Buying and Selling. Chapter Nine. Buying and Selling. Endowments. Endowments. Endowments. Buying and Selling

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1 Buying and Selling hapter Nine Buying and Selling Trade involves exchange -- hen soething is bought soething else ust be sold. What ill be bought? What ill be sold? Who ill be a buyer? Who ill be a seller? Buying and Selling And ho are incoes generated? Ho does the value of incoe depend upon coodity prices? Ho can e put all this together to explain better ho price changes affect deands? Endoents The list of resource units ith hich a consuer starts is his. A consuer s ill be denoted by the vector (oega). ω Endoents ω = ( ω1, ) = ( 10, ) E.g. states that the consuer is endoed ith 10 units of good 1 and units of good. Endoents ω = ( ω1, ) = ( 10, ) E.g. states that the consuer is endoed ith 10 units of good 1 and units of good. What is the s value? For hich consuption bundles ay it be exchanged? 1

2 Endoents p 1 = and p =3 so the value of the is ( ω1, ) = ( 10, ) p1ω 1 + pω = = 6 Q: For hich consuption bundles ay the be exchanged? A: For any bundle costing no ore than the s value. { Budget onstraints evisited So, given p 1 and p, the budget constraint for a consuer ith an ( ω1, ) is p 1 + p = p1 + p. The budget set is ( x1, x) p1x1 + px p1ω 1 + pω, } x1 0, x 0. Budget onstraints evisited Budget onstraints evisited p p = p1ω pω p p = p1ω pω { Budget set ( x1, x) p1x1 + px p1ω 1 + pω, x1 0, x 0 } Budget onstraints evisited Budget onstraints evisited p p = p1ω pω p p = p1ω pω Budget set p 1 + px = p1 ω1 + p ω p 1 + px = p1 ω1 + p ω

3 Budget onstraints evisited The point is alays on the budget constraint. p p = p1ω pω p 1 + px = p1 ω1 + p ω Budget onstraints evisited The point is alays on the budget constraint. p p = p1ω pω So price changes pivot the constraint about the point. p 1 + px = p1 ω1 + p ω Budget onstraints evisited The constraint p p = p1ω pω is p1( x1 ω1) + p( x ). That is, the su of the values of a consuer s net deands is zero. Suppose ( ω1, ) = ( 10, ) and p 1 =, p =3. Then the constraint is p 1 + p = p1 + p = 6. If the consuer deands ( *, *) = (7,4), then 3 good 1 units exchange for good units. Net deands are *- = 7-10 = -3 and *- = 4 - = +. p 1 =, p =3, *- = -3 and *- = + so p1( x1 ω1) + p( x ) = ( 3) + 3. The purchase of extra good units at $3 each is funded by giving up 3 good 1 units at $ each. * p1( x1 ω1) + p( x ) At prices (p 1,p ) the consuer sells units of good 1 to acquire ore units of good. * 3

4 p1( x1 ω1) + p( x ) At prices (p 1,p ) the consuer sells units of good to acquire ore of good 1. At prices (p 1,p ) the consuer consues her ; net deands are all zero. x p 1 px p1 1 p * + = ω + ω *= px " px " = p " 1ω1 + p " ω * *= p1( x1 ω1) + p( x ) p1( x1 ω1) + p( x ) Price-offer curve contains all the utility-axiizing gross deands for hich the can be exchanged. Price-offer curve Sell good 1, buy good p1( x1 ω1) + p( x ) Price-offer curve Buy good 1, sell good A orker is endoed ith $ of nonlabor incoe and hours of tie hich can be used for labor or leisure. ω = (,). onsuption good s price is p c. is the age rate. 4

5 The orker s budget constraint is pc = ( ) + here, denote gross deands for the consuption good and for leisure. That is pc + = + { expenditure { value pc = ( ) + rearranges to. p + ($) p + + p c p + + p c p + slope =, the real age rate p c 5

6 + p c * leisure deanded * p + labor supplied Slutsky: changes to deands caused by a price change are the su of a pure substitution effect, and an incoe effect. This assued that incoe y did not change as prices changed. But y = p1ω pω does change ith price. Ho does this odify Slutsky s equation? A change in p 1 or p changes y = p1ω pω so there ill be an additional incoe effect, called the incoe effect. Slutsky s decoposition ill thus have three coponents a pure substitution effect an (ordinary) incoe effect, and an incoe effect. Initial prices are (p 1,p ). Initial prices are (p 1,p ). Final prices are (p 1,p ). Initial prices are (p 1,p ). Final prices are (p 1,p ). Ho is the change in deand fro (, ) to (, ) explained? 6

7 Initial prices are (p 1,p ). Initial prices are (p 1,p ). Final prices are (p 1,p ). Ordinary incoe effect Ordinary incoe effect 7

8 Ordinary incoe effect Endoent incoe effect Ordinary incoe effect Endoent incoe effect Overall change in deand caused by a change in price is the su of: (i) a pure substitution effect (ii) an ordinary incoe effect (iii) an incoe effect 8