本文介绍学习华罗庚经济最优化的数学理论的新体会. 一是研究市场经济中价格参数 p = (p_i), i = 1, 2, . . . , n 变化时，初始投入与崩溃时间的关系，根据计划经济与市场经济结 构方阵的关系，首先给出市场经济下的崩溃定理，也即初始投入 x₀等于其最大特征值所 对应的左特征向量 uV 时，崩溃时间 T = ∞. 并在第二章给出了严格证明，第三章中也结合 例子提供了大量数据予以说明；二是给出了市场经济中带消费实用模型更加合理化的刻 画. 在先前的工作中，华先生和陈先生已经就计划经济的带消费实用模型进行了讨论，包 括第 n 年的消费量 ξ_n的选取, 陈先生在 2022 年 4 月份发表的文[1] 中就带消费实用模型中 的消费比例 α ∈ (0, 1) 的含义进行了详细的阐述，本文是在已有的计划经济基础上给出市场经济中的带消费实用模型的刻画；三是研究经济系统崩溃时所做出的两种调整方案. 第 一个调整方案是根据经典的华罗庚基本定理，当初始投入向量等于其结构方阵最大特征值 所对应的左特征向量时，经济系统永不崩溃. 将这种初始投入向量取正特征矢量的方法就 称为正特征矢量法，基于此，第一种调整方案考虑在崩溃年限 Tx₀ 前一 (几) 年将其投入向 量用正特征矢量去代替，这样可以将整个生产过程中的崩溃时间得到延长. 第二个调整方案是根据产品的等级排序来进行的. 若考虑无消费理想模型 (带消费实用模型可类似处理)， 对于经济系统中的结构方阵 A, 作变换 P = D_v^-1 A/ ρ(A)D_v，其中 D_v: 以向量 v = (v ⁽ⁿ⁾ : n ∈ E) 作 为对角线元素的对角矩阵，v 为 A 的最大特征值所对应的右特征向量，故作此变换可将其转化为转移概率 P，记 P 的左特征向量为 µ，按照 µ 的大小将各产品进行一个等级排序，µ 越大，等级排序越高，从高至低，可将所有产品分为支柱产品、中间产品以及弱势产品. 故我们可以通过淘汰经济系统中的弱势产品来达到延长系统的崩溃时间，通过计算能说明， 淘汰产品等级排序越靠后的弱势产品，对维持系统的稳定性越有利，将这种调整方法称为等级排序法.

This paper introduces the new experience of learning Hua’s mathematical theory of economic optimization. The first is to study the relationship between initial input and collapse time when price parameters p = (p_i), i = 1, 2, . . . , n change in market economy. According to the relationship between planned economy and market economy structure square, the collapse theorem under market economy is first given. That is, when the initial input x₀ is equal to the left eigenvector uV corresponding to its maximum eigenvalue, the collapse time T = ∞. In the second chapter, strict proof is given, and in the third chapter, a large number of data are provided with examples.Second, it gives a more reasonable description of the practical model with consumption in the market economy. In previous work, Hua and Chen had discussed practical models of planned economies with consumption, Including the selection of consumption ξ_n in the first n year, Chen elaborated on the meaning of consumption ratio α ∈ (0, 1)in[1] published in April 2022. Based on the existing planned economy, this paper gives a description of the practical model of market economy with consumption.The third is to study the two adjustments made when the economic system collapses. The first adjustment scheme is based on the classic Hua’s fundamental theorem, when the initial input vector is equal to the left eigenvector corresponding to the maximum eigenvalue of its structure square matrix, the economic system will never collapse. The method of taking the initial input vector as the positive eigenvector is called the positive eigenvector method. Based on this, the first adjustment scheme considers replacing the input vector with the positive eigenvector one (few) years before the collapse year Tx₀ , so as to prolong the collapse time in the whole production process.The second adjustment scheme is based on the ranking of products. If no consumption ideal model (with consumer utility model can be similar to treatment), the economic system structure of the phalanx A, transforming P = D_v^-1 A /ρ(A)D_v, Where Dv: the diagonal matrix with the vector v = (v ⁽ⁿ⁾ : n ∈ E) as the diagonal element,vis the right eigenvector corresponding to the maximum eigenvalue of A, which can be converted into the transfer probability P by pretending to transform this transformation, and the left eigenvector denoted as µ, Rank each product according to the size of µ. The larger the µ is, the higher the rank rank will be from high to low，all products can be divided into pillar products, intermediate products, and weak products. Therefore, we can extend the collapse time of the system by eliminating the weak products in the economic system. It can be shown by calculation that eliminating the weak products with the lower product ranking is more beneficial to maintain the stability of the system. This adjustment method is called the ranking method.