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Abstract
We present an envelope theorem for establishing firstorder 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 firstorder conditions apply universally, even if optimal policies are not (S,s). Finally, we incorporate indivisible choices into a classic dynamic insurance analysis.
Original language  English 

Publisher  Edinburgh School of Economics Discussion Paper Series 
Number of pages  35 
Publication status  Published  31 Dec 2013 
Publication series
Name  ESE Discussion Papers 

No.  248 
Keywords
 Firstorder conditions
 Discrete choice
 Unsecured credit
 Adjustment costs
 Informal
 Insurance arrangements
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 1 Participation in workshop, seminar, course

London School of Economics STICERD seminar
Andrew Clausen (Invited speaker)
2015Activity: Participating in or organising an event types › Participation in workshop, seminar, course