A self-reflective inverse demand system

Abstract

This article introduces an inverse differential demand system that has exactly the same form as the corresponding direct version. Its application is illustrated with the case of Australian fruit, whose prices were substantially affected by Severe Tropical Cyclone Larry in 2006.

Keywords:

• inverse demand
• fruit prices

JEL Classification:

• D12

Acknowledgements

We acknowledge the help of Josh Ellis of the Perth Market Authority for assistance with the data. We have benefited from helpful discussions with Ernst Berndt and Keith McLaren, as well as comments on an earlier draft from Grace Gao and Callum Jones. This research was supported in part by the ARC.

Notes

¹See, for example, Anderson (1980), Barten and Bettendorf (1989), Brown et al. (1995), Huang (1983), Laitinen and Theil (1979), Salvas-Bronsard et al. (1977) and Theil (1976).

For a longer version of this article, see Clements and Maesepp (2008).

²For example, the Rotterdam's model under preference independence has on the right-hand side of its ith equation the change in the deflated price of good i, , where the deflator is the Frisch price index defined as , with the marginal share. The reciprocal version of this model has z_it on the left-hand side, but not a similarly marginally deflated quantity on the right (Theil, 1976, sec. 9.5). The same comment applies to the Central Bureau of Statistics (CBS) system of Keller (1984) and Keller and van Driel (1985). It is to be noted that there is a related concept of self-duality of preferences, according to which the utility function and the indirect utility function have the same form, as do the direct and inverse demand systems (Houthakker, 1965; Sato, 1976). The differences between self-duality and self-reflectivity are that (1) the former applies to levels of variables, whereas the latter applies to differentials; and (2) differential demand systems are not associated with any particular algebraic form of the utility function.

³For the sources and a listing of the data, see Clements and Maesepp (2008).

⁴Imports of bananas into Australia are prohibited by quarantine regulations.