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					              L10


Buying and Selling: Applications
           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
 Renting vs buying?
              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 
            Leasing or Buying A Car
 Leasingor buying a car?
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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