Kam, TimothyKao, TinaLee, Junsang2026-07-032026-07-031365-1005https://hdl.handle.net/1885/733812869We study long-run inflation in a competitive-search model with heterogeneous agents. Under competitive search, individuals' matching-probability (extensive) margins trade off against quantity (intensive) margins. With money and unfettered market participation, these trade-offs depend on inflation and individuals' heterogeneous money holdings. We find that welfare falls as inflation increases. However, money-holdings inequality is not monotonic in inflation. As inflation rises, liquid-wealth inequality first falls. For sufficiently high inflation, the overall extensive-margin effect dominates the intensive margin, and liquid-wealth inequality rises. The model also poses a new computational challenge to which we propose a novel solution method.This paper was previously circulated under the title “Cost of Inflation and Inequality in a Competitive-search Heterogeneous-agent Model.” We thank the Editor, Associate Editor and three anonymous referees for comments that have improved the paper. We thank Nejat Anbarci, Suren Basov, Chris Carroll, Gaston Chaumont, Jonathan Chiu, Wing Feng, Pedro Gomis-Porqueras, Ippei Fujiwara, Allen Head, Tai-Wei Hu, Benoît Julien, Kuk Mo Jung, Hyung Seok Kim, Ian King, Beverly Lapham, Simon Mishricky, Miguel Molico, Sam Ng, Sihui Ong, Guillaume Rocheteau, Shouyong Shi, John Stachurski, Amy Sun, Serene Tan, Satoshi Tanaka, Chung Tran, Pablo Winant, Liang Wang, and Randall Wright for discussions. We acknowledge funding support through the Australian Research Council’s Discovery Project Grant No. DP180103680. A companion Online Appendix and open-source codes for this work can be found at: https://github.com/phantomachine/csm .enPublisher Copyright: © The Author(s), 2025.Competitive searchcomputational geometrydistributional trade-offsinflation2025-05-2610.1017/S136510052500032X105006781570