The Austrian theory of the marginal use and of ordinal marginal utility
The Austrian theory of the marginal use raises almost as many problems as it has solved. We list here a few of these unsolved problems.
Complementarity and rivalness do lead to the ALEP criterion in the examples we worked out above, but we have made no attempt to formalize this rule into a general theorem. Intuitively, the ALEP condition must appear when the complementary or rival relationships are somehow active in the inner or outer marginal uses, but it is not clear exactly what the circumstances are under which this holds.
Although the theory leads to quasi-concavity of commodity preferences over goods in the particular cases we worked out, even when rival or complementary interactions are present, it has only been proven that this must be generally true when there are two goods, and then only in the case when the two goods are independent. Perhaps preferences do not really have to be quasi-concave after all.
And finally, it must be resolved whether the possibility of intrinsically ordinal preferences nullifies the von Neumann-Morgenstern axiom system, or if instead the validity of those axioms rules out intrinsically ordinal preferences.
After over a century, the Austrian theory is still in its youth. Perhaps the day has come for Felix Kaufmann's youngGrenznutzler to return from the netherworld of economic doctrine: There I will quietly lie in wait, Amid my neglected writings, Until I hear the trumpet call of Complementary Goods. Then through the sky will gallop Böhm-Bawerk, Polemics will thunder and flash! Then armed with a quill I'll rise up from the grave, To fight for theGrenznutzen school!27
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