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The dual expansion method is an extension of the expansion method, a technique for creating or modifying mathematical models. The dual expansions method builds upon the proposition that when an expansion is defined, a dual expansion is also implicitly defined, much in the same way as dual mathematical programming formulations are implied by primal ones. Several uses of the dual expansions method are outlined and one of them is demonstrated. The dual expansion method is applied to investigating the effects of the rate of population growth on the rate of economic development. The findings obtained reveal significant negative effects of population growth on development that contrast with the inconclusive results of related empirical analyses reported in the literature.