A Modern Analysis of Giffen's Paradox
重新审视吉芬悖论，指出在标准两商品模型中，若一种商品为吉芬商品，其价格变化不仅影响自身消费，还会通过预算约束导致另一种商品消费同向变化，这一简单推论长期被忽视。
Concern over the possibility of an upward sloping demand curve started with Marshall, who credited Robert Giffen, an English statistician, with having first observed that more of a commodity may be consumed when its rises.' Nearly 100 years after Marshall published his remarks, the received analysis of a Giffen good is almost entirely contained in the assertion that in the Slutsky equation for the own price effects on consumption of the good, the income term may be sufficiently large to outweigh the negative pure substitution term. Even the elementary question of the impact of this large income effect on the consumption of other commodities seems to have been overlooked.2 In the standard two-good (x1 and x2) world, for example, if x1 is a Giffen good, i.e., if Ox1/lp, > 0, then from the budget constraint, p1OX1/P1 +p2aX2/p1= x1 and thus ax2/ap1 O. To satisfy the budget constraint, the large negative income term for x1 must produce a large positive income effect for x2 that outweighs the net substitution term in the Slutsky equation for the effects of changes in Pi on x2. When the of the Giffen good changes, therefore, not only does the income term outweigh the substitution term for the Giffen good, but a similar result is produced for the cross effect on the other commodity. This simple result seems to have gone unnoticed. Many economists have studied the Giffen paradox but a satisfactory analysis appears to be lacking. Marshall believed that the marginal utility of money, i, must rise with an increase in the of the Giffen good. George Stigler asserted [1950, p. 327], that the Giffen case is inconsistent with an additively separable utility function.3 William Gramm [1970] also examined the paradox, but his interpretation was not intended to add to knowledge about the economics of the