• Chapter 9 Buying And Selling• People earn their income buy selling

things that they own.• Endowment: (w1,w2)• Gross demand: (x1,x2)• Net demand: (x1-w1,x2-w2) (observed)• x1-w1>0, net buyer, net demander• x1-w1<0, net seller, net supplier• Budget constraint becomes: p1x1+ p2x2 =

p1w1+ p2w2

• Changing the endowment from (w1,w2) to (w1’,w2’) so that p1w1+ p2w2 < p1w1’+ p2w2’, then the consumer must be better off (the point is no need to consume endowment and the budget set is larger).

• Suppose p1 decreases, (w1,w2) always on the budget line: before change, a net seller of good 1, now could be a net seller (worse off) or a net buyer (?); before, a net buyer, now must a net buyer (better off)

• Revisit Slutsky equation

• p1w1+ p2w2, no way to hold nominal income fixed when, say, p1 changes

• Holding purchasing power fixed (SE)

• Holding nominal income fixed (OIE) (ordinary income effect)

• In addition, when prices change, the value of the endowment bundle changes, this additional income effect is called the endowment income effect (EIE)

• Abbreviate p1w1+ p2w2 by pw. • x1(p1, pw) → x1(p1’, p1’x1(p1, pw)+p2x2(p1, pw)) (SE) → x1(p1’, pw) (OIE) → x1(p1’, p1’w1+ p2w2) (EIE)• A dairy farmer produces 40 quarts of

milk per week, p1=3 and p1’=2, x1=10+m/(10p1)

• [10+2*40/(10*2)]-[10+3*40/(10*2)]=-2 (EIE)

• p1 → p1’

• m → m’ → m’’• m = p1x1+ p2x2 = p1w1+ p2w2

• m’ = p1’x1+ p2x2

• m’’= p1’w1+ p2w2

• m’’-m=(p1’-p1)w1 and m’-m=(p1’-p1)x1

• x1(p1’,m’’)-x1(p1,m)=[x1(p1’,m’)-x1(p1, m)]+[(x1(p1’,m)-x1 (p1’,m’)]+[x1(p1’,m’’)-x1(p1’,m)] (Slutsky identity)

• TE/(p1’-p1)=(x1(p1’,m’’)-x1(p1,m)) /(p1’-p1)

• SE/(p1’-p1)=(x1(p1’,m’)-x1(p1,m)) /(p1’-p1)

• OIE/(p1’-p1)=(x1(p1’,m)-x1(p1’,m’)) /(p1’-p1) =-[(x1(p1’,m’)-x1(p1’,m)) /(m’-m)] x1(p1, m))

• EIE/(p1’-p1)=(x1(p1’,m’’)-x1(p1’,m))/(p1’-p1)=[(x1(p1’,m’’)-x1(p1’,m))/(m’’-m)] w1

• ∆xa/∆pa = ∆xas/∆pa+(wa-xa) ∆xa

m/∆m• Apply to labor supply• M: non labor income• w: wage rate• p: price of consumption• C: consumption, R: leisure, R’: max• pC=w(R’-R)+M, pC+wR=wR’+M (full

income or implicit income, the value of her endowment of consumption and her endowment of time)

• Consider an increase in w, what will happen to R?

• ∆R/∆w = ∆Rs/∆w+(R’-R) ∆Rm/∆m

• SE is (-) and assuming leisure is normal, then total IE is (+), since L=R’-R, this means we might have a backward bending labor supply if the IE is large enough

• Note that if (R’-R) is large (work hard enough) then IE is likely to be big

• Overtime and labor supply (increase w, may reduce labor because of IE, but overtime wage w’>w is a pure SE)