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哈罗德·霍特林（Harold Hotelling）

哈罗德·霍特林（Harold Hotelling,1895—1973）:统计学界、经济学界、数学界公认大师

　　哈罗德·霍特林1895年9月29日出生在美国明尼苏达的福达，他原本在华盛顿大学主修新闻学，但后来转向数学作拓扑领域之相关研究，并于1924年获得博士学位。霍特林起初服务于斯坦福大学，他对统计理论最重要的贡献是多变量分析及或然率，最重要的论文则是 《The generalization of Student's ratio》，即目前著称的霍特林T方(Hotelling's T2 )。 他在主成分分析 (principal components analysis)和正准相关(canonical correlations)的发展上也扮演重要的角色。 1972年他被选为美国国家科学研究院的院士， 1973年被选为罗马 Academia Nazionale dei Lincei。 1973年12月26日，卒于北卡罗来纳的教堂山。

　　埃奇沃思模型的说明描述了只有两个卖者的市场中的不稳定因素。霍特林在1929年对这一观点提出挑战；提出霍特林模型，他认为价格或产出的不稳定并非是寡头垄断的基本特征。霍特林模型显然是对埃奇沃思和伯特兰的批评。霍特林不同意消费者由一个卖者突然转向另一个卖者是市场的特征这一观点。他预期价格的下降实际上吸引不了多少消费者。因而他认为，只要消费者逐渐转向竞争者，市场就仍将保持稳定。

　　1929年霍特林提出了空间竞争理论，把产品差异划分为空间中直线段上的不同点，从而使产品差异具有可检验的经验含意。其中有名的例子是霍特林的卖冰淇淋理论：在一平直的海滩上有两个冰淇淋小贩。假设二者的生产成本均为零，产品的质量都是一样，顾客都平均分布在线型市场上，他们的品味均一致，他们对产品需求的价格弹性等于零，购买者都会从最近的供给者购买。

　　1931年哈罗德?霍特林发表了《可耗尽资源的经济学》。这被认为是资源经济学产生的标志。

　　Harold Hotelling's articles on econoimcs were few, but his contributions were profound enough to make him one of the "leaders" of the Paretian School, the "resurrectors" the Marginalist Revolution in the 1930s.

　　Hotelling's 1929 paper on the stability of competition introduced the notion of spatial competition in a duopoly situation. The solution to this problem was in fact an early statement of a very well-known game-theoretic solution concept: the subgame-perfect equilibrium (as later defined by Selten.).　 His 1929 paper on depreciation provided its modern definition as the decline in discounted future values.　 In 1931, he advanced another technique into economics, the calculus of variations, into a now famous analysis of resource exhaustion.　　

　　His 1932 piece reworked the theory of production into a choice-theoretic framework based on profit-maximization, setting the foundations of the modern Neoclassical approach.　His 1935 derivation of demand was actually simultaneous with that of Hicks and Allen.　 His famous 1938 presidential address to the Econometric Society introduced the "marginal cost pricing" equilibrium as a general welfare proposition: roughly, that economic efficiency is achieved if every good is produced and priced at marginal cost.　This would be the foundation of the Fundamental Welfare Theorems of Paretian general equilibrium theory.　It was also here that he introduced his famous "two-part" tariff as an alternative solution in situations of natural monopoly.

　　Although appointed as a professor of economics at Columbia (oddly, one of the strongholds of the American Institutionalist school), one can argue that Harold Hotelling was a statistician first, economist second.　 His work in mathematical statistics included his famous 1931 paper on the Student's t distribution for hypothesis testing, in which he laid out what has since been called "confidence intervals".　At Columbia, he ensured that the economics students under him were well immersed in statistical theory.　He trained both Kenneth Arrow and Milton Friedman, and was instrumental in the appointment of Abraham Wald.

• "A General Mathematical Theory of Depreciation", 1925, Journal of ASA.
• "Differential Equations Subject to Error", 1927, Journal of ASA
• "Applications of the Theory of Error to the Interpretation of Trends", with H. Working, 1929, Journal of ASA.
• "Stability in Competition", 1929, EJ.
• "The Economics of Exhaustible Resources", 1931, JPE.
• "The Generalization of Student's Ratio", 1931, Annals of Mathematical Statistics.
• "Edgeworth's Taxation Paradox and the Nature of Supply and Demand Functions", 1932, JPE.
• "Analysis of a Complex of Statistical Variables with Principal Components",1933, J of Educational Psychology
• "Demand Functions with Limited Budgets", 1935, Econometrica.
• "Relation Between Two Sets of Variates", 1936, Biometrika.
• "The General Welfare in Relation to Problems of Taxation and of Railway and Utility Rates", 1938, Econometrica.