arXiv subjects

Jiyuan Lyu

Publications and source records attributed to Jiyuan Lyu.

6 recordsLinked to original sources

arXiv2026

Mean-Field Analytical Solution of the Mesa Boltzmann Wealth Model

The Boltzmann wealth model provided by the Mesa framework is a classic example in agent-based modeling, yet its statistical properties are typically analyzed only through numerical simulation. This paper studies a mean-field version of the model, replacing local interactions with global random matching and adopting a synchronous update scheme. By establishing a mean-field master equation for the wealth distribution and employing the probability generating function method, we obtain a closed-form expression for the steady-state generating function, and analytically determine the model parameters. We further derive the variance, Gini coefficient, and tail asymptotic behavior of the steady-state wealth distribution. Numerical simulations of the corresponding mean-field agent-based model agree well with the theoretical predictions. This paper provides an analytical benchmark for this mean-field model, which can serve as a reference for theoretical analysis and result validation in related agent-based simulations.

physics.soc-ph↗

arXiv2026

Minimum Wages, Firm Size Distribution, and the Labor Share

The sustained decline of the labor share challenges the classic Kaldor facts. This paper proposes a ``weighting effect'' mechanism: because large firms systematically adopt more capital-intensive technologies, a shift of economic activity toward large firms mechanically depresses the macro labor share, even under perfect competition. We test this mechanism by exploiting minimum wage hikes in China as an exogenous shock that forces small labor-intensive firms to exit. Using the Chinese Annual Survey of Industrial Firms (1998--2007) and a Bartik instrument based on pre-sample small-firm shares interacted with provincial minimum wage growth, we find that a one-standard-deviation shock reduces the market-level labor share by approximately 0.11 percentage points (3.5\% of the mean). The effect is robust to controlling for market concentration, alternative measures, and a battery of placebo tests including randomization inference. Direct mechanism tests confirm that the shock raises exit rates, reduces the number and share of small firms, and reallocates output toward large, capital-intensive firms. Supplementary IV estimates confirm that a more equal firm size distribution raises the labor share. The findings identify a complete causal chain from labor market institutions to macro distribution through the firm size structure, offering a ``technology-structure'' channel that is independent of market power.

econ.TH↗

arXiv2026

Fixed Capital, the Cost Criterion, and the Falling Rate of Profit

Existing studies that introduce the concept of fixed capital into the Okishio Theorem show that, under an unchanged real wage, cost-reducing technical progress still necessarily raises the equilibrium rate of profit. This paper argues that this conclusion depends on how cost is defined in fixed capital models. In the original model of Okishio (1961), cost corresponds to what is termed operating cost in accounting, which excludes any form of profit; by contrast, the classical fixed capital frameworks adopted by Roemer (1979) and Woods (1985) cannot mathematically separate depreciation from profit, so that cost comparison in fact corresponds to capitalized cost inclusive of profit. This paper employs the annuity method to treat fixed capital, thereby separating depreciation from profit, and grounds the capitalist's technology choice on the basis of operating cost. The results show that two distinct thresholds exist in the fixed capital model: a profit-rate threshold that determines the direction of change in the rate of profit after the diffusion of the new technology, and an operating-cost threshold that determines whether the capitalist will adopt the new technology. When the lifetime of fixed capital exceeds one production period, the two thresholds are strictly separated, giving rise to a nonempty interval. Within this interval, the new technology lowers operating cost and is adopted by capitalists, yet the new equilibrium rate of profit falls below its initial level. The pure circulating capital model corresponds to the special case in which the two thresholds coincide, so that the Okishio Theorem can be regarded as a special case of the results obtained in this paper.

econ.TH↗

arXiv2026

The Evolution of Intersectoral Financial Relations between Industry and Agriculture in China's Planned Economy Period

This paper examines intersectoral financial relations between industry and agriculture during 1949--1977 through four channels: fiscal, price, quantity procurement, and foreign trade. We find that these relations underwent staged evolution rather than constituting a persistent transfer mechanism: agriculture supported industry in the 1950s, the year 1961 marked a turning point, and the 1970s witnessed the emergence of mutual interdependence between the two sectors. No stable empirical pattern of price mechanisms persistently affecting industrial profitability is observed.

econ.EM↗

arXiv2026

A Geometric Approach to the Transformation Problem of Values

The reduction of complex labour to simple labour is an unresolved difficulty in Marx's labour theory of value, and a key obstacle that has prevented the transformation problem from being settled definitively. This paper proposes a two-step solution framework. First, we prove that as long as the macroeconomy generates a physical surplus, the reduction coefficients that respect the floor of labour-power reproduction form a bounded ``value feasible region''; within this region the two macro aggregate equalities can hold simultaneously for a reasonable range of the profit rate. Second, we propose a linear mapping method that exploits the observable structure of nominal wages and the reproduction floor constraint to systematically construct the implicit reduction coefficients from the value feasible region. We show that this mapping is a homeomorphism between the price feasible region and the value feasible region, and that it preserves the boundary structure. An empirical calibration based on China's 2017 inter-provincial input--output table with 1272 sectors shows that the reduction coefficients obtained by the mapping method substantially outperform the homogeneous labour method and the wage-proxy method in matching the macro profit share.

econ.TH↗

arXiv2026

Feasible Sets and the Transformation of Values

This paper proposes a change in perspective on the ``transformation of values'' problem: from ``searching for a single constant solution'' to ``characterizing the allocation space under objective constraints imposed by the physical production network.'' Building an input--output model, we show mathematically that whenever the macroeconomy features a physical surplus, the set of skilled-to-simple labor reduction vectors that can sustain the subsistence floor of the entire labor force forms a bounded value-feasible set . Within this multidimensional region, the classical ``two great macro equalities'' necessarily hold simultaneously for a reasonable range of profit rates. Hence, without violating the physical minimum conditions for reproduction, the law of value and the nominal price system can be made logically consistent.

econ.TH↗