6 Chapter Highlights 4. lump sum tax or subsidy -amount of tax or subsidy is independent of the consumers choices. Also called a head tax or a poll tax 5. rationing -can't consume more than a certain amount of some good J. Example -food stamps 1. before 1979 was an ad valorem subsidy on food a)paid a certain amount of money to get food stamps which were worth more than they cost b)some rationing component- could only buy a maximum amount of 2. after 1979 got a straight lump-sum grant of food coupons. Not the san as a pure lump-sum grant since could only spend the coupons on food e
6 Chapter Highlights 4. lump sum tax or subsidy — amount of tax or subsidy is independent of the consumer’s choices. Also called a head tax or a poll tax 5. rationing — can’t consume more than a certain amount of some good J. Example — food stamps 1. before 1979 was an ad valorem subsidy on food a) paid a certain amount of money to get food stamps which were worth more than they cost b) some rationing component — could only buy a maximum amount of food stamps 2. after 1979 got a straight lump-sum grant of food coupons. Not the same as a pure lump-sum grant since could only spend the coupons on food
Chapter 3 Preferences This chapter is more abstract and therefore needs somewhat more motivation than the previous chapters. It might be a good idea to talk about relations in general before introducing the particular idea of preference relations. Try the relations of"taller, and "heavier. " and "taller and heavier. Point out that aller and heavier" isnt a complete relation, while the other two are. This general discussion can motivate the general idea of preference relations Make sure that the students learn the specific examples of preferences suck as perfect substitutes, perfect complements, etc. They will use these examples any, many times in the next few weeks When describing the ideas of perfect substitutes, emphasize that the defining characteristic is that the slope of the indifference curves is constant, not that it is-1. In the text, I always stick with the case where the slope is -l, but in the workbook, we often treat the general case. The warning goes with the perfect complements case. I work out the symmetric case in the text and try to get the students to do the asymmetric case in the workbook. The definition of the marginal rate of substitution is fraught with "sign confusion. "Should the mrs be defined as a negative or a positive number? I've chosen to give the MRS its natural sign in the book, but I warn the students that many economists tend to speak of the MRS in terms of absolute value. Example diminishing marginal rate of substitution refers to a situation where the absolute value of the mrs decreases as we move along an indifference curve. The actual value of the MRS (a negative number) is increasing in this movement Students often begin to have problems with the workbook exercises here The first confusion they have is that they get mixed up about the idea that indifference curves measure the directions where preferences are constant, and instead draw lines that indicate the directions that preferences are increasing The second problem that they have is in knowing when to draw just arbitrary curves that qualitatively depict some behavior or other, and when to draw exact Try asking your students to draw their indifference curves between five dollar ills and one dollar bills. Offer to trade with them based on what they draw. In ddition to getting them to think, this is a good way to supplement your facult salary
Chapter 3 7 Chapter 3 Preferences This chapter is more abstract and therefore needs somewhat more motivation than the previous chapters. It might be a good idea to talk about relations in general before introducing the particular idea of preference relations. Try the relations of “taller,” and “heavier,” and “taller and heavier.” Point out that “taller and heavier” isn’t a complete relation, while the other two are. This general discussion can motivate the general idea of preference relations. Make sure that the students learn the specific examples of preferences such as perfect substitutes, perfect complements, etc. They will use these examples many, many times in the next few weeks! When describing the ideas of perfect substitutes, emphasize that the defining characteristic is that the slope of the indifference curves is constant, not that it is −1. In the text, I always stick with the case where the slope is −1, but in the workbook, we often treat the general case. The same warning goes with the perfect complements case. I work out the symmetric case in the text and try to get the students to do the asymmetric case in the workbook. The definition of the marginal rate of substitution is fraught with “sign confusion.” Should the MRS be defined as a negative or a positive number? I’ve chosen to give the MRS its natural sign in the book, but I warn the students that many economists tend to speak of the MRS in terms of absolute value. Example: diminishing marginal rate of substitution refers to a situation where the absolute value of the MRS decreases as we move along an indifference curve. The actual value of the MRS (a negative number) is increasing in this movement! Students often begin to have problems with the workbook exercises here. The first confusion they have is that they get mixed up about the idea that indifference curves measure the directions where preferences are constant, and instead draw lines that indicate the directions that preferences are increasing. The second problem that they have is in knowing when to draw just arbitrary curves that qualitatively depict some behavior or other, and when to draw exact shapes. Try asking your students to draw their indifference curves between five dollar bills and one dollar bills. Offer to trade with them based on what they draw. In addition to getting them to think, this is a good way to supplement your faculty salary
8 Chapter Highlights Preferences A. Preferences are relationships between bundles 1. if a consumer would choose bundle(r1, r2)when(y1, y2)is available, then it is natural to say that bundle (a1, r2)is preferred to(y1, y2) by thi consumer 2. preferences have to do with the entire bundle of goods, not with individual B. Notation 1.(1, r2)>(y1, y2) means the x-bundle is strictly preferred to the y- bundle 2.(1, T2)N(y1, y2) means that the x-bundle is regarded as indifferent to 3.(31, 122(91, y2) means the x-bundle is at least as good as(preferred to or indifferent to) the y-bundle C. Assumptions about preferences 1. complete- any two bundles can be compared 2. reflexive any bundle is at least as good as itself 3. transitive-if X >Y and Y>Z, then X>Z a)transitivity necessary for theory of optimal choice D. Indifference curves 1. graph the set of bundles that are indifferent to some bundle. See Figure 2. indifference curves are like contour lines on a map 3. note that indifference curves describing two distinct levels of preference cannot cross. See Figure 3.2. a)proof- use transitivity E. Examples of preferences 1. perfect substitutes. Figure 3.3 a)red pencils and blue pencils; pints and quarts b) constant rate of trade-off between the two goods b)right shoes and left shoes; coffee and crean 3. bads. Figure 3.5. 4. neutrals. Figure 3.6 5. satiation or bliss point Figure 3.7. F. Well-behaved preference monotonicity more of either good is better a)implies indifference curves have negative slope. Figure 3.9 2. convexity -averages are preferred to extremes. Figure 3.10 a)slope gets Hatter as you move further to righ b) example of non-convex preferences G. Marginal rate of substitution l. slope of the indifference curve 2. MRS=A r2/ AT1 along an indifference curve. Figure 3.11 3. sign problem - natural sign is negative, since indifference curves will generally have negative sloy for consumption of good 2. Figure 3. 12 trade off consumption of good 1 4. measures how the consumer is willing to
8 Chapter Highlights Preferences A. Preferences are relationships between bundles. 1. if a consumer would choose bundle (x1, x2) when (y1, y2) is available, then it is natural to say that bundle (x1, x2) is preferred to (y1, y2) by this consumer. 2. preferences have to do with the entire bundle of goods, not with individual goods. B. Notation 1. (x1, x2) (y1, y2) means the x-bundle is strictly preferred to the ybundle 2. (x1, x2) ∼ (y1, y2) means that the x-bundle is regarded as indifferent to the y-bundle 3. (x1, x2) (y1, y2) means the x-bundle is at least as good as (preferred to or indifferent to) the y-bundle C. Assumptions about preferences 1. complete — any two bundles can be compared 2. reflexive — any bundle is at least as good as itself 3. transitive — if X Y and Y Z, then X Z a) transitivity necessary for theory of optimal choice D. Indifference curves 1. graph the set of bundles that are indifferent to some bundle. See Figure 3.1. 2. indifference curves are like contour lines on a map 3. note that indifference curves describing two distinct levels of preference cannot cross. See Figure 3.2. a) proof — use transitivity E. Examples of preferences 1. perfect substitutes. Figure 3.3. a) red pencils and blue pencils; pints and quarts b) constant rate of trade-off between the two goods 2. perfect complements. Figure 3.4. a) always consumed together b) right shoes and left shoes; coffee and cream 3. bads. Figure 3.5. 4. neutrals. Figure 3.6. 5. satiation or bliss point Figure 3.7. F. Well-behaved preferences 1. monotonicity — more of either good is better a) implies indifference curves have negative slope. Figure 3.9. 2. convexity — averages are preferred to extremes. Figure 3.10. a) slope gets flatter as you move further to right b) example of non-convex preferences G. Marginal rate of substitution 1. slope of the indifference curve 2. MRS = ∆x2/∆x1 along an indifference curve. Figure 3.11. 3. sign problem — natural sign is negative, since indifference curves will generally have negative slope 4. measures how the consumer is willing to trade off consumption of good 1 for consumption of good 2. Figure 3.12
5. measures marginal willingness to pay(give up) a)not the same as how much you have to pay b)but how much you would be willing to pay
Chapter 3 9 5. measures marginal willingness to pay (give up) a) not the same as how much you have to pay b) but how much you would be willing to pay
10 Chapter Highlights Chapter 4 Utility In this chapter, the level of abstraction kicks up another notch. Students often Lave trouble with the idea of utility. It is sometimes hard for trained economists to sympathize with them sufficiently, since it seems like such an obvious notion Here is a way to approach the subject. Suppose that we return to the idea of the"heavier than"relation discussed in the last chapter. Think of having a big palance scale with two trays. You can put someone on each side of the balance scale and see which person is heavier, but you don't have any standardized weights. Nevertheless you have a way to determine whether a is heavier than y Now suppose that you decide to establish a scale. You get a bunch of stones, check that they are all the same weight, and then measure the weight of individuals in stones. It is clear that z is heavier than y if z's weight in stones is heavier than ys weight in stones Somebody else might use different units of measurements--kilograms, pounds or whatever. It doesnt make any difference in terms of deciding who is heavier At this point it is easy to draw the analogy with utility-just as pounds give to represent the" heavier than"order numerically, utility gives a way to represent the preference order numerically. Just as the units of weight are the units of utility This analogy can also be used to explore the concept of a positive monotonic transformation, a concept that students have great trouble with. Tell them that a monotonic transformation is just like changing units of measurement in the weight example However, it is also important for students to understand that nonlinear changes of units are possible. Here is a nice example to illustrate this. Suppose hat wood is always sold in piles shaped like cubes. Think of the relation"one pile has more wood than another. Then you can represent this relation by looking at the measure of the sides of the piles, the surface area of the piles, or he volume of the piles. That is, a, x or a' gives exactly the same comparison between the piles. Each of these numbers is a different representation of the utility of a cube of wood Be sure to go over carefully the examples here. The Cobb-Douglas example is an important one, since we use it so much in the workbook. Emphasize that it is just a nice functional form that gives convenient expressions. Be sure to
10 Chapter Highlights Chapter 4 Utility In this chapter, the level of abstraction kicks up another notch. Students often have trouble with the idea of utility. It is sometimes hard for trained economists to sympathize with them sufficiently, since it seems like such an obvious notion to us. Here is a way to approach the subject. Suppose that we return to the idea of the “heavier than” relation discussed in the last chapter. Think of having a big balance scale with two trays. You can put someone on each side of the balance scale and see which person is heavier, but you don’t have any standardized weights. Nevertheless you have a way to determine whether x is heavier than y. Now suppose that you decide to establish a scale. You get a bunch of stones, check that they are all the same weight, and then measure the weight of individuals in stones. It is clear that x is heavier than y if x’s weight in stones is heavier than y’s weight in stones. Somebody else might use different units of measurements—kilograms, pounds, or whatever. It doesn’t make any difference in terms of deciding who is heavier. At this point it is easy to draw the analogy with utility—just as pounds give a way to represent the “heavier than” order numerically, utility gives a way to represent the preference order numerically. Just as the units of weight are arbitrary, so are the units of utility. This analogy can also be used to explore the concept of a positive monotonic transformation, a concept that students have great trouble with. Tell them that a monotonic transformation is just like changing units of measurement in the weight example. However, it is also important for students to understand that nonlinear changes of units are possible. Here is a nice example to illustrate this. Suppose that wood is always sold in piles shaped like cubes. Think of the relation “one pile has more wood than another.” Then you can represent this relation by looking at the measure of the sides of the piles, the surface area of the piles, or the volume of the piles. That is, x, x2, or x3 gives exactly the same comparison between the piles. Each of these numbers is a different representation of the utility of a cube of wood. Be sure to go over carefully the examples here. The Cobb-Douglas example is an important one, since we use it so much in the workbook. Emphasize that it is just a nice functional form that gives convenient expressions. Be sure to