消费者偏好与效用概念

?A
?C
x
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y
?A
?B IC1
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y
?A (.5A, .5B) ?C
?B IC1
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y
?A (.5A, .5B)
?C
IC 2
?B IC1
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y
?A
? A & B 一樣好。 ? C 優於A。
(.5A, .5B) ? C 優於B。
?C
IC 2
?B IC1
x
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邊際替代率 的定義有許多方法 定義 1: 為了維持同一效用水準，當增加一個單位 X
? Utility is an ordinal concept ? The precise magnitude of the number that the function assigns has no significance.
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? Ordinal ranking gives information about the order in which a consumer ranks baskets ? E.g. a consumer may prefer A to B, but we cannot know how much more she likes A to B
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定義: 一條無異曲線，乃是兩種物品產生同樣總效用
水準的所有不同組合的軌跡。
定義:無異曲線圖(indifference curve map) 是由許多
條形狀相同但偏好程度不同的無異曲線所組成 的。
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1. 完整性(Completeness) ? 每一個消費組何只能位在一條無異曲線上。
2. 單調性(Monotonicity) ? 無異曲線是負斜率。 ? 無異曲線不是一條厚的線。
eg. U = xy U = xy + 2
U = 2xy
all represent the same preferences.
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y Example: Utility and a single indifference curve
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2 02
10 = xy
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x
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y Example: Utility and a single indifference curve
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Example:
Fra Baidu bibliotek
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
物品的消費時，可以放棄的 Y 物品數量，就 是以 X 替代 Y 的邊際替代率 (MRS)。
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定義 2:
無異曲線的斜率是負的：
MRS
x, y
?
?
dy dx
(偏好固定 )
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無異曲線呈現邊際替代率遞減 ：
1. 你擁有更多的財貨 x ，你所願意放棄的財貨 y會 愈少。
2. 無異曲線 ? 愈靠近橫軸愈平坦。 ? 愈靠近縱軸愈平坦。
? Cardinal ranking gives information about the intensity of a consumer's preferences. ? We can measure the strength of a consumer's preference for A over B.
Source: Hirshleifer, Jack and D. Hirshleifer, Price Theory and Applications. Sixth Edition. Prentice Hall: Upper Saddle River, New Jersey. 2019.
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We can express the MRS for any basket as a ratio of the marginal utilities of the goods in that basket
? 無異曲線凸向原點。
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y
IC1
?B ?A
? 假設一位消費者對A和C有相同 偏好。
? 假設B優於A。
?C
x
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y
? 包含B和C的 IC是不可能的情形。 ? 為什麼? 因為，根據IC的定義， 消費
者是：
? A & C 一樣好。
IC 1 IC 2
?B
? B & C 一樣好。 因此A & B 也一樣好(遞移性) 。 => 矛盾。
=> Averages preferred to extremes ? Marginal rate of substitution:
MRSx,y = MUx = y MUy x
? Indifference curves do not intersect the axes
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y Example: Graphing Indifference Curves
鮮 例子: 完全替代 (鮮奶油 與 人工奶油) 奶 油
IC 1 0
人工奶油
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鮮 例子: 完全替代 (鮮奶油 與 人工奶油) 奶 油
IC 1
IC 2
0
人工奶油
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鮮 例子: 完全替代 (鮮奶油 與 人工奶油) 奶 油
斜率 = -a/b
IC 1
IC 2
IC 3
0
人工奶油
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3. 完全互補: U = min {x/a, y/b}
MUx = dU dx
? It is is the slope of the utility function with respect to x.
? It assumes that the consumption of all other goods in consumer's basket remain constant.
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例子: 邊際替代率遞減
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Definition: The utility function measures the level of satisfaction that a consumer receives from any basket of goods.
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? The utility function assigns a number to each basket ? More preferred baskets get a higher number than less preferred baskets.
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Example: Consider the result of an exam
? An ordinal ranking lists the students in order of their performance E.g., Harry did best, Sean did second best, Betty did third best, and so on.
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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.
IC1
x
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y Example: Graphing Indifference Curves
偏好方向
IC 2 IC 1
x
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1. Cobb-Douglas (“標準例子” ) U = Ax? y?
這裡: ? + ? = 1; A, ? ,? 正的常數
特性:
1.
MUx = ? Ax? -1y? MUy = ? Ax? y?-1
? Difference in magnitudes of utility have no interpretation per se
? Utility is not comparable across individuals
? Any transformation of a utility function that preserves the original ranking of bundles is an equally good representation of preferences.
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2 02
Preference direction
20 = xy
10 = xy
5
x
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Definition: The marginal utility of good x is the additional utility that the consumer gets from consuming a little more of x
? Suppose the consumer changes the level of consumption of x and y. Using differentials: dU = MU x . dx + MU y . dy
? Along a particular indifference curve, dU = 0, so: 0 = MUx . dx + MU y . dy
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? Solving for dy/dx: dy = _ MU x dx MUy
? By definition, MRS x,y is the negative of the slope of the indifference curve: MRSx,y = MUx MU y
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? Diminishing marginal utility implies the indifference curves are convex to the origin (implies averages preferred to extremes)
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Example: Relative Income and Life Satisfaction (within nations)
Relative Income Lowest quartile Second quartile Third quartile Highest quartile
Percent > “Satisfied” 70 78 82 85
? 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.
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Implications of an ordinal utility function:
消費者偏好與效用概念
1. 無異曲線(Indifference Curves ) 2. 邊際替代率 (The Marginal Rate of Substitution) 3. 效用函數(The Utility Function)
? 邊際效用(Marginal Utility) 4. 特殊函數型態 (Some Special Functional Forms)
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y
?A
x
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y
偏好優於 A
?A
x
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y
偏好優於A
?A
偏好劣於A
x
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y
偏好優於A
?A
偏好劣於A
IC 1
x
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y
B
? ?
A
IC 1
x
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3. 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，其效用愈高 5. 平均優於臨界 (Averages preferred to extremes)
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
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螺 栓
例子: 完全互補 (螺帽 與 螺栓)
IC 1
0
螺帽
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螺 栓
例子: 完全互補 (螺帽 與 螺栓)
IC 2 IC 1
0
螺帽
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4. 準線性效用函數 (Quasi-Linear Utility Functions): U = aV(x) + by
MRSx,y = ? y ?x
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y 例子: Cobb-Douglas
IC 1
x
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y 例子: Cobb-Douglas
偏好方向
IC 2 IC 1
x
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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
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