Homothetic preferences, market equilibrium, and interior-point methods

2026年10月15日（周四）14:00 – 15:30

信息管理与工程学院308会议室

Chuwen Zhang (张楚文) is a Principal Researcher at the University of Chicago Booth School of Business. He received his PhD from the Shanghai University of Finance and Economics in 2025, advised by Yinyu Ye and Dongdong Ge. He previously worked at Cardinal Operations and holds degrees from the University of Texas at Austin and Shanghai Jiao Tong University. His research has appeared in leading journals such as Mathematics of Operations Research and Mathematical Programming.

Homothetic preferences, market equilibrium, and interior-point methods

Since Samuelson’s classical work, economists have studied how to allocate resources efficiently in the presence of public goods. Despite this long-standing interest, the computational theory of equilibria in these settings is less developed than its counterpart for economies containing only private goods. We characterize market equilibria in economies with private goods, public goods, or both. Under homothetic preferences, we show that an equilibrium allocation and its supporting price system solve a primal-dual pair of convex optimization problems whose objectives encode a particular notion of social welfare. Building on this characterization, we develop two interior-point methods and analyze how their worst-case complexities depend on preference primitives, including Allen-Uzawa elasticities and the dimensions of conic representations. Both methods can be accelerated by exploiting the decentralized structure of the economy: at each iteration, agents perform local calculations in parallel, and the auctioneer performs a single collective update.