Algebra : B(p1, … , pn, m) ={ (x1, … , xn) | x1
³ 0, … , xn
³ 0 and p1x1
+ … + pnxn
£ m }
–
Graph: u
Describe changes in budget constraintu
Government programs and budget constraintsu
Non-linear budget lines上图是基本的,税收和补贴、Quantity Discount,Quantity Penalty,One Price Negative The Food Stamp Program,Uniform Ad
Valorem Sales Taxes,都可以看做商品价格或收入发生变动,从而预算线斜率,截距发生变动。
3. Preferences
l
Describe preferences:strict preference;
indifference;
weak preference
l
三大公理:完备性,反身性,传递性l
Indifference curves (
无差异曲线)无差异曲线形状很多:良好性状的、完全互补、完全替代等。
l
Well-behaved preferences:
Monotonicity(单调性): More of any commodity is always preferred (i.e. no satiation and every commodity is a good).
Convexity (凸性): Mixtures of bundles are (at least weakly) preferred to the bundles themselves.
l
Marginal rate of substitution (
边际替代率)MRS= dx2/dx1,大概讲就是为放弃一单位x1,需要多少单位x2补偿以保持相同效用。
4. Utilityu
Utility function (效用函数)–
Definition–
Monotonic transformation (单调转换)效用函数能够进行单调转化本身表明我们使用的是序数效用论。单调转换的特性在解题中能起到简化的作用。
常见的效用函数有:V(x1,x2) = x1 + x2.,W(x1,x2) = min{x1,x2}.,U(x1,x2) = f(x1) + x2 ,U(x1,x2) = x1a x2b
拟线性偏好在科斯定理那里有重要运用。
u
Marginal rate of substitution 边际替代率 这个式子推导:U(x1,x2) º k,全微分:
既然单调变换后表示的是同一组无差异曲线,当然MRS不变