Equilibrium price. Equilibrium allocation: x=xi(p,p·w2), Note: A p* for any >0 is also an equilibrium price. Offer curve: (p)(p, p. w;). The equilibrium is the intersection point of the offer curves. Excess demand function:

(1)i(p, u) is zero homogeneous in p (2) substitution matrix: Dpi(p, u)<0 (3)symmetric cross-price effects: 23i(p 2=2z(p, u) (4) decreasing:=n≤0

Production Plans with Multiple Outputs Lety≡(m,,…,ym) be a net output vector, YArn be a convex set,G:Y→R be twice differentiable Production possibility set:{y∈Y|G(y)≤0} Assumption 1.1. Gy (y)>0, Vi,yEY. Proposition 1. 12. Production frontier yEY G(y)=0 contains technologically efficient production plans Definition 1.1. Marginal rate of transformation

Thus, to find Nash equilibria in IN=N, A(Si)), uin, we use the conditions: for ach player i (1)he is indifferent among all strategies in St,and (2)any strategy in St is at least as good as any strategy in S Example 3.7.(Meeting in an Airport ). Mr Wang and Ms Yang are to meet in an irport. However, they do not know whether they are to meet at door a or door B. The payoffs are specified in the following

Optimization See Sydsaeter(2005, Chapters 2, 3)and Chiang(1984, Chapters 9, 11, 12 and 21) Positive definite matrix Definite matrices are directly related to optimization. A symmetric matrix A is positive semi- definite(A≥0) if rAr≥0,Vx; positive definite(A>0)

then there exists AE R\ such that (Kuhn-Tucker condition) G(s') =0 and 1. Lagrange Method for Constrained Optimization FOC: D.L(,\)=0. The following classical theorem is from Takayama(1993, p.114). Theorem A-4 (Sufficieney). Let f and, i= ,..m, be quasi-concave, where Theorem A-1. (Lagrange). For f: and G\\, consider the following G=(.8 ) Let r' satisfy the Kuhn-Tucker condition and the FOC for (A.2). Then, x' problem is a global maximum point if max f() (1)Df(x') =0, and f is locally twice continuously differentiable,or

第一讲导论 (一)企业的性质 1、从道德人到经济人 2、经济学的若干基本前提(假设) 3、企业的性质:传统观点 4、企业的性质:基于经济人的讨论

就像读写能力一样,统计能力有一天会成为 每一个公民必备的能力,。” H.G. Wells 统计推断: 根据从总体中抽取的样本信息来得出总体情况 的方法。 点估让:估计一个未知总体的参数。 置信区间佔计:找到以预先指定概率包含参数 的区间。 假设检验:对一个未知的总体参数的假设的检 验

幻灯片主要由 Elizabeth newton(麻省理工学院) 制作,其中一部分由 Jacqueline Telford(约翰斯 霍普金斯大学)制作

图形的优越性 “使复杂的思想能够显示得清楚、准确、有 效。” 显示数据。 让你考虑实质而不是方法、图形设计或者其 它的。 在很小的空间中有很多的数字。 使大的数据集有条理。 使数据的不同部分显示得更清楚