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 to10 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