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Chapter 9 Buying And Selling People earn their income buy selling things that they own.

Chapter 9 Buying And Selling People earn their income buy selling things that they own. Endowment: (w 1 ,w 2 ) Gross demand: (x 1 ,x 2 ) Net demand: (x 1 -w 1 ,x 2 -w 2 ) (observed) x 1 -w 1 >0, net buyer, net demander x 1 -w 1 <0, net seller, net supplier

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Chapter 9 Buying And Selling People earn their income buy selling things that they own.

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  1. 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

  2. Fig. 9.1

  3. 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)

  4. Fig. 9.2

  5. Fig. 9.3

  6. Fig. 9.4

  7. 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)

  8. 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)

  9. Fig. 9.7

  10. 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

  11. 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

  12. ∆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)

  13. Fig. 9.8

  14. 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

  15. Fig. 9.9

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

  17. Fig. 9.10

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