A General and Intuitive Envelope Theorem

Andrew Clausen and Carlo Strub ()

Edinburgh School of Economics Discussion Paper Series from Edinburgh School of Economics, University of Edinburgh

Abstract: Previous envelope theorems establish differentiability of value functions in convex settings. Our envelope theorem applies to all functions whose derivatives appear in first-order conditions, and in non-convex settings. For example, in Stackelberg games, the leader’s first-order condition involves the derivative of the follower’s policy. Similarly, we differentiate (i) the borrower’s value function and default cut-off policy function in an unsecured credit economy, (ii) the firm’s value function in a capital adjustment problem with fixed costs, and (iii) the households’ value functions in insurance arrangements with indivisible goods. Our theorem accommodates optimization problems involving discrete choices, infinite horizon stochastic dynamic programming, and Inada conditions.

Keywords: First-order conditions; policy functions; discrete choice; Inada conditions; dynamic programming; reverse calculus dynamic programming; reverse calculus. (search for similar items in EconPapers)
Pages: 38
Date: 2016-04
New Economics Papers: this item is included in nep-dge and nep-mic
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Citations: View citations in EconPapers (28)

Downloads: (external link)
http://www.econ.ed.ac.uk/papers/id274_esedps.pdf

Related works:
Working Paper: A General and Intuitive Envelope Theorem (2014)
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:edn:esedps:274

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