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1、消費者偏好與成效概念1.無異曲線(Indifference Curves )2.邊際替代率(The Marginal Rate of Substitution)3.成效函數(The Utility Function)4.邊際成效(Marginal Utility) 5.特殊函數型態(Some Special Functional Forms)定義:一條無異曲線，乃是兩種物品產生同樣總成效水準的一切不同組合的軌跡。定義:無異曲線圖(indifference curve map)是由許多條形狀一样但偏好程度不同的無異曲線所組成的。1.完好性(Completeness) 2.每一個消費組何只能位在一
2、條無異曲線上。3.單調性(Monotonicity) 4.無異曲線是負斜率。5.無異曲線不是一條厚的線。xyA偏好優於偏好優於 AxyAxyA偏好優於偏好優於A偏好劣於偏好劣於AIC1xyA偏好優於偏好優於A偏好劣於偏好劣於AIC1xyAB3. 遞移性(Transitivity) 任兩條無異曲線不相交。4. 愈往右上方的無異曲線，其成效愈高5. 平均優於臨界(Averages preferred to extremes) 無異曲線凸向原點。 xyAIC1假設一位消費者對A和C有一样偏好。假設B優於A。BCxyABIC1IC2C包含B和C的 IC是不能够的情形。為什麼? 因為，根據IC的定義，
3、消費者是：A & C 一樣好。B & C 一樣好。因此A & B 也一樣好(遞移性) 。= 矛盾。xyABIC1xyAB(.5A, .5B)IC1CIC2xyAB(.5A, .5B)IC1CIC2xyAB(.5A, .5B)IC1CA & B 一樣好。C 優於A。C 優於B。邊際替代率的定義有許多方法邊際替代率的定義有許多方法定義定義 1: 為了維持同一成效水準，當添加一個單位為了維持同一成效水準，當添加一個單位 X 物品的消費時，可以放棄的物品的消費時，可以放棄的 Y 物品數量，就物品數量，就是以是以 X 替代替代 Y 的邊際替代率的邊際替代率(MRS)。 定義 2: 無異曲線的斜率是負的：
4、 (偏好固定)無異曲線呈現邊際替代率遞減：他擁有更多的財貨 x ，他所願意放棄的財貨y會愈少。無異曲線 愈接近橫軸愈平坦。愈接近縱軸愈平坦。例子: 邊際替代率遞減 Definition:The utility function measures the level of satisfaction that a consumer receives from any basket of goods.The utility function assigns a number to each basketMore preferred baskets get a higher number than l
5、ess preferred baskets.Utility is an ordinal conceptThe precise magnitude of the number that the function assigns has no significance. Ordinal ranking gives information about the order in which a consumer ranks basketsE.g. a consumer may prefer A to B, but we cannot know how much more she likes A to
6、BCardinal ranking gives information about the intensity of a consumers preferences.We can measure the strength of a consumers preference for A over B.Example: Consider the result of an examAn ordinal ranking lists the students in order of their performance E.g., Harry did best, Sean did second best,
7、 Betty did third best, and so on. A cardinal ranking gives the marks of the exam, based on an absolute marking standard E.g. Harry got 90, Sean got 85, Betty got 80, and so on. Implications of an ordinal utility function:Difference in magnitudes of utility have no interpretation per seUtility is not
8、 comparable across individualsAny transformation of a utility function that preserves the original ranking of bundles is an equally good representation of preferences.eg. U = xyU = xy + 2U = 2xyall represent the same preferences.10 = xyxy20525Example: Utility and a single indifference curve Example:
9、 Utility and a single indifference curve 10 = xy20 = xyxyPreference direction20525Definition:The marginal utility of good x is the additional utility that the consumer gets from consuming a little more of xMUx = dU dx It is is the slope of the utility function with respect to x.It assumes that the c
10、onsumption of all other goods in consumers basket remain constant.Definition:The principle of diminishing marginal utility states that the marginal utility of a good falls as consumption of that good increases.Note: A positive marginal utility implies monotonicity.Example: Relative Income and Life S
11、atisfaction (within nations)Relative Income Percent “SatisfiedLowest quartile70Second quartile78Third quartile82Highest quartile85Source:Hirshleifer,JackandD.Hirshleifer,PriceTheoryandApplications.SixthEdition.PrenticeHall:UpperSaddleRiver,NewJersey.2019.We can express the MRS for any basket as a ra
12、tio of the marginal utilities of the goods in that basketSuppose the consumer changes the level of consumption of x and y. Using differentials:dU = MUx . dx + MUy . dyAlong a particular indifference curve, dU = 0, so:0 = MUx . dx + MUy . dySolving for dy/dx:dy = _ MUxdx MUyBy definition, MRSx,y is t
13、he negative of the slope of the indifference curve:MRSx,y = MUx MUyDiminishing marginal utility implies the indifference curves are convex to the origin (implies averages preferred to extremes)Example:U= (xy)0.5MUx=y0.5/2x0.5MUy=x0.5/2y0.5Marginal utility is positive for both goods:= Monotonicity sa
14、tisfiedDiminishing marginal utility for both goods= Averages preferred to extremesMarginal rate of substitution:MRSx,y = MUx = y MUy xIndifference curves do not intersect the axesExample: Graphing Indifference Curves IC1xyIC1IC2xy偏好方向偏好方向Example: Graphing Indifference Curves 1.Cobb-Douglas (“標準例子)2.
15、U = Axy3. 這裡: + = 1; A, , 正的常數 4.特性:5.MUx = Ax-1y 6.MUy = Axy-17.MRSx,y = y8. x例子: Cobb-DouglasIC1xyIC1IC2xy偏好方向偏好方向例子: Cobb-Douglas2. 完全替代:U = ax + by 這裡: a,b 是正的常數特性:MUx = aMUy = bMRSx,y = a(固定 MRS) b例子: 完全替代 (鮮奶油 與 人工奶油) 人工奶油人工奶油0鮮鮮奶奶油油IC10IC1IC2例子: 完全替代 (鮮奶油 與 人工奶油) 鮮鮮奶奶油油人工奶油人工奶油0IC1IC2IC3斜率斜率
16、= -a/b例子: 完全替代 (鮮奶油 與 人工奶油) 鮮鮮奶奶油油人工奶油人工奶油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 0MUy = B or 0MRSx,y = 0 or or 無法認定例子:完全互補(螺帽與螺栓)0螺螺栓栓IC1螺帽螺帽螺帽螺帽0IC1IC2例子:完全互補(螺帽與螺栓)螺螺栓栓4. 準線性成效函數(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 = bMRSx,y = av(x) (僅受x影響)b飲料飲料y0IC1例子: 準線性偏好(飲料的消費)IC在一在一样样的飲料數量的飲料數量下，邊際替代率一下，邊際替代率一样样y0IC2IC1例子: 準線性偏好(飲料的消費)飲料飲料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, MUy0 或 MUy = 0, MUx0消費消費0儲儲蓄蓄IC1IC2例子:中性偏好(守財奴，儲蓄與消費)蔬菜蔬菜0肉肉IC1IC2例子:中性偏好(素食者，蔬菜與肉)
