L08

Buying and Selling

Model of choice We know preferences and

we find demands

Q: Where does the mysterious income come from?

From selling goods (e.g. labor)! Today: Model of choice with endowments

Review

mpp ,, 21

*2

*1 , xx

m

21xxU

Endowments

Instead of nominal income: goods The list of commodities with which a

consumer starts is his endowment. A consumer’s endowment will be

denoted by the vector (omega).

Example 21,

6,3

Budget constraint

Suppose p1=2 and p2=3 and

what is the value of endowment?

What is a collection of all affordable bundles (budget set)?

)2,10(),( 21

m

Budget Constraints Revisited Given p1 and p2, the budget constraint

for a consumer with an endowment

is

Example:

),( 21

.22112211 ppmxpxp

1,1 21 pp

Budget Constraints Revisited

x2

)5,5( 1,1 21 pp 1,2 21 pp 1,3 21 pp

x1

Q: shift of the budget lineA)Is parallel, outwardsB)Is parallel inwardsC)Is a rotation around D)Is a rotation around

Quizx2

x1

''

2

1

pp

1

2

1 pp 21,

Net Demands Net demands: actual trades of a

consumer

Example

Net demands (buying, selling)?

1*1 x 2

*2 x

)10,1( )4,10(* x

Budget Constraints Revisited

The constraint

is

The sum of the values of a consumer’s net demands is zero.

Buying, selling?

.0)()( 222111 xpxp

22112211 ppxpxp

Buying, Selling?

x2

x1=5

=5

)5,5( 1,1 21 pp

.1021 xx

Quiz

x2

x1

Q: Consumer isA)Buying , selling B)BuyingC)Selling D)Buying , selling

Optimal Choice

Almost the same as before We only need to find m first

When are we net buyers of good 1? We first answer it graphically Price offer curve

2211 ppm

2/1,1,2 111 ppp1p )5,5( 2

Magic Formulas

Cobb Douglass

Perfect Complements

Optimal Choicex2

x1

)5,5( 1,2 21 pp

|MRS( )| =1 )5,5(2/ 21 pp

Optimal Choicex2

x1

)5,5( 1,2/1 21 pp

|MRS( )| =1 )5,5(2/1/ 21 pp

Optimal Choicex2

x1

)5,5( 1,1 21 pp

MRS( ) =1 )5,5(1/ 21 pp

Gains-to-Trade

Consumer engages in trade if:

In particular:

Price Offer Curvex2

x1

)5,5( 2/1,2,1 111 ppp

)5,5(

Price offer curve

With initial endowments price offer curve is ``enveloped’’ by the indifference curve that passes though endowment

Intuition: Agents engage in trade only trade gives higher utility

Cobb-Douglass)5,5(12 p

1p215.0

2121 ),( xxxxU

m *2

*1 , xx nd