TL;DR: Can insurance be a Giffen good? This can never happen if the coefficient of relative risk aversion is less than or equal to one as mentioned in this paper, and if this coefficient is greater than one it is possible but not empirically plausible.
TL;DR: The Giffen Paradox as mentioned in this paper is the inability of demand theory to explain why Giffens goods are apparently so rare, and the resolution of the paradox arises from the distinction between the shape of market demand curves and the sequence of equilibrium prices that will be observed in markets in which quantity supplied changes.
Abstract: The paradoxical aspect of the Giffen Paradox is the inability of demand theory to explain why Giffen goods are apparently so rare. The resolution of the paradox arises from the distinction between the shape of market demand curves and the sequence of equilibrium prices that will be observed in markets in which quantity supplied changes. The sense in which the Giffen case is "unlikely" to occur is that the probability of identifying a Giffen good is less than the probability that such a good exists.
TL;DR: This paper showed that a well-behaved utility function can generate Giffen behavior, where "wellbehaved" means that its indifference curves are smooth, convex, and closed in a commodity space; the resulting demand function of each good is differentiable with respect to prices and income.
Abstract: We demonstrate that a well-behaved utility function can generate Giffen behavior, where “well-behaved” means that its indifference curves are smooth, convex, and closed in a commodity space; the resulting demand function of each good is differentiable with respect to prices and income. Moreover, we show that Giffen behavior is compatible with any level of utility and an arbitrarily low share of income spent on the inferior good. This contrasts sharply with the common view that the Giffen paradox tends to occur when households’ wealth levels are low.
TL;DR: The authors showed that the risk free asset can not only fail to be a normal good but can in fact be a Giffen good even for widely popular members of the hyperbolic absolute risk aversion (HARA) class of utility functions.
Abstract: It is standard in economics to assume that assets are normal goods and demand is downward sloping in price. This view has its theoretical foundation in the classic single period model of Arrow with one risky asset and one risk free asset, where both are assumed to be held long, and preferences exhibit decreasing absolute risk aversion and increasing relative risk aversion. However when short selling is allowed, we show that the risk free asset can not only fail to be a normal good but can in fact be a Giffen good even for widely popular members of the hyperbolic absolute risk aversion (HARA) class of utility functions. Distinct regions in the price-income space are identified in which the risk free asset exhibits normal, inferior and Giffen behavior. An example is provided in which for non-HARA preferences Giffen behavior occurs over multiple ranges of income.
TL;DR: In this article, a necessary and sufficient condition for a good to be normal is given in terms of the second derivatives of the expenditure function, which is easily interpreted as requiring that, with utility held constant, an increase in the price of the good in question decrease the marginal utility of income.