertility model

Utility: U = U(X, n, q)
Constr­ain:X + p
c
qn = I
n=(I-x­)/(qp
c
)
goods (X)
number of kids (n)
“higher quality” child (q)
I:total income

Graphing Budget constraint

Intera­ction between q and q

Total child costs = p
n
n +p
q
q + p
c
qn
p
n
per child price (of any quality) (pregn­ancy, -contr­ace­ption, ...)
p
q
per quality price (indep­endent of n) (a set of encycl­ope­dias, ...)
p
c
price depending on q & N (school fees, visits to doctor, new shoes, ...)
How much does it cost to increase n by +1?
πn∼ p
n
+p
c
q
How much does it cost to increase q by +1?
πq∼ p
q
+p
c
n
reason for low fertility rate:
(1) costs of contra­ception fall – causing n to go down because fewer unintended births.
(2) Price of a unit of quality goes down too – and people purchase more q.
(3) But price per child goes up. This has a further negative effect on the number of kids, n.
(4) Which can result in further increases in q and further declines in n until a new equili­brium is reached
  

why fertility decline irreve­rsi­bility?

 
Fertility generally falling over time as wages rise
• Puzzle: why in economic crisis doesn’t fertility rise again – as wages go down?
• Possible answer:
– Norms about child quality appear fairly irreve­rsible.
– So to reduce pcqn, parents reduce n

Summary (1)

Quanti­ty-­quality intera­ction good for explaining demogr­aphic transition (rapid, big fertility declines) • Cost-o­f-time model good for explaining more recent trends, especially as female wages rise • Can combine two models

Summary (2)

 
Answers to puzzle of how fertility could fall with economic growth
1. It doesn't (because income effect dominates)
2. It does, substi­tution effect (cost of time) dominates
3. Parents get utility from quality, too. And so once fertility starts falling, big shifts
toward quality.
20

Becker’s theory of “gains to marriage”

gains:come from compar­ative advantage
1.econ­omies of scale
ES:Easier and cheaper to vacuum 2 rooms
2.hous­ehold public goods
PG:A clean house, magazines
3.K:ow­n-c­hildren
Biological childr­en,­provide utility to both parents
4.K: can build marria­ge-­spe­cific capital
partners. Important point: a contract (to stay together) provides incentive to invest in marria­ge-­spe­cific capital. Risky without contract.
Compar­ative Advantage vs Production possib­ility frontiers
why not just live with roommates?
1.own children
2.Marriage contract