消费者偏好与效用概念.pptVIP

We can express the MRS for any basket as a ratio of the marginal utilities of the goods in that basket Suppose the consumer changes the level of consumption of x and y. Using differentials: dU = MUx . dx + MUy . dy Along a particular indifference curve, dU = 0, so: 0 = MUx . dx + MUy . dy Solving for dy/dx: dy = _ MUx dx MUy By definition, MRSx,y is the negative of the slope of the indifference curve: MRSx,y = MUx MUy Diminishing marginal utility implies the indifference curves are convex to the origin (implies averages preferred to extremes) Example: U= (xy)0.5 MUx=y0.5/2x0.5 MUy=x0.5/2y0.5 Marginal utility is positive for both goods: = Monotonicity satisfied Diminishing marginal utility for both goods = Averages preferred to extremes Marginal rate of substitution: MRSx,y = MUx = y MUy x Indifference curves do not intersect the axes Example: Graphing Indifference Curves IC1 x y IC1 IC2 x y 偏好方向 Example: Graphing Indifference Curves Cobb-Douglas (“標準例子”) U = Ax?y? 這裡: ? + ? = 1; A, ?,? 正的常數 特性: MUx = ?Ax?-1y? MUy = ?Ax?y?-1 MRSx,y = ?y ?x 例子: Cobb-Douglas IC1 x y IC1 IC2 x y 偏好方向 例子: Cobb-Douglas 2. 完全替代: U = ax + by 這裡: a,b 是正的常數 特性: MUx = a MUy = b MRSx,y = a (固定 MRS) b 例子: 完全替代 (鮮奶油 與 人工奶油) 人工奶油 0 鮮奶油 IC1 0 IC1 IC2 例子: 完全替代 (鮮奶油 與 人工奶油) 鮮奶油 人工奶油 0 IC1 IC2 IC3 斜率 = -a/b 例子: 完全替代 (鮮奶油 與 人工奶油) 鮮奶油 人工奶油 3. 完全互補: U = min {x/a, y/b} 這裡: A,B 是正的常數 特性: MUx = A or 0 MUy = B or 0 MRSx,y = 0 or ? or 無法認定 例子: 完全互補 (螺帽 與 螺栓) 0 螺栓 IC1 螺帽 螺帽 0 IC1 IC2 例子: 完全互補 (螺帽 與 螺栓) 螺栓 4. 準線性效用函數(Quasi-Linear Utility Functions): U = aV(x) + by 這裡: a,b 是正的常數, 而且 v(0) = 0 特性: MUx = av’(x) MUy = b MRSx,y = av’(x) (僅受x影響) b ? 飲料 y 0 IC1 例子: 準線性偏好(飲料的消費) ? ? IC在相同的飲料數量下，邊際替代率相同 y 0 IC2 IC1 例子: 準線性偏好(飲料的消費) 飲料 4. 中性偏好(neutral preference): U(x, y) =V(x) 或 U(x, y) =V(y) 這裡: v(0) = 0 特性: MUx = 0, MUy＞0 或 MUy = 0, MUx＞0 消費