2025/09/15 by Qingyin Ma, Ma, Qingyin, Alexis Akira Toda +1
Business, Management and Accounting · Economics, Econometrics and Finance · #Economic Growth and Productivity #FOS: Economics and business #FOS: Mathematics #Fiscal Policy and Economic Growth #Optimization and Control (math.OC) #State Capitalism and Financial Governance #Theoretical Economics (econ.TH)
paper · pdf · doi:10.48550/arxiv.2509.12195
openalex publication_date 2025/09/15 · openalex created_date 2025/10/12 · openalex updated_date 2026/07/28
The consumption function maps current wealth and the exogenous state to current consumption. We prove the existence and uniqueness of a consumption function when the agent has a preference for wealth. When the period utility functions are restricted to power functions, we prove that the consumption function is asymptotically linear as wealth tends to infinity and provide a complete characterization of the asymptotic slopes. When the risk aversion with respect to wealth is less than that for consumption, the asymptotic slope is zero regardless of other model parameters, implying wealthy households save a large fraction of their income, consistent with empirical evidence.