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The envelope theorem is a theorem used in optimisation problems (max & min) in microeconomics. It may be used to prove Hotelling''s lemma, Shephard''s lemma, and Roy''s identity. It also allows for easier computation of comparative statics in generalised economic models. The theorem exists in two versions, a regular version (unconstrained optimisation) and a generalised version (constrained optimisation). The regular version can be obtained from the general version because unconstrained optimisation is just the special case of constrained optimisation with no constraints (or constraints that…mehr

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The envelope theorem is a theorem used in optimisation problems (max & min) in microeconomics. It may be used to prove Hotelling''s lemma, Shephard''s lemma, and Roy''s identity. It also allows for easier computation of comparative statics in generalised economic models. The theorem exists in two versions, a regular version (unconstrained optimisation) and a generalised version (constrained optimisation). The regular version can be obtained from the general version because unconstrained optimisation is just the special case of constrained optimisation with no constraints (or constraints that are always satisfied, i.e. constraints that are identities e.g. 0 = 0 or (x + 1)2 = x2 + 2x + 1.