The logsum formula, which provides the expected maximum utility for the multinomial logit model, is often used as a measure of welfare. We provide here a closed form formula of the welfare measure of an individual who has not access to his first-best choice, but has access to his rth-best choice, r = 2, ...n, where n is the number of alternatives. The derivation is based on a standard identity ...

In [2, Chapter VII (p. 133)], Ritt shows an example of two irreducible differential variety of differential dimension 2 in U whose intersection consists of a single point: the origin. The details below follow Ritt’s exposition using more modern language and notation. The first part is taken from my tutorial paper [3], with some change in notation. That paper provides the basic background needed...