Abstract
The problem of recognising Giffen behaviour is approached from the standpoint of the indirect utility function (IUF) from which the Marshallian demands are easily obtained via Roy’s identity. It is shown that, for the two-good situation, downward convergence of the contours of the IUF is necessary for giffenity, and sufficient if this downward convergence is strong enough, in a sense that is geometrically determined. A family of IUFs involving hyperbolic contours convex to the origin, and having this property of (locally) downward convergence is constructed. The Marshallian demands are obtained, and the region of Giffen behaviour determined. For this family, such regions exist for each good, and are non-overlapping. Finally, it is shown by geometric construction that the family of Direct Utility Functions having the same pattern of hyperbolic contours also exhibits giffenity in corresponding subregions of the positive quadrant.
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Notes
- 1.
The vanishing of c for \(a = (1 - \lambda )/\lambda \) means that the particular contour \(a = (1 - \lambda )/\lambda \) has a right-angled corner at the point (μ, μ), where \(\mu = (1 - \lambda )/\lambda \). This singularity may be removed by adopting a modified c(a) such that \({c}^{2} = {(1 - \lambda - \lambda a)}^{2} + {\epsilon }^{2}\), for suitably small ε. We shall not pursue this refinement here.
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Moffatt, P.G. (2012). A Class of Indirect Utility Functions Predicting Giffen Behaviour. In: Heijman, W., von Mouche, P. (eds) New Insights into the Theory of Giffen Goods. Lecture Notes in Economics and Mathematical Systems, vol 655. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21777-7_10
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DOI: https://doi.org/10.1007/978-3-642-21777-7_10
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