[讨论]哥本哈根大学证明吉芬商品存在的函数能成立吗？
Consider an individual consumer with standard consumption set R2+ and utility functionu(x1, x2) = min{x1 + B, A (x1 + x2)} where A > 1 and B > 0. An interpretation is thatthe intake (x1, x2) of coffee and Danish pastry will allow x1 + B > 0 of thinking and
A (x1 + x2) ≥ 0 of walking, and that these two activities are perfect complements for the consumer。
where A = 2 and B = 10. The straight dotted line indicates where the curves are kinked.The right panel illustrates the Giffen good effect, as the consumer’s income is m = 5.The price of good 1 is fixed at p1 = 12. When initially p2 = 4, the consumer demandsx = (4, 3), but a price increase to p2 = 9 changes the demand to x = (2, 4). The Giffeneffect is that the demand of good 2 rises from 3 to 4 as its price rises.
图示我画不上去。总之，无差异曲线不是凸向原点的曲线，是三角形两个边的那种线。
我认为这函数不满足凸性公理及边际替代率递减定理，由此导出的证明价格与需求量同向变化，进而吉芬商品存在的结论是不能成立的。
你们认为对吗？