equal to V z (p p ]/V zjp, ,pj. If V.zApu,p ) ^ 0, then, bv

1 aba 1 b b a 1 oba differentiating both sides of the budget constraint

Pw^vJPu'P ) + P Z *Pu>P ) = (1 - c}p, b b b a a a ^b a rb with respect to p.^, we obtain

Zfacpb'pa} + pb7lzb(pb'pa) + paVa(pb'pa3 = 1 "

Since V z. (p. ,p ) s 0 and z. (p. ,p ) ^ 0, this implies that 7 z (p. rp ) > 0. i o o a Doa 1 a * d a

Hence condition (20.H.3) is satisfied and the slope of the offer curve is negative (or the curve is vertical if V z (p p ) = 0). If V z, (p ,p ) > 0, i d d a i o o a then condition (20.H.3) is satisfied if and only if the slope is greater than one. Therefore, the offer curve must look as in the following figures (or a mixture of the two, in which case the curve has both positive and negative slODes):

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