Chapter 9 Buying and Selling Key Concept: People earn income by selling things they own, so there is an additional income effect called endowment income effect. When price of apple goes up, is it possible that apple growers eat more apples? ∆xa/∆pa = ∆xas/∆pa+(wa-xa) ∆xam/∆m

Chapter 9 Buying and Selling People earn their income by selling things that they own. Endowment: (w1,w2)

Endowment: (w1,w2) Gross demand: (x1, x2) Net demand observed: (x1-w1, x2-w2) x1-w1>0, net buyer, net demander x1-w1<0, net seller, net supplier Budget constraint becomes p1x1+ p2x2 = p1w1+ p2w2

Fig. 9.1

The value of endowment increases (w1,w2) to (w1’,w2’) p1w1+ p2w2 < p1w1’+ p2w2’ then the consumer must be better off No need to consume endowment and the budget set is larger.

Fig. 9.2

Suppose p1 decreases. Before change, a net seller of good 1, now could be a net seller (worse off) or a net buyer (?). Before change, a net buyer, now must a net buyer (better off)

Fig. 9.3

Fig. 9.4

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 price changes, 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)

Continue from the example in Chapter 8. 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)

Fig. 9.7

p1 → p1’ m → m’ → m’’ m = p1x1+ p2x2 = p1w1+ p2w2 m’ = p1’x1+ p2x2 m’’= p1’w1+ p2w2 m’’-m = (p1’-p1)w1 m’-m = (p1’-p1)x1

x1(p1’, m’’)-x1(p1, m) TE =[x1(p1’, m’)-x1(p1, m)] SE +[(x1(p1’, m)-x1 (p1’, m’)] OIE +[x1(p1’, m’’)-x1(p1’, m)] EIE (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) EIE/(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) ∆xam/∆m (-) (+ if net supplier)(+)

 

Fig. 9.8

Consider an increase in w, what will happen to R? ∆R/∆w = ∆Rs/∆w+(R’-R) ∆Rm/∆m (-) (+)

∆R/∆w = ∆Rs/∆w+(R’-R) ∆Rm/∆m SE makes R decrease If leisure is normal, IE makes R increase TE might increase if IE is large enough w goes up, R goes up or labor goes down A backward bending labor supply

Fig. 9.9

increase w, may reduce labor because of IE We want a pure SE if we want to increase labor supply. Overtime will work. overtime wage w’>w, a pure SE

Fig. 9.10

Chapter 9 Buying and Selling Key Concept: People earn income by selling things they own, so there is an additional income effect called endowment income effect. When price of apple goes up, is it possible that apple growers eat more apples? ∆xa/∆pa = ∆xas/∆pa+(wa-xa) ∆xam/∆m