L9

Buying and Selling: Applications

Model of choice We know preferences and

we find

The two differences – net demands

Buying, selling?

Review

1 2, ,p p

*2

*1 , xx

21xxU

* *1 1 2 2,x x

More generally

x2

x1

21,

1

2

pslope

p

1. Labor Supply

(Labor-Leisure Choice)

2. Intertemporal Choice

(Consumption-Savings Choice)

3. Uncertainty (Insurance)

(Consumption across states of the world)

Three Applications

Intertemporal Choice

Two periods: Today and Tomorrow Goods: consumtion today and

tomorrow Endowment: income today and

income tomorrow Possibility of borrowing and lending

1C2C

1m

2mr

Intertemporal Choice

1C

1 2( , ) (50,50)m m

2C

0%r

Intertemporal Budget Constraint

1C

2C100%r

1 2( , ) (50,50)m m

Present Value (PV) and Future Value (FV)

The interest rate is FV: Future equivalent of today’s $1

PV: Today’s equivalent of tomorrows $1

What is PV and FV of cashflow

1 r

r

1/(1 )r

1 2( , )m m

FV PV

Budget constraint (2 versions)

FV of spending = FV of income

PV of spending = PV of income

Prices and income

Comparing two cashflows

1C

: (10,200)Manager

2C100%r

: (100,40)Sportsman

Intertermporal Choice

2121 ln1

1ln),( CCCCU

Discount rate Discount factor Magic formulas

1,0 )1/(1

Borrower, Lender? Savings

1C

2C

2121 ln1

1ln),( CCCCU

%100r

)0,300(:S

Borrower, Lender? Savings

1C

2C

2121 ln1

1ln),( CCCCU

%100r

)600,0(:M

Consumption Smoothing

)0,300(:

)600,0(:

S

M

%100r

Consumption Tilting

2121 ln1

1ln),( CCCCU

r