消費者偏好與效用概念

1. 消費者偏好與效用概念

2. 內容綱要 • 無異曲線(Indifference Curves ) • 邊際替代率(The Marginal Rate of Substitution) • 效用函數(The Utility Function) • 邊際效用(Marginal Utility) • 特殊函數型態(Some Special Functional Forms)

3. 無異曲線 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。

4. 無異曲線圖的特性 • 完整性(Completeness) • 每一個消費組何只能位在一條無異曲線上。 • 單調性(Monotonicity) • 無異曲線是負斜率。 • 無異曲線不是一條厚的線。

5. y 單調性 • A x

6. y 單調性 偏好優於 A • A x

7. y 單調性 偏好優於A • A 偏好劣於A x

8. y 單調性 偏好優於A • A 偏好劣於A IC1 x

9. y 無異曲線不厚 B • • A IC1 x

10. 無異曲線圖的特性 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) • 無異曲線凸向原點。

11. y 無異曲線不能相交 • 假設一位消費者對A和C有相同偏好。 • 假設B優於A。 IC1 B • • A C • x

12. y 無異曲線不能相交 • 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。 • B & C 一樣好。 • 因此A & B 也一樣好(遞移性) 。 • => 矛盾。 IC2 IC1 B • • A C • x

13. y 平均優於臨界 A • • IC1 B x

14. y 平均優於臨界 A • (.5A, .5B) • C • IC1 B x

15. y 平均優於臨界 A • (.5A, .5B) • C IC2 • IC1 B x

16. y 平均優於臨界 • A& B 一樣好。 • C 優於A。 • C 優於B。 A • (.5A, .5B) • C IC2 • IC1 B x

17. 邊際替代率 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 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)。

18. 定義 2: 無異曲線的斜率是負的： (偏好固定) 邊際替代率

19. 邊際替代率遞減 無異曲線呈現邊際替代率遞減： • 你擁有更多的財貨 x ，你所願意放棄的財貨y會愈少。 • 無異曲線 • 愈靠近橫軸愈平坦。 • 愈靠近縱軸愈平坦。

20. 例子:邊際替代率遞減

21. 效用函數 Definition: The utility function measures the level of satisfaction that a consumer receives from any basket of goods.

22. The Utility Function • The utility function assigns a number to each basket • More preferred baskets get a higher number than less preferred baskets. • Utility is an ordinal concept • The precise magnitude of the number that the function assigns has no significance.

23. Ordinal and Cardinal Ranking • Ordinalranking 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 • 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.

24. 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. • 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.

25. The Utility Function Implications of an ordinal utility function: • 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. eg. U = xy U = xy + 2 U = 2xy all represent the same preferences.

26. y Example: Utility and a single indifference curve 5 2 10 = xy 0 x 2 5

27. y Example: Utility and a single indifference curve Preference direction 5 20 = xy 2 10 = xy 0 x 2 5

28. Marginal Utility Definition: The marginal utility of good x is the additional utility that the consumer gets from consuming a little more of x 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.

29. Diminishing Marginal Utility 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.

30. Example: Relative Income and Life Satisfaction (within nations) Relative IncomePercent > “Satisfied” Lowest quartile 70 Second quartile 78 Third quartile 82 Highest quartile 85 Source: Hirshleifer, Jack and D. Hirshleifer, Price Theory and Applications. Sixth Edition. Prentice Hall: Upper Saddle River, New Jersey. 1998.

31. Marginal Utility and the Marginal Rate of Substitution 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

32. Marginal Utility and the Marginal Rate of Substitution • 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

33. Marginal Utility and the Marginal Rate of Substitution • Diminishing marginal utility implies the indifference curves are convex to the origin (implies averages preferred to extremes)

34. 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

35. y Example: Graphing Indifference Curves IC1 x

36. y Example: Graphing Indifference Curves 偏好方向 IC2 IC1 x

37. 特殊函數型態 • 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

38. y 例子: Cobb-Douglas IC1 x

39. y 例子: Cobb-Douglas 偏好方向 IC2 IC1 x

40. 特殊函數型態 • 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

41. 例子:完全替代 (鮮奶油 與人工奶油) 鮮奶油 IC1 0 人工奶油

42. 例子:完全替代 (鮮奶油 與人工奶油) 鮮奶油 IC2 IC1 0 人工奶油

43. 例子:完全替代 (鮮奶油 與人工奶油) 鮮奶油 斜率 = -a/b IC2 IC3 IC1 0 人工奶油

44. 特殊函數型態 • 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

45. 例子: 完全互補 (螺帽 與螺栓) 螺栓 IC1 0 螺帽

46. 例子: 完全互補 (螺帽 與螺栓) 螺栓 IC2 IC1 0 螺帽

47. 特殊函數型態 • 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

48. y 例子:準線性偏好(飲料的消費) IC1 • 0 飲料

49. y 例子:準線性偏好(飲料的消費) IC2 IC在相同的飲料數量下，邊際替代率相同 IC1 • • 0 飲料

50. 特殊函數型態 • 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