AI 中文总结
构建权益证明网络模型分析代币价格动态与投机资本效应，先考虑活跃效用用户网络，证明稳态均衡并估计松弛半衰期，后引入投资者类别，发现被动质押影响价格与所有权，主动投机资本有不同影响，利于共识去中心化。
AI 中文摘要
在本文中，我们构建了一个权益证明网络的开放经济宏观经济模型，以分析名义代币价格动态和投机资本的系统效应。首先考虑一个仅由活跃效用用户组成的网络，他们通过法定货币的稳定外生流入为网络活动融资。我们证明了存在唯一且全局渐近稳定的稳态均衡，其具有明确的名义代币价格，并推导出网络松弛时间的闭式表达式。通过使用代表当前以太坊网络参数校准模型，估计出松弛半衰期约为46年。这种极端的宏观经济惯性意味着代币价格可能持续偏离其不断演变的稳态基准，在网络适应基本面变化时产生持续的价格超调。接着引入投资者类别来研究被动和主动投机资本的影响。我们表明被动机构质押压缩了原生质押收益率并造成结构失衡，系统性提高名义代币价格并将共识所有权从活跃效用用户转移。主动投机资本有质的不同影响。响应资本冲击，消费者类别对法定货币计价消费的刚性偏好产生内生恒定价值策略。此机制将质押代币所有权从投资者类别转向活跃效用用户，对共识去中心化可能有有利影响。
英文摘要
In this paper, we develop an open-economy macroeconomic model of a Proof-of-Stake network to analyze nominal token-price dynamics and the systemic effects of speculative capital. We first consider a network populated solely by active utility users, who finance network activity through a steady exogenous inflow of fiat currency. We prove the existence of a unique, globally asymptotically stable steady-state equilibrium with a well-defined nominal token price and derive a closed-form expression for the network's relaxation time. Calibrating the model using parameters representative of the current Ethereum network, we estimate a relaxation half-life of approximately 46 years. This extreme macroeconomic inertia implies that the token price may remain persistently displaced from its evolving steady-state benchmark, producing sustained price overshooting as the network adjusts to changing fundamentals. We then introduce an Investor class to examine the effects of passive and active speculative capital. We show that passive institutional staking compresses the native staking yield and creates a structural imbalance that systematically raises the nominal token price while shifting consensus ownership away from active utility users. Active speculative capital has a qualitatively different effect. In response to capital shocks, the Consumer class's rigid preference for fiat-denominated consumption generates an endogenous constant-value strategy. This mechanism shifts staked-token ownership from the Investor class toward active utility users, with potentially favorable implications for consensus decentralization.
Comments20 pages, 2 figures
