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Minimisation problem turned into Maximisation

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Berge's theorem of maximum's application to expenditure minimisation problem

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Lump sum transfers to implement any Pareto efficient equilibrium as the market outcome

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Determine if goods are substitutes or Complements based on demand function

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Can the following statement be rationalized if it yields a choice function?

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Clarifying question about utility theory and preferences

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What is a utility function rationalizes these preferences?

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