A General and Intuitive Envelope Theorem

Carlo Strub () and Andrew Clausen

No 235, 2014 Meeting Papers from Society for Economic Dynamics

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.

Date: 2014
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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 (2013)
Working Paper: Envelope theorems for non-smooth and non-concave optimization (2012)
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Persistent link: https://EconPapers.repec.org/RePEc:red:sed014:235

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