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以发展的视域认识马尔萨斯的《人口理论》【摘要】马尔萨斯作为经济学家和人口学家，提出了《人口理论》以及与之相关的观念，对社会发展产生了深远影响。
他的人口理论核心原则包括人口增长受限于食物供应、人口增长以指数级增长而资源增长以线性增长等。
这些理论对当代社会仍有启示，如提醒我们关注资源匮乏问题、实行人口控制政策等。
马尔萨斯的人口理论也受到了很多批评，如忽视科技进步带来的资源扩增等。
尽管如此，马尔萨斯的《人口理论》对经济学和人口问题仍产生了持续的影响。
马尔萨斯的《人口理论》在现代社会启示我们要认真对待人口问题，努力寻找可持续发展的解决方案。
【关键词】关键词：马尔萨斯，人口理论，社会发展，经济学，核心原则，启示，批评与发展，持续影响。
1. 引言1.1 马尔萨斯及其《人口理论》的背景马尔萨斯（Thomas Robert Malthus，1766-1834）是一位英国经济学家和人口学家，他的著作《人口原理》（An Essay on the Principle of Population）于1798年首次发表，引起了广泛的争议与关注。
马尔萨斯的人口理论背景主要是基于18世纪末英国的社会环境。
当时，英国经历了工业革命和城市化的快速发展，社会经济状况不断变化，贫困、失业和食品供应问题成为突出的社会难题。
马尔萨斯在这样的背景下提出了人口理论，认为人口的增长速度远远超过了食品供应和资源生产的增长速度，从而导致了贫困和社会动荡。
马尔萨斯的人口理论在当时是极具争议的，他的观点挑战了当时普遍认为人口增长是社会进步的观念。
他的理论对后世学者和政策制定者产生了深远的影响，在经济学、社会学和人口学等领域都产生了重要的启示和影响。
.1.2 人口理论在经济学发展中的地位人口理论在经济学发展中的地位可以说是至关重要的。
马尔萨斯的《人口理论》首次将人口问题引入到经济学讨论的范围之内，从而开创了人口经济学的研究领域。
人口是一个国家或地区经济社会发展的基础，人口的数量和结构对经济增长、社会变迁和资源分配等方面都有着深远的影响。
malthus模型方程Malthus模型方程及其应用引言：Malthus模型是由英国经济学家托马斯·罗伯特·马尔萨斯于1798年提出的一种人口增长理论。
该模型基于两个基本假设：人口会以指数增长，而食物供应只能以线性增长。
本文将详细介绍Malthus 模型方程及其应用。
Malthus模型方程：Malthus模型方程可以用以下数学表达式表示：dP/dt = rP - aP^2其中，P代表人口数量，t代表时间，r代表人口的自然增长率，a 代表人口的调控系数。
该方程的含义是，人口数量的变化率等于人口的自然增长率减去人口数量与调控系数的乘积。
Malthus模型方程的理论基础：Malthus模型方程的提出基于马尔萨斯对人口与食物供应之间的关系的观察和思考。
马尔萨斯认为，人口数量呈指数增长，而食物供应只能以线性增长，因此必然会导致人口数量与食物供应之间的不平衡。
当人口数量超过食物供应能力时，将会出现人口危机，例如饥荒、疾病等。
Malthus模型方程的应用：Malthus模型方程在人口学、生态学和环境科学等领域都有重要的应用价值。
在人口学领域，Malthus模型方程可以用来预测人口的增长趋势。
通过测量人口的自然增长率和调控系数，可以估计未来人口数量的变化。
这对于政府制定人口政策、规划社会资源分配等方面具有指导意义。
在生态学领域，Malthus模型方程可以用来研究物种的增长和调控。
通过将人口数量替换为物种数量，可以分析物种数量的变化规律，预测物种灭绝和生态平衡的可能性。
这有助于保护生物多样性和维持生态系统的稳定性。
在环境科学领域，Malthus模型方程可以用来研究资源的可持续利用和环境容量的限制。
通过将人口数量替换为资源消耗量或环境负荷，可以评估资源的供需关系和环境承载能力，为可持续发展提供科学依据。
Malthus模型方程的局限性：尽管Malthus模型方程具有一定的应用价值，但也存在一些局限性。
第七章马尔萨斯（Malthus）“马尔萨斯早已死去，已经去见上帝，但是并不安分守己，他至今尚未长眠，他的幽灵仍然到处游荡。
”马尔萨斯（Thomas Robert Malthus 17661-18342），是人口论史上一个尽人皆知的名字，是一代风云人物。
他出身于英国英格兰一个乡村土绅士的家庭，其父亲，丹尼尔·马尔萨斯是卢梭和休谟的亲密朋友。
1788年毕业于剑桥大学耶稣学院（Jesus College）并被委任为一个教堂的牧师。
在社会活动方面，马尔萨斯还参与创办了有名的“政治经济学俱乐部”（1821年）和伦敦统计协会（1834年）。
主要著作：《人口论》（即《论影响社会将来进步的人口原理，反对葛德文·康多塞及其他作家思想的评论》）1798年，并于1803年又出版了一个扩充的版本；1820年《政治经济学原理》。
马尔萨斯的《人口原理》是一本“人所不读，人又咒骂”的书。
它既给马尔萨斯带来了无上光荣，也给他引来了无数的抨击，他成了当时最受欢迎、最被人议论，也是最遭污辱的人。
《人口原理》出版已经200年了，但其作品的思想和名字至今仍是尖锐的思想上和政治上论战的对象。
历史背景：两大论战，（1）济贫法，规定了不论穷人收入多少都要为其提供最低保障，如果家庭收入跌至规定水平下，这些家体内将被给予补助以弥补这一差额。
（2）谷物法：谷物法要求对进口谷物征收关税并且对英国从国外进口的谷物设置了一个最低价格。
地主赞成，斯密等人反对。
废除，导致谷物价格降低，地租减少；商业行会则赞成废除。
一、马尔萨斯的《人口论》一、背景1、葛德文和康多赛的观点葛德文（Godwen，1756-1836），英国社会哲学家，政治报刊撰稿人。
他倡导无神论、自由主义和个人主义，认为理性有能力作出正确的抉择，在人的活动中应占绝对统治地位，并以此作为自由主义的根本原则。
1清·乾隆三十一年，丙戌年。
十年之后《国富论》发表；1766年，英国发明家瓦特(1736-1819)改进了蒸汽机,拉开了第一次工业革命的序幕。
人口问题漫谈The problem of population商会141班学生：陈正豪学号：14815102引言：作为近代人口理论的奠基者和古典政治经济学家中的代表人物,英国学者马尔萨斯在人口学和经济学的形成与发展过程中都做出了杰出的贡献,引起了后世学者对其理论体系深入、持续的研究。
本文基于对马尔萨斯思想体系的理解,试图探讨和梳理在他的人口理论和他的经济学理论之间存在的内在逻辑一致性关系,并进一步分析他之所以能够成为“有效需求理论”的开拓者和奠基人的深层原因。
马尔萨斯的人口理论源于前人的思想。
它在客观上提醒了人们注意人口与生活资料比例协调，防止人口的过速增长，从而成为现代理论的开端。
马尔萨斯的人口理论在经济学上也被得到广泛的应用，可以说，也是当今人类被关注的焦点，从辩证法的角度来讲，马尔萨斯永远是超前的。
As a representative of the foundation of modern theory of population and the classical political economists, the British scholar Malthus has made outstanding contribution in the process of formation and development of demography and economics, by later scholars on the theoretical system of in-depth, sustained research. In this paper, based on the understanding of Malthus's ideological system, trying to internal logic consistency relationship exists between his theory and his theory of population economics to explore and comb, and further analysis of the reason why he can become the deep causes of "effective demand theory" and founder of the.Population theory of Malthus's previous ideas. It reminds people to pay attention to the population and the living material proportion, to prevent the over rapid growth of population, thus becomes the beginning of modern theory. Malthus's population theory in economics has also been widely used, can say, is alsothe focus of the current human concern, from the dialectical point of view, Malthus is always ahead of the.摘要：马尔萨斯人口论的内容可以简单概括为：两个公理、两个级数、两个抑制、一条规律、一个适度、三个命题、四点结论。
malthus模型方程Malthus模型方程引言Malthus模型方程是由英国经济学家托马斯·罗伯特·马尔萨斯于18世纪末提出的，用于描述人口与资源之间的关系。
该模型方程对人口增长和资源供给的平衡进行了预测，揭示了人口增长可能引发的问题和限制。
本文将详细介绍Malthus模型方程的背景、假设和应用，并探讨其对人类社会发展的启示。
背景在18世纪末，人口增长迅速成为社会关注的焦点。
马尔萨斯观察到，人口呈指数增长，而资源供给增长缓慢，因此提出了马尔萨斯模型方程。
他认为，人口将以指数方式增长，而资源供给则以线性方式增长，这种不平衡将导致人口过剩和资源匮乏的问题。
假设Malthus模型方程基于以下假设：1. 人口增长率是指数函数，即人口数量以指数方式增长。
2. 资源供给增长率是线性函数，即资源供给以固定的速度增长。
3. 人口和资源之间的平衡取决于人口增长率和资源供给增长率之间的关系。
4. 当人口增长率大于资源供给增长率时，将发生人口过剩和资源匮乏的问题。
Malthus模型方程可以表示为：dP/dt = rP - k其中，dP/dt表示人口数量随时间的变化率，r表示人口增长率，P 表示人口数量，k表示资源供给增长率。
解读与应用Malthus模型方程的解释和应用可以从以下几个方面进行探讨：1. 人口过剩与资源匮乏根据Malthus模型方程，当人口增长率大于资源供给增长率时，将导致人口过剩和资源匮乏。
这意味着人口数量超过了资源供给的可持续范围，人们将面临食物、水源、能源等资源的短缺问题。
这对人类社会的可持续发展构成了挑战，需要采取相应的措施来调整人口增长和资源利用的平衡。
2. 人口控制与资源管理Malthus模型方程的应用之一是提醒人们注意人口控制和资源管理的重要性。
通过控制人口增长率，可以避免人口过剩和资源匮乏的问题。
此外，合理利用和管理资源，提高资源利用效率，也是解决人口与资源平衡问题的关键。
马克思英文简介卡尔·海因里希·马克思,马克思主义的创始人之一，被称为全世界无产阶级和劳动人民的伟大导师。
下面是小编为你整理的马克思英文简介，希望对你有用!卡尔·海因里希·马克思简介Karl Heinrich Marx (German: Karl Heinrich Marx, May 5, 1818 - March 14, 1883), one of the founders of Marxism, the organizer and leader of the first international A great mentor for the proletariat and working people all over the world. The spiritual leader of the proletariat, the pioneer of the international communist movement.Marx is a great German thinker, politician, philosopher, economist, revolutionist and sociologist. The main works are "Capital", "Communist Manifesto" and so on.Marx founded the well-known philosophical thought as historical materialism, its greatest wish is for the individual's comprehensive and free development. Marx founded the great economic theory. In his personal terms, his great work is "Capital", and Marx established his principles of elaboration as "Critique of Political Economy". Marx believes that this is the "political economy principle" thing, this is the "essence", and later people can continue to study on this basis.Marx argues that the demise of the bourgeoisie and the victory of the proletariat are equally unavoidable. He and Engels co-founded the Marxist doctrine, is considered to guide the working people around the world to achieve the socialist and communist great ideals of the struggle of the theoretical weapons and action guide.卡尔·海因里希·马克思人物生平Early schoolMarx was born on May 5, 1818 in the German Federal Prussian kingdom Rhine province (belonging to the German Rhineland-Palatinate) Terry City, a lawyer family. His grandfather Rabbin Marc Levy was a Jewish law jurist, his father, Hirsch Karl Marx, later renamed Heinrich Marx, born in 1782, with Dutch Jewish woman Henriette Presborck married, gave birth to many children, but found in a document of the heir, only Karl Marx and three daughters Sofia, Emir, Luisa survived.In October 1830, Marx entered Trier Middle School. After graduating from high school, enter the University of Bonn, 18 years after the transfer to the University of Berlin to study the law, but most of his focus is on the philosophy and history. In 1840, the Prussian New King Frederick William IV ascended the throne, persecuted Liberal Democrats, demanding that all publications must pass a rigorous review, the university lost academic freedom, and the new king appointed the University of Berlin professor FWvon Schelling would review the , But the position of Marx's scholar in philosophy is higher than the theological position can not be accepted by the anti-Hegelian professor, so Marx will be sent to the doctoral thesis to the Saxony - Weimar - Eisenach Grand Duchy of the University of Jena ( Jena) examines doctoral qualifications. In 1841 Marx applied for a degree from the distinction between the natural philosophy of Democritus and the natural philosophy of Epicurus, and successfully received the PhD in the University of Jena from the unanimous approval of the committee. After graduation as "Rheinland" editor, met in the history of Marx thought quite famous "forest theft problem".Revolutionary careerAt the beginning of the nineteenth century, the industrialrevolution swept through Germany, which promoted the development of the economy of the country's Junke landlords, and also exacerbated the extreme poverty of the lower working people. Hunger drives the poor to pick up dead branches in the forest, picking wild fruits, and some even break the hunting grounds and ranches. Although the 1826 "Prussian Penal Code" on the unauthorized logging and theft of trees severely punished, but the incident is still increasing. And many people do so in order to be sent to the detention center to receive a prison rations, it is hunger and homeless to force people to violate the forest management regulations.In 1836, there were 150,000 people who were subject to criminal penalties in Prussia, accounting for 77 per cent of all criminal cases. In the face of this rather serious social situation, the Prussian rulers did not find the root of the problem and the solution to the problem from the social system level. Instead, it introduced a tougher bill that would pick up dead branches in the forest, Some other violations of the forest management regulations have also been upgraded to theft and criminal penalties. According to the record of the Sixth Rheinland Parliament in 1841, in October the following year, the article "Debate on the Forest Burglary Law" was written to condemn the legislature's favor of the interests of the owners of the trees, to deprive the poor of the right to pick up dead branches, To put forward their own view of forest legislation.The Prussian government was very angry at the views expressed by the Rheinische Zeitung, who immediately sent a seizure of the Rheinland newspaper to force it to stop printing. Marx angrily resigned from the editorial duties of the newspaper. Marx did not regret his own actions, on the contrary, herecognized the government's ugly. He is looking for the opportunity to continue to resolutely fight against the government.1843 "Rheinische" issue license was revoked by King Prussia, because Marx published in the newspaper criticized the Russian czar article, triggering the dissatisfaction of the Russian Tsar Nicholas I, King of Prussia received a protest after the arrest of the ban Reported that Marx was unemployed. During this period, Marx met Friedrich Engels. Engels is the owner of the factory owner is very much appreciate the idea of Marx, often money to sponsor Marx's activities and life, Marx to do learning seriously serious but life with nature, often delayed to the newspaper to the manuscript, Engels often help Marx's work and pens Some articles.married familyFebruary 14, 1814, Yanni Marx was born in Teller a famous family. Yanni Marx (February 12, 1814 - December 2, 1881, formerly known as Johanna "Jenny" · Bernard Jolie von Weston Warren (Johanna "Jenny" Bertha Julie von Westphalen) is A German sociologist, who is only a few minutes away from the home of Marx.In the late summer of 1836, at the University of Bonn, the first year of the study of Marx, back to Terrier to his girlfriend to marry him. Yanni and 18-year-old Marx agreed for life. In accordance with the custom at that time, this is unprecedented. Aristocratic birth, the daughter of Yan Ni, was recognized as the most beautiful girl and the "Queen of the Queen", many handsome aristocratic youth dumping, suitors who lack some people, no doubt, you can conclude a glory Wealthy marriage. But she is contempt for all the traditional concept of society,without the knowledge of their parents to promise to a citizen of the community, she can not predict and Marx's future life how to live. Marx thought that he could not marry Yanni in front of his father, Yan Ni's father, as a temporary adviser. So at first he could only reveal his secret to his father. He believes that his father will be in front of the parents of Jenny for a successful pro-ready for a variety of preparations.In October 1836, Marx moved from the University of Bonn at home near the University of Berlin at home, which meant that they were to be loyal to each other for a long time. In Berlin, because of the feelings of the mind and "love" and the love and the suspense and anxiety, once influenced the Marx wholeheartedly into learning. He had told his father frankly that he had "fallen into the real tranquility" because he was far from the Moose Valley and was far from his "infinite beauty of Jenny". Troubled him is not a guessing heart, because he had never had the slightest doubt on the love of Jenny, but because of the thought of her and long years in the long years of separation, so that he felt very heavy mood.So, 18-year-old Marx wrote writing poetry, poems to express their feelings and feelings. Most of Marx's poems are singing Yanni and pouring himself into her, but there are many of them that express their own thoughts and aspirations and desire to make a difference.On April 15, 1841, Marx received a Ph.D. degree in advance. Young philosopher had just arrived in Trill, hastened to his most beloved home, the doctoral thesis personally sent to the hands of Jenny's father. Yan Ni and Marx after years of separation, had intended to immediately get married. But there is a doctoral thesis and can not be used as a basis for subsistence, so he andYanni had to cancel the idea of marriage, continue to wait. Beginning in April 1842, Marx began writing for the "Rheinische Zeitung". In October 1842, the shareholders of the Rheinland newspaper appointed Marx as editor, and in March 1843, Marx was forced to withdraw from the editorial board of the Rheinburger. And then with Arnold Luger in consultation with the work on the joint publication of the plan. Then on June 19, 1843 he went to Croznach (Yanni after her father died in March 1842 and his mother moved to this place), and waited for him for seven years, was born 1814 born in the German aristocratic (Baron) family of Jenny von Westphalia married. From their private agreement to life together, Yanni waited for a long seven years. In the past seven years, in addition to her had a few times with the fiance of Marx had a few times together, only from the distant with their thoughts and letters to accompany him. She wrote in a letter to Marx: "How brilliant is your image in front of me, how magnificent it is! How far is it from my heart that you can always be by my side, my heart, How is the joy of joy for your beating, my heart, what is anxious to follow you on the way you follow ... ... everywhere I am with you, walking in front of you, but also with you I hope that I can fill the road where you are going, and clear all the obstacles that will stop you from moving forward. "At the same time, she has to struggle with her aristocratic relatives.After the wedding, Marx and Jenny then set off a short wedding trip. In the autumn of 1843, the young Marx and his wife set foot on the exile journey to Paris. During this period he proceeded to study political economy, the French social movement and the French history, and eventually led to its becoming a communist.At the end of October 1843, Marx and Yanni came to Paristogether, and they came to Luga for two months earlier to organize and publish the magazine "German and French Yearbook". At this point, they opened a life full of hardship and self-sacrifice.Because of Marx's outstanding contribution to the cause of communism and to the landlords and bourgeoisians ruthlessly expose and criticize, so that all the conservative forces to exclude him, expelled him. He had to carry a small home around the transfer of their difficulties sometimes difficult to imagine the point of life. At the end of March 1850, with the death of London in London, Jenny wrote a letter to a friend Joseph Weiderme, depicting her life at that time: "Because here the nurse is too high wages, although I often have a bad chest , But still their own children to feed the poor children from my body sucked so much sadness and anxiety, so he has been frail, day and night to endure severe pain.He has been born since the night, Can fall asleep for two or three hours, and recently with violent ventilation, so the child struggles all day on the death line, because of these pains, he desperately sucked milk, so that my breasts were injured and cracked; blood often flow One day, I was holding him sitting, suddenly the female landlord came, I paid her five pounds of arrears, but we have no money at hand.Then came the two bailiffs, Will be my meager home - bed clothes and so on - and even my poor children's cradle and the better toys are seized. They threatened me to say two hours later to all West and I have to sleep with the shivering children sleep light board. "Marx and Yanni symbiotic four women and two children, for the above reasons, only three daughters (ie eldest daughter Jenny Marx, second daughter Laura Marx, Three daughter Elena Marx) grew up [at that time thanks to Helen de Mute Lin Heng, Yanni if thereis no such a loyal assistant, it is difficult to imagine her and her children later how to go down] TheIn this situation, Yan Ni is still deeply in love with Marx. In addition to her mother and housewife's responsibility, in addition to worry about the daily life, but also take on a lot of other work. Yanni is an indispensable secretary to Marx, and almost all manuscripts of Marx - most of which are hard to recognize - must be clearly written by her before being sent to a printing or publishing house.And publishers and editorial office negotiations, some cumbersome procedures, it is difficult to deal with the affairs, must write the situation, many by her agent. Marx was not the kind of person who was easily present in his mouth, but when Yanni left him for a few months because of his mother's death, he wrote in her letter: "Deep passion Because of the close proximity of its object The performance of the daily habits, and in the next resort under the influence of magic will grow up and re-have its inherent strength of my love is the case.As long as we are forced for the space, I immediately understand that time in my Love is like a sun and rain in the plant - to grow.I love you, as long as you stay away from me, it will show its true colors, like a giant face. In this love focused on all my energy and all the feelings. ... ... if I can put your gentle and pure heart close to his heart, I will be silent, not for a cry. I can not kiss you with lips, but have to resort to the text, to the text to convey the kiss. "The love of Marx and Jenny's dusk is more intense. 1880, may suffer from liver cancer, she with amazing restraint ability, endured great pain. In this scared of the years, Marx took care of his wife, not left or right in order to make her happy, Marx in 1881in July and August, accompanied her to France to see the eldest daughter and a few grandson. In the fall of 1881, due to anxious and insomnia, excessive physical exertion, Marx was ill. He is suffering from pneumonia, life is dangerous, but he still can not forget the yanni. Their little daughter talked about her parents' life, "I will never forget the scene of the morning." He felt that he was much better and had gone to the mother's room. Young people, like a pair of young men and women who are beginning to live together, are not like a sick man and a dying old woman, unlike a man who is about to farewell.December 2, 1881, Yan Ni sleepy. This is the biggest blow that Marx has never suffered. On the day of his death, Engels said: "Moore (from India, who describes the dark skin) is also dead." In the next few months, he accepted the doctor's advice, to the mild climate to rest. But no matter where they can not forget Yan Ni, could not stop grief. He wrote to the best friend, "By the way, you know that few people are more disgusted than I am sad, but if I do not admit that I miss my wife at all times - she is the best of my life Everything is inseparable - that 's how I'm lying. "How awesome these words are.January 11, 1883, came the sudden death of the eldest daughter of the bad news, Marx's condition increased. At noon on March 14, 1883, Marx resigned peacefully. On March 17, 1883, Marx was buried next to the grave of Haget's Cemetery, Jenny.Great friendshipIn 1844 September, Engels visited Paris, the two sides began to study the scientific socialism, and formed a deep friendship. Marx wrote the "Economic Philosophy Manuscript", the manuscript until 1933 was discovered and published, known as the "1844 economic philosophy manuscript." In 1845, Marxparticipated in the preparation of "forward magazine", in which the authoritarianism of Germany made a sharp criticism. The Prussian government was very dissatisfied and asked the French government to expel Marx. In the autumn of the same year, Marx was beaten by the French government rogue, deported, forced to come to Brussels, Belgium. In December 1845, Marx declared his departure from Prussian nationality.And then Engels completed with the "German ideology." The book criticizes Hegel's dialectics and analyzes the incompleteness of Feuerbach materialism, which for the first time systematically expounded the historical materialism they founded and made clear that the proletariat seized power The historical task laid the initial theoretical foundation for socialism from fantasy to science. At the beginning of 1846, Marx and Engels established the Brussels Communist Communications Commission. In 1847, Marx and Engels were invited to the righteous alliance. In June 1847, the reorganization of the alliance and renamed the communist alliance, Marx and Engels drafted the alliance program "Communist Manifesto." Since then the revolution of 1848 swept through Europe, also spread to Belgium. In March 1848, Marx was expelled by the Belgian authorities. At the invitation of the French new government, the Marxist couple returned to Paris, France, Engels arrived in Paris.In April 1848, under the auspices of the German proletariat, Marx and Engels returned to Prussia Cologne and founded the "New Rheinische Zeitung". Followed by almost all editors or judicial arrests, or deportation. On May 16, 1849, Marx received a deportation order from the Prussian authorities. May 19, published in the red ink published "New Rheinische" the last one No. 301 published. In early June, Marx came to Paris. He wasforced to choose or be imprisoned in Brittany, France, or was forced to expel again. In August, Marx was expelled from the French government to London, England. From the Prussian stationed in the British spy report that Marx seems to never scratch the beard, Marx is still in the UK by the Prussian government to monitor.In London, Marx spent the most difficult day of his life. In five years, Marx because of economic and debt problems, mental anxiety, suffering from the poor mood of the disease, four children in three deaths. But during this period, Marx wrote his most important work - "Capital" (Volume 1). Marx is thought to be rich, economically poor and poor, and the great economist who has a thorough study of the capitalist economy is itself poor, and his life is almost in poverty. Marx did not have a fixed job, and the family's economic origins was mainly due to his extremely unstable and extremely meager royalties, coupled with the persecution and blockade of the bourgeoisie, which had always plagued the Marxist family with hunger and survival. To death. In the life of the displaced, he is often empty, clean clothes, struggling in the dilemma of the struggle. If not Engels in economic long-term selfless assistance, Marx can not engage in leading the international proletarian movement and concentrate on theoretical creation.From the letter to Engels on February 27, 1852, we saw the plight of the world famous theorist, Marx wrote: "A week I have reached the point of great pain: because the coat into the pawn shop, I can not And then go out, because not to credit, I can not eat meat. "Soon wrote to Engels talked:" My wife is sick, little Yanni disease, Linheng suffering from a nerve heat, the doctor I can not please , And now can not please, because there is nomoney to buy medicine. Eight to ten days since the home to eat bread and potatoes, whether today can get these, but also a problem. "Hungry poverty and housework trivia, troubled Marx, he Feeling angry and irritable, unable to concentrate and wisdom to carry out theoretical creation. On the plight of Marx, Engels as their own difficulties. "I will send you five pounds in early February," he wrote in a letter to Marx. "You can receive this number every month, even if I do not have a debt to the new year." ... of course, you do not because I promised to pay 5 pounds a month in the difficult time no longer write to me to ask for money, because as long as possible, I must do so. "At this time Engels in the door - Engels The company is just an ordinary small clerk, the income is very low.Engels later made the company's care, the monthly salary has improved. From 1860 onwards, the support of Marx increased to 10 pounds per month, but also often "other" to give some funding. From 1851 to 1869, Marx received a total of £ 3121 remittances of Engels. For Engels at the time, it was a matter of course. It is precisely because of the generosity of Engels, so that Marx relentlessly survived, to be engaged in long-term scientific writings, writing for the "capital" for extensive and in-depth economic research. Just as Lenin said: "If not Engels sacrificed himself and continue to give funding, Marx not only can not be written as" capital "and is bound to die from poverty." Engels's selfless dedication, Marx was very moved, and very disturbed, in 1867 Wrote to Engels' letter: "frankly told you that my conscience is often as heavy as the dream of the devil, because your excellence is mainly for me to waste in business, only to let them deserted, and But also to share all my trivial worries. "This is the words of Marx's heart. The concern of Marx and his family life,Engels is meticulous. Marx's life is suffering from hardships, whenever Marx suffered setbacks and blows, thoughts and feelings with grief and depression, Engels always think of ways to soothe, he has become a Marx to avoid the storm of life in the harbor, Marx arrived in this harbor, Quiet and happy. Poverty and suffering have claimed the four children of Marx.In April 1855, Marx's favorite son, Edgar, died, which gave Marx a heavy blow, and he felt he could not support it. In the letter to Engels, Marx talked about the infinite sadness: "In these days, I have been able to bear all this terrible pain, because always miss you, miss your friendship, always hope that the two of us also To make some meaningful things together in the world. "Engels brought the couple to Manchester, in Engels's careful arrangements and care, the Marx and the couple spent the most difficult moments of life. Engels is a "supernumerary" member of Marx's house, and every time he goes to Marx's house, the whole family is as happy as the holidays, and Marx's daughters see Engels as "the second father". Of course, the Marx family of Engels on the health concerns, it is worrying. In 1857 July, when Engels was sick, Marx wrote a letter of comfort: "Dear Engels, you can believe that no matter how unfortunate we are, my wife and I are more concerned about your recent health situation than our own. "Two old comrades in the work of different places, often communicate with each other ideas, without reservation to talk about personal life and political life in the emotions, in their more than 1,000 communications, we see the two comrades Deep Yi Benedict, a few days can not get each other letters, each other to each other up. In his letter to Engels, Marx wrote, "Dear Engels, are you crying or laughing, sleeping or awake? In the last three weeks, I sent a variety of letters to Manchester, but Did notreceive a reply, but I believe are sent to. "Similarly, if you can not hear a few days of Marx's audio, Engels will be issued" even the gun "like questioning" old Moore, old Moore, big beard old Do you have anything to do? What are you doing, what are you doing? Are you sick or falling into the abyss of your political economy? "They are doing nothing Said, nothing to talk about. And the friendship between Engels, Marx made a high degree of evaluation, February 20, 1866 to Engels in the letter said: "This friendship between us is how happy, you have to know that I am any relationship Have not made such a high evaluation. "Engels and Marx's noble friendship, for the human to establish a brilliant example, the two great great friendship to tell the world: based on common faith and the pursuit of the foundation of friendship, is evergreen, unbreakable.Old age and deathSeptember 28, 1864, Marx participated in the first international congress, was elected to the leadership committee. He drafted the Declaration on the Establishment of the International, the Provisional Constitution and other important documents. September 14, 1867, "Capital" first volume published. After the two volumes for the death of Marx, by Engels finishing its legacy, respectively, in 1885, published in 1894. In October 1870 Marx reunited with Engels in London. As many countries were expelled and exiled everywhere, he claimed to be "the world's citizens".On December 2, 1881, Yanni Marx died. March 14, 1883 at 2:33 pm, the great thinker of Marx died in London, at the age of 65 years old. And later with Yanni buried in the northern suburbs of London Haget cemetery. Engels published the tomb speech, about 20 people attended the funeral.。
马尔萨斯定律
马尔萨斯定律，又称人口论，是由英国经济学家马尔萨斯于1798年提出的一种人口增长理论。
该定律认为，人口的增长速度远远超过食物和资源供应的速度，因此会出现人口过剩和资源匮乏的现象。
马尔萨斯定律的核心观点是，人口的增长是呈指数级别增长的，而食物和资源的增长只是呈线性增长，因此在某个时刻，人口数量将会超过资源的供应能力，从而导致资源的匮乏和人口的死亡。
马尔萨斯认为，人口增长的主要原因是人类的性欲和生育欲望，而食物和资源的供应则受限于自然界的生产力和技术水平。
因此，他提出了一系列限制人口增长的措施，包括婚姻晚婚、节制生育、戒烟戒酒等。
马尔萨斯定律在当时引起了广泛的关注和争议，一些人认为这是对人口增长的恐慌和过度悲观，而另一些人则认为这是一个引起人们警惕的重要警示。
如今，随着人类社会的发展和技术的进步，马尔萨斯定律的适用性已经受到了质疑，但其对人口增长和资源管理方面的研究仍然具有重要的参考价值。
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马尔萨斯定律马尔萨斯定律，又称人口论，是由英国经济学家马尔萨斯在18世纪末提出的一种人口增长理论。
该理论认为，人口的增长速度远远超过了资源的增长速度，从而导致人口与资源之间的矛盾不断加剧，最终将引发人口灾难。
马尔萨斯定律的核心观点是，人口的增长呈几何级数增长，而资源的增长只是以算术级数增长。
这种不平衡的增长速度必然导致资源的供给无法满足人口的需求，从而引发人口危机。
马尔萨斯认为，人口增长受到生育率和死亡率的影响，而资源的增长则受到生产力和科技水平的制约。
根据马尔萨斯的理论，当人口增长过快时，资源供给将无法跟上人口的需求，从而导致资源匮乏、粮食短缺、环境恶化等问题。
为了解决这一问题，马尔萨斯提出了两种调节人口增长的办法，即“正性检查”和“预防性检查”。
所谓“正性检查”，就是指通过战争、疾病和饥荒等方式来限制人口的增长。
马尔萨斯认为，这种方式是一种自然选择的过程，通过消除一部分人口，可以减少人口与资源之间的矛盾。
然而，这种方法并非长久之计，因为它无法解决根本问题，且会带来人道主义灾难。
相对于“正性检查”，“预防性检查”则更加人道和可持续。
这种方式主要通过控制生育率来实现人口的调控。
马尔萨斯主张通过道德约束和教育提高人们的生育观念，同时鼓励晚婚晚育和节育等措施，以控制人口的增长速度，从而使人口与资源达到相对平衡。
然而，马尔萨斯定律在现实中的适用性受到了一些质疑。
首先，科技的进步和生产力的提高使得资源的供给能够更好地满足人口的需求，从而缓解了人口与资源之间的矛盾。
其次，社会经济的发展和人口结构的变化也会影响人口增长的速度和趋势。
因此，马尔萨斯定律并不是一个全面准确的理论，而是一种以人口与资源关系为基础的思考方式。
然而，尽管马尔萨斯定律存在一定的局限性，但人口与资源之间的关系仍然是一个重要的问题。
随着全球人口的不断增长和资源的有限性，我们仍然需要关注人口增长对资源的影响，以及如何通过可持续发展的方式来实现人口与资源的平衡。
马尔萨斯人口原理的基本内容马尔萨斯人口原理，又称马尔萨斯人口理论，是由英国经济学家托马斯·罗伯特·马尔萨斯在18世纪末19世纪初提出的一种人口理论。
该理论主要阐述了人口增长与资源供给之间的关系，对于人口问题的研究具有重要意义。
以下将从马尔萨斯人口原理的基本内容、论证过程和现实意义三个方面进行阐述。
首先，马尔萨斯人口原理的基本内容是：人口增长的速度大于可供给的资源增长速度，从而导致人口过剩和贫困的问题。
马尔萨斯认为，人口的生长有其内在的规律，而且是以几何级数增长的，即每一代人将要再生产出多于他们的数量。
而资源的增长则只是以算术级数增长，即按照相等的数额来增加。
因此，人口会以迅猛的速度增长，而资源供给的增长则相对缓慢。
当人口超过了资源的承载能力时，就会出现人口过剩，引发贫困、饥荒、战争和疾病等群体性问题，以实现人口数量和资源供给之间的动态平衡。
其次，马尔萨斯人口原理的论证过程可以概括为三个要点。
第一，马尔萨斯提出了人口有一个内在的生长规律，即人口具有生物本性，趋于以乘法形式增长。
第二，资源的增长存在一定的限制，即资源的提供是有限的，无法以与人口乘法增长的速度同步。
第三，由于人口自然增长的速度远远超过资源供给的速度，一旦人口超过了资源的承载能力，就会出现社会问题。
因此，人口增长会引发资源短缺、饥荒、贫困和社会动荡等问题。
最后，马尔萨斯人口原理的现实意义是启示了人们对人口问题的思考和研究。
首先，它提醒人们应关注资源的可持续利用和环境保护，避免资源过度开发和浪费。
其次，它指导人们重视人口政策的制定和实施，为人口控制提供理论支持。
尤其在发展中国家，人口增长过于迅速，人口控制成为实现可持续发展的重要措施。
此外，马尔萨斯人口原理还引起了一系列人口与经济、人口与社会、人口与环境等领域的研究，成为人口学、社会学、经济学等学科的理论基础，推动了人口学和社会科学的发展。
总之，马尔萨斯人口原理是对人口增长与资源供给之间关系的一种理论描述。
《人口原理》附：人口原理概观〔英〕马尔萨斯著朱泱、胡企林、朱和中译2009年7月版商务印书馆评马尔萨斯《人口原理》第一版李宗正书的本质：马尔萨斯的《人口原理》是从出版直到现在二百多年来在社会科学领域争议最多的一部著作。
这本书第一版的书名《人口原理》，人口对社会未来进步的影响，兼评葛德文先生、孔多塞先生和其他著述家的推测》，明白地说明了它一出版就是论战性的著作，是为攻击当时风行一时的社会改革论和空想社会主义而写作的。
此后，关于人口理论的论争一直不断。
传播到中国的情况：在中国远者不说，在20世纪1初，《东方杂志》、商务印书馆就发表过不少作品，介绍马尔萨斯的人口思想，到30年代，论述马尔萨斯人口思想和中国人口问题的著作就更多了。
1949年，毛泽东同志发表著名的《唯心史观的破产》一文，继承马克思的观点，否认马尔萨斯主义，此后我国学术界对马尔萨斯主义基本上采取批判的态度。
1958年，马寅初先生的《新人口论》遭受错误的攻击与批判，于是在全国掀起了批判马尔萨斯主义的热潮。
1978年后对马寅初先生的错误批判得到了平反。
大概是物极必反，在马寅初先生的《新人口论》得到正确评价的同时，国内学术界不少人提出要重新评价马尔萨斯主义，有的全部肯定马尔萨斯主义，有的主张一分为二，认为马尔萨斯的《人口原理》包含部分真理，甚至认为我国计划生育的某些做法是起源于马尔萨斯。
当然也有一些人坚持马克思主义观点，仍然对马尔萨斯的人口论持批判态度。
出版情况：事实上，马尔萨斯的《人口原理》译成中文时间较晚，出版的数量也很少。
1933年世界书局才出版郭大力同志译的《人口论》，印数很少。
1959年为了批判马尔萨斯主义，商务印书馆征得郭大力同志的同意，将旧译重印，印数也仅1500册。
1961年又出版了马尔萨斯《人口原理》的第二版。
不论对马尔萨斯主义采取批判的态度，抑或加以肯定，我认为首先要认真阅读原著，进行实事求是的研究，然后才能准确地进行评论。
现在朱泱和胡企林二位同志将马尔萨斯的《人口原理》重新翻译出版，使更多的人能够读到马尔萨斯的原著，这对我国学术界和计划生育工作者将大有裨益。
malthus人口模型常微分方程在数学建模中的应用这里介绍几个典型的用微分方程建立数学模型的例子. 一、人口预测模型由于资源的有限性,当今世界各国都注意有计划地控制人口的增长,为了得到人口预测模型,必须首先搞清影响人口增长的因素,而影响人口增长的因素很多,如人口的自然出生率、人口的自然死亡率、人口的迁移、自然灾害、战争等诸多因素,如果一开始就把所有因素都考虑进去，则无从下手.因此,先把问题简化,建立比较粗糙的模型,再逐步修改,得到较完善的模型.例1（马尔萨斯（Malthus ）模型）英国人口统计学家马尔萨斯（1766—1834）在担任牧师期间,查看了教堂100多年人口出生统计资料,发现人口出生率是一个常数,于1789年在《人口原理》一书中提出了闻名于世的马尔萨斯人口模型,他的基本假设是：在人口自然增长过程中,净相对增长（出生率与死亡率之差）是常数,即单位时间内人口的增长量与人口成正比,比例系数设为r ,在此假设下,推导并求解人口随时间变化的数学模型.解设时刻t 的人口为)(t N ,把)(t N 当作连续、可微函数处理（因人口总数很大,可近似地这样处理,此乃离散变量连续化处理）,据马尔萨斯的假设,在t 到t t ?+时间段内,人口的增长量为t t rN t N t t N ?=-?+)()()(,并设0t t =时刻的人口为0N ,于是==．，00)(d d N t N rN t N这就是马尔萨斯人口模型,用分离变量法易求出其解为)(00e )(t t r N t N -=,此式表明人口以指数规律随时间无限增长.模型检验：据估计1961年地球上的人口总数为91006.3?,而在以后7年中,人口总数以每年2%的速度增长,这样19610=t ,901006.3?=N ,02.0=r ,于是)1961(02.09e1006.3)(-?=t t N .这个公式非常准确地反映了在1700—1961年间世界人口总数.因为,这期间地球上的人口大约每35年翻一番,而上式断定34.6年增加一倍（请读者证明这一点）．但是,后来人们以美国人口为例,用马尔萨斯模型计算结果与人口资料比较,却发现有很大的差异,尤其是在用此模型预测较遥远的未来地球人口总数时,发现更令人不可思议的问题,如按此模型计算,到2670年,地球上将有36 000亿人口.如果地球表面全是陆地（事实上,地球表面还有80%被水覆盖）,我们也只得互相踩着肩膀站成两层了,这是非常荒谬的,因此,这一模型应该修改.例2（逻辑Logistic 模型）马尔萨斯模型为什么不能预测未来的人口呢？这主要是地球上的各种资源只能供一定数量的人生活,随着人口的增加,自然资源环境条件等因素对人口增长的限制作用越来越显著,如果当人口较少时,人口的自然增长率可以看作常数的话,那么当人口增加到一定数量以后,这个增长率就要随人口的增加而减小.因此,应对马尔萨斯模型中关于净增长率为常数的假设进行修改.1838年,荷兰生物数学家韦尔侯斯特(Verhulst)引入常数m N ,用来表示自然环境条件所能容许的最大人口数（一般说来,一个国家工业化程度越高,它的生活空间就越大,食物就越多,从而m N 就越大）,并假设将增长率等于-m N t N r )(1,即净增长率随着)(t N 的增加而减小,当m N t N→)(时,净增长率趋于零,按此假定建立人口预测模型.解由韦尔侯斯特假定,马尔萨斯模型应改为00d 1d ()m N N r N t N N t N=-? ?????=?，，上式就是逻辑模型,该方程可分离变量,其解为,)(00e11)(t t r m mN N N t N ---+=.下面,我们对模型作一简要分析.（1）当∞→t ,m N t N →)(,即无论人口的初值如何,人口总数趋向于极限值m N ；（2）当m N N <<0时,01d d >-=N N N r t N m ,这说明)(t N 是时间t 的单调递增函数；（3）由于N N N N N r t N m m ???? ??-???? ??-=211d d 222,所以当2m N N <时,0d d 22>t N ,t N d d 单增；当2m N N >时,0d d 22<t< bdsfid="105" p=""></t<>N,t N d d 单减,即人口增长率t N d d 由增变减,在2m N 处最大,也就是说在人口总数达到极限值一半以前是加速生长期,过这一点后,生长的速率逐渐变小,并且迟早会达到零,这是减速生长期；（4）用该模型检验美国从1790年到1950年的人口,发现模型计算的结果与实际人口在1930年以前都非常吻合,自从1930年以后,误差愈来愈大,一个明显的原因是在20世纪60年代美国的实际人口数已经突破了20世纪初所设的极限人口.由此可见该模型的缺点之一是m N 不易确定,事实上,随着一个国家经济的腾飞,它所拥有的食物就越丰富, m N 的值也就越大；(5）用逻辑模型来预测世界未来人口总数.某生物学家估计,029.0=r ,又当人口总数为91006.3?时,人口每年以2%的速率增长,由逻辑模型得-=m N N r t N N 1d d 1, 即-=m N 91006.31029.002.0, 从而得 91086.9?=m N ,即世界人口总数极限值近100亿.值得说明的是：人也是一种生物,因此,上面关于人口模型的讨论,原则上也可以用于在自然环境下单一物种生存着的其他生物,如森林中的树木、池塘中的鱼等,逻辑模型有着广泛的应用.二、市场价格模型对于纯粹的市场经济来说,商品市场价格取决于市场供需之间的关系,市场价格能促使商品的供给与需求相等(这样的价格称为(静态)均衡价格).也就是说,如果不考虑商品价格形成的动态过程,那么商品的市场价格应能保证市场的供需平衡,但是,实际的市场价格不会恰好等于均衡价格,而且价格也不会是静态的,应是随时间不断变化的动态过程.例3 试建立描述市场价格形成的动态过程的数学模型解假设在某一时刻t ,商品的价格为)(t p ,它与该商品的均衡价格间有差别,此时,存在供需差,此供需差促使价格变动.对新的价格,又有新的供需差,如此不断调节,就构成市场价格形成的动态过程,假设价格)(t p 的变化率tpd d 与需求和供给之差成正比,并记),(r p f 为需求函数,)(p g 为供给函数（r 为参数）,于是()()[]??=-=，，0)0(,d d p p p g r p f tpα 其中0p 为商品在0=t 时刻的价格,α为正常数.若设b ap r p f +-=),(,d cp p g +=)(,则上式变为=-++-=，，0)0()()(d d p p d b p c a t pαα ① 其中d c b a ,,,均为正常数,其解为ca db c a d b p t p t c a +-+??? ??+--=+-)(0e)(α.下面对所得结果进行讨论:（1）设p 为静态均衡价格 ,则其应满足0)(),(=-p g r p f ,即d p c b p a +=+-,于是得ca db p +-=,从而价格函数)(t p 可写为 p p p t p t c a +-=+-)(0e )()(α , 令+∞→t ,取极限得p t p t =+∞→)(lim这说明,市场价格逐步趋于均衡价格.又若初始价格p p =0,则动态价格就维持在均衡价格p 上,整个动态过程就化为静态过程；（2）由于t c a c a p p tp)(0e )()(d d +-+-=αα , 所以,当p p >0时,0d d <t p="" ,)(t="" 单调下降向p="" 靠拢；当p="" <0时,="" 0d="" d="" bdsfid="167">t。
