• 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)
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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
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∆xa/∆pa = ∆xas/∆pa+(wa-xa) ∆xam/∆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)