Hanbaek Lee, University of Cambridge

"The Convex Origin of Fixed Costs"

Abstract

Are models with fixed and convex adjustment costs different? This paper shows they are ex-ante equivalent via Fenchel duality: with fixed costs drawn from a distribution G, the threshold rule coincides with a convex cost over the adjustment probability - same value functions, same choice probabilities. Different shapes of G generate the cost functions used in menu costs, lumpy investment, rational inattention, discrete choice, and control costs, connecting these literatures in one G-indexed family. For pricing, a power law G with parameter γ traces a continuous spectrum between Calvo (dispersed costs, weak selection) and Golosov-Lucas (concentrated costs, strong selection), and decomposes the Phillips curve slope into repricing frequency and a selection term linear in γ. Illustrative CPI calibration yields γ ≈ 0.4, with selection contributing 44% of the slope.

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Contact person: Manuel Menkhoff