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This paper adds to the relatively scant Australian literature on modelling the demand and supply of Australian imports. We build on earlier demand modelling by deriving conditional import demand relationships via representative household/firm-level utility-maximisation/cost-minimisation problems, which explicitly assume households/firms have both a taste for variety and rival sources of supply. Our estimates of disaggregated price elasticities are consistent with earlier studies in finding relatively low substitutability between imported and domestically produced varieties. Our derivation of the long-run supply framework also adds to the existing literature by explaining why it is necessary for researchers to employ trade-weighted foreign prices in place of individual country prices and providing conditions under which this approach is consistent with the underlying theory. We find that the extent of the foreign cost pass-through to import prices depends critically on the choice of foreign cost variable.