ABSTRACT

I aual . (t~) tJ. - = - pzPl~e/ 1 + P -- zitI . ata q 1 + t~ 1'= 0 (16) The bracketed term of (16) can be written as 1 + [pI(1 + t~)]Zelt~, where [pI(1 + tP)]f,} is the marginal propensity of ~ to consume the first commodity; moreover, tJ., zPl and Z~l are all negative. In the absence of inferiority and for 1 + t P > 0, therefore,

(17)

From (15) and (17) we can infer that the locus aua/ata = 0 leaves point C in a south-easterly direction with slope steeper than that of AB at C

Consider next the locus auP/ata = O. On AB, ZPI = 0; from (9), therefore,

tJ. auPI _ t P .:z al PI ata AB - (1+ tP)21' Zq Zq (18)

implying that

Hence

From (19) and (20), the locus alll'>/a,a = 0 leaves D either with a positive slope or with a negative slope greater than that of AB at D. Moreover, from (9), the locus remains everywhere above the line ,I'> = - 1.