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No, there are very weak assumptions made about the properties of preferences and then they just do the work in abstract to arrive at the functional form of the solution.
From there you can evaluate how different parameter values change the solution.
I would say that they are weak. Assumptions of a steady state always seem to be weak, to me. Marginalism and Subjectivism seem to dictate that situation.
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Modern micro is also founded on Marginal and Subjective Utility. The assumptions made about preferences are "Rationality Assumptions" that are only slightly stronger than what the Austrians also assume.
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