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

Defining the Field-what do you think that economics is? (1) Subject Matter Based Definitions (2)UItra-pragmatic definitions( what economists do) (3)Methodology Based Definitions This much is certain a. Economics pretty much includes all topics related to human society

Social welfare function W: Rn-R gives social utility W(u1, u2,. un ). W is strictly increasing is socially optimal if it solves max Wu(a1), u2(a2),., un(n) st>Tis>w Proposition 1.29. If is SO, it is PO. I Proposition 1. 30. Suppose that preferences are continuous, strictly monotonic, and strictly convex. Then, for any PO allocation x* with >>0,v i, there exist ai

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

Then =1-91=1(3+:2)(3+2n 可=-1-3)=1(4-+2)(1-2+a With 1 0 O: Thus, in equilibrium, we must have ai=.2. In fact, the two firms must sit in the middle By Proposition 2.1, Pi=p?=c Discussion

第十二章排污权交易 第一节排污权交易的主要思想 第二节排污权交易的微观效应和宏观效应 第三节排污权交易的主要特点 第四节实行排污权交易的条件 第五节美国的排污权交易政策 第六节中国的排污权交易

1.使用范围:第一章导论 2.要考核的知识点:影响供求的因素; 均衡价格的决定及其变动趋势;

1.使用范围:第一章导论 2.要考核的知识点:供求理论; 影响需求的因素; 需求弹性及其与企业收入的关系

1.使用范围:第二章消费者行为理论 2.要考核的知识点:决定消费者选择的因素; 替代效应和收入效应; 偏好的改变与需求规律; 奢侈品消费与需求规律

Chapter 3 includes: • 3.1 Revealed Preference Theory(显示性偏好理论) • 3.2 Choice Under Uncertainty(不确定条件下的 选择理论) 4.1 Production Function 4.2 Cost Function 5.1 The Optimal Output Decision in the Short Run 5.2 The Optimal Output Decision in the Long Run