# L10 by fanzhongqing

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```									              L10

Three Applications
Model with real endowments
1. Labor Supply
(Labor-Leisure Choice)
2. Intertemporal Choice
(Consumption-Savings Choice)
3. Uncertainty (Insurance)
(Consumption across states of the world)
Intertemporal Choice
 Two periods: Today and Tomorrow
 Goods: consumtion today C1 and
tomorrow C2
 Endowment: income today m1 and
income tomorrow m2
 Possibility of borrowing and lending r
Intertemporal Choice
r  100%
C2

( m1 , m2 )  (50, 50)

C1
Many Periods
 Cashflows
Many Periods
 Cashflow
m1 m2 m3 m4 m5 m6

0 1 2 ...                  time
PV0 

 E: T=3, r=100%. Choose:
\$1 in each of the three period or \$8 in the third
Important cashflow: Perpetuity
 Gives constant payment x forever
 Cashflow

0 1 2 ...                   time
PV0 
Perpetuity (Example)
can rent an apartment for \$1000 each
 You
month (r=0.5%=0.005)

PV0 
 You can buy it P=300.000
Perpetuity (Example)
a consol that pays \$10,000 per year.
 Valuate
(r=5%=0.05)

PV0 
 You inherit \$1000,000. How much monthly
interest are you going to get ? (r=5%=0.05)
Important cashflow: Annuity
 “Tree” that gives constant payment in T
following periods
 Cashflow
0 1 2 ...      T T 1     time

PV0 
Lease T=3, x=\$800, r=100% or buy P=750

 Takea loan (how much do you pay monthly)
Loan=1000, T=3, r=100% and x=?
Asset Valuation: Bonds
 Treasury    bill: Face, Coupon, Maturity

0 1 2 ...          T
 PV   of T-bills (F, c, T) and r

PV0 
Asset Valuation: Example
 T-bond   (F=100, c=10, T=6) and r=5%
Life cycle problems
 Consumption   – savings problem
 Pension:
– How much to put aside?
– How much am I going to get?

20 21 ...   60        80 time
Consumption Smoothing
 Income:m=100 in the first 40 years
 Consumption C during 60 years,
 Constant consumption! Find C if r=5%

20 21 ...                  time
60        80
Pension Plan
 Youwant C=100 when retired (61-80)
 How much do you have to save if r=5%,

20 21 ...   60         80   time
Pension Plan
 Yousave S=100 (21-60)
 How much will you get (per year) if r=5%,

20 21 ...   60          80 time

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