A General and Intuitive Envelope Theorem

Andrew Clausen and Carlo Strub ()

No 2015-43, SIRE Discussion Papers from Scottish Institute for Research in Economics (SIRE)

Abstract: We present an envelope theorem for establishing first-order conditions in decision problems involving continuous and discrete choices. Our theorem accommodates general dynamic programming problems, even with unbounded marginal utilities. And, unlike classical envelope theorems that focus only on differentiating value functions, we accommodate other endogenous functions such as default probabilities and interest rates. Our main technical ingredient is how we establish the differentiability of a function at a point: we sandwich the function between two differentiable functions from above and below. Our theory is widely applicable. In unsecured credit models, neither interest rates nor continuation values are globally differentiable. Nevertheless, we establish an Euler equation involving marginal prices and values. In adjustment cost models, we show that first-order conditions apply universally, even if optimal policies are not (S,s). Finally, we incorporate indivisible choices into a classic dynamic insurance analysis.

Keywords: First-order conditions; discrete choice; unsecured credit; adjustment costs; informal insurance arrangements (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (7)

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Related works:
Working Paper: A General and Intuitive Envelope Theorem (2016)
Working Paper: A General and Intuitive Envelope Theorem (2014)
Working Paper: A General and Intuitive Envelope Theorem (2014)
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Persistent link: https://EconPapers.repec.org/RePEc:edn:sirdps:631

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