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Consumers’ preferences

Consumers’ preferences. ECO61 Udayan Roy Fall 2008. Goods bundles. Origin. Preferences . Consumers have preferences that they can use to compare different goods bundles The preferences may be over goods bundles consumed by oneself or over goods bundles consumed by someone else

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Consumers’ preferences

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  1. Consumers’ preferences ECO61 Udayan Roy Fall 2008

  2. Goods bundles Origin

  3. Preferences • Consumers have preferences that they can use to compare different goods bundles • The preferences may be over goods bundles consumed by oneself or over goods bundles consumed by someone else • For example, a parent may have preferences over various bundles of food and clothing bought by the parent but consumed by a child

  4. Assumptions about Preference Orderings • Completeness: the consumer is able to rank all possible bundles of goods and services. • For any two bundles A and B, the consumer knows whether A is better, or B is better, or they are equally good • Transitivity: for any three bundles A, B, and C, if A is at least as good as B and B is at least as good as C, then A is at least as good as C. • These two assumptions imply the ranking principle

  5. The Ranking Principle • A consumer can rank, in order of preference, all potentially available alternatives

  6. Assumption: More-Is-Better • Other things equal, more of a good is preferred to less. • We ignore goods that are harmful or poisonous, for which more is not better than less. Such goods are jokingly referred to as ‘bads’

  7. Indifference W is worse than A. Z is better than A. So, on the line joining W and Z, there must exist a goods bundle such as B that the consumer considers equally good as A. By using this logic repeatedly, we can find many other bundles—such as B, C, and D—that are equally good as A. Z2 D W2 Indeed, for any consumption bundle, it is possible to find other bundles that are equally good Origin

  8. An Indifference Curve An indifference curve is a set of consumption bundles that the consumer prefers equally K is inferior and L is superior to the bundles on the indifference curve Origin

  9. Part of an Indifference Map Origin

  10. Properties of Indifference Maps • Bundles on indifference curves farther from the origin are preferred to those on indifference curves closer to the origin. • There is an indifference curve through every possible bundle. • Indifference curves cannot cross. • Indifference curves slope downward.

  11. Impossible Indifference Curves • Lisa is indifferent between e and a, and also between e and b… • so by transitivity she should also be indifferent between a and b… • but this is impossible, since b must be preferred to a given it has more of both goods. itos per semester r , Bur B e b 1 I a 0 I Z , Pizzas per semester

  12. Impossible Indifference Curves • Lisa is indifferent between b and a since both points are in the same indifference curve… • But this contradicts the “more is better” assumption. Can you tell why? • Yes, b has more of both and hence it should be preferred over a. itos per semester b r , Bur B a I Z , Pizzas per semester

  13. Impossible Indifference Curves

  14. Substitution Between Goods • Economic decisions involve trade-offs • Indifference curves provide information on the amount of one good that the consumer is willing to give up to gain a unit of another good 4-14

  15. Rates of Substitution • Consider moving along an indifference curve, from one bundle to another • This is the same as taking away units of one good and compensating the consumer for the loss by adding units of another good • Slope of the indifference curve shows how much of the second good is needed to make up for a loss of the first good 4-15

  16. Figure 4.8: Rates of Substitution • Look at the move from bundle A to C • Consumer loses 1 soup (S = -1); gains 2 bread (B = +2) • A and C are equally desirable • Slope of indifference curve = B/S = -2 • Consumer is willing to substitute for soup with bread at 2 ounces per pint 4-16

  17. Marginal Rate of Substitution • The marginal rate of substitution for X with Y, MRSXY, is the rate at which a consumer must adjust Y to maintain the same level of well-being when X changes by a tiny amount, from a given starting point • Tells us how much Y a consumer needs to compensate for losing a little bit of X, per unit of X • Tells us the maximum amount of Y a consumer would be willing to pay per additional unit of X • That is, MRSXY is the consumer’s willingness to pay Y for a unit of X 4-17

  18. Figure 4.9: Marginal Rate of Substitution • Slope = DB/DS = 3/(-2) = -3/2 • MRSSB= -DB/DS=-3/(-2) = 3/2 • The slope—and its negative, the MRS—at bundle A can be approximated by the slope of the line AD, or the line AE, or the line AF, etc. • But the precise value is obtained from the slope of the line that is tangent to the indifference curve at bundle A. 4-18

  19. What Determines Rates of Substitution? • Tastes • Preferences for one good over another affect the slope of an indifference curve and MRS • Starting point on the indifference curve; the initial goods bundle • People like variety. So most indifference curves get flatter as we move from top left to bottom right • Link between slope and MRS implies that MRS declines; the amount of Y required to compensate for a given change in X decreases as X increases • One gets bored with X as consumption of X increases. Therefore, one needs less Y to compensate for a unit loss of X 4-19

  20. Figure 4.10: Indifference Curves and Consumer Tastes 4-20

  21. Preferences and time • To a non-economist, food is food is food. • To an economist, “food delivered this year” and “food delivered next year” are different goods

  22. Preferences and chance • To an economist, “food delivered tomorrow if it is sunny” and “food delivered tomorrow if there is a hurricane” are different goods

  23. Figure 4.11: MRS along an Indifference Curve 4-23

  24. Perfect Substitutes and Complements • Two products are perfect substitutes if their functions are identical; in such a case, a consumer is willing to swap one for the other at a fixed rate • Two products are perfect complements if they are valuable only when used together in fixed proportions 4-24

  25. Figure 4.12: Perfect Substitutes MRSRE = ½ 4-25

  26. Figure 4.13: Perfect Complements 4-26

  27. Utility • Recall that under the completeness and transitivity assumptions, the ranking principle is true: • the consumer can rank all bundles according to her preference • Therefore, the consumer can assign a number to each bundle such that the numbers assigned to the bundles represent the consumer’s preferences • The number assigned to a bundle is called its utility

  28. Utility functions • If the utility numbers assigned by a consumer to the various consumption bundles can be represented by a mathematical formula, that formula is called a utility function • Example: • Consider two goods, food and clothing and let the quantities consumed be F and C. • Then, the formula U(F,C) = F C can be used to assign a number to any bundle. (For example, if F = 11 and C = 3, then U = 33.) • And if the assigned numbers agree with the consumer’s preference ranking, then the formula is a utility function.

  29. CONSUMER PREFERENCES ●utility Numerical score representing the satisfaction that a consumer gets from a given market basket. • Utility and Utility Functions ●utility function Formula that assigns a level of utility to individual market baskets. Utility Functions and Indifference Curves A utility function can be represented by a set of indifference curves, each with a numerical indicator. This figure shows three indifference curves (with utility levels of 25, 50, and 100, respectively) associated with the utility function: u(F,C) = FC

  30. Indifference Curves for the Utility Function U = F  S

  31. Marginal Utility • Marginal utility is the increase in a consumer’s utility resulting from the addition of a very small amount of some good, per unit of the good 4-31

  32. MU and MRS • Consider changes in consumption, DX and DY, that leave utility unchanged • A small change in X, DX, causes utility to change by MUXDX • Small change in Y, DY, causes utility to change by MUYDY • If we stay on same indifference curve, then MUXDX + MUYDY = 0. Therefore, 4-32

  33. (a) Utility Utility and Marginal Utility 350 Utility function, U (10, Z ) , Utils U 250 DU = 20 230 DZ = 1 • As Lisa consumes more pizza, holding her consumption of burritos constant at 10, her total utility, U, increases… • and her marginal utility of pizza, MUZ, decreases (though it remains positive). • Marginal utility is the slope of the utility function as we hold the quantity of the other good constant. 0 1 2 3 4 5 6 7 8 9 10 Z , Pizzas per semester (b) Marginal Utility 130 , Marginal utility of pizza Z MU 20 MU Z 0 1 2 3 4 5 6 7 8 9 10 Z , Pizzas per semester

  34. Ordinal utility • The indifference map of the utility function U = XY will look identical to the indifference map of the utility function V = (XY)2 = U2 or of the utility function W = (XY)2 + 12 = U2 + 12 • That is, the way a utility function ranks various goods bundles is unchanged if the utility numbers given to every bundle are transformed in an order-preserving manner • The utility numbers themselves are unimportant • Only the implied rankings are important

  35. Ordinal utility • As was just claimed, the indifference map of the utility function U = XY will look identical to the indifference map of the utility function V = (XY)2 = U2 or of the utility function W = (XY)2 + 12 = U2 + 12 • In particular, MRSXY at any goods bundle will be unaffected if the utility numbers given to every bundle are transformed in an order-preserving manner

  36. Figure 4.12: Perfect Substitutes Utility function: U = 2E + RMRSRE = ½ 4-36

  37. Figure 4.13: Perfect Complements Utility function: U = min{R, L} 4-37

  38. Quasi-linear utility • U = f(X) + Y • Example: U = X0.5 + Y • MRSXY depends on X but not on Y • That is, at any value of X, all indifference curves have the same slope • As all indifference curves are parallel to each other, the vertical distance between any two indifference curves is always the same • We will see later why this utility function is significant Y X

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