elaborate on the idea that riz2 is the general form for Cobb-Douglas preferences ons(e ke it look different. It's a good idea to calculate the MRS for a few representations of the Cobb-Douglas utility function in class so that people can see how to do them and, more importantly, that the MrS doesnt change as you change the representation of utility The example at the end of the chapter, on commuting behavior, is a very nice one. If you present it right, it will convince your students that utility is an operational concept. Talk about how the same methods can be used in marketing surveys, surveys of college admissions, etc. The exercises in the workbook for this chapter are very important since they drive home the ideas. A lot of times, students think that they understand some point, but they don't, and these exercises will point that out to them. It is a good idea to let the students discover for themselves that a sure-fire way to ell whether one utility function represents the same preferences as another is to compute the two marginal rate of substitution functions. If they don't get this idea on their own, you can pose it as a question and lead them to the answer Utility A. Two ways of viewing utility 1. old way a) measures how“ satisfied” you are 1)not operational 2)many other problems a)summarizes preferences b)a utility function assigns a number to each bundle of goods so that more preferred bundles get higher numbers at is, u(a1, r2)>u(y1, y2)if and only if(a1, r2)>(y1, y2) d)only the ordering of bundles counts, so this is a theory of ordinal tility 1)op 2) gives a complete theory of demand B. Utility functions are not unique 1. if u(a1, I2)is a utility function that represents some preferences, and f() is any increasing function, then f(u(r1, r2))represents the same preferences 2. why? Because u(r1, r2)>u(y1, y2) only if f(u(a1, a2))>f(u(y1, y2)) 3. so if u(r1, r2)is a utility function then any positive monotonic transfor- mation of it is also a utility function that represents the same preferences C. Constructing a utility function 1. can do it mechanically using the indifference curves. Figure 4.2 2. can do it using the "meaning " of the preferences D. Examples 1. utility to indifference curves a)easy -just plot all points where the utility is constant 2. indifference curves to utility 3. examples a) perfect substitutes - all that matters is total number of pencils, soChapter 4 11 elaborate on the idea that xa 1xb 2 is the general form for Cobb-Douglas preferences, but various monotonic transformations (e.g., the log) can make it look quite different. It’s a good idea to calculate the MRS for a few representations of the Cobb-Douglas utility function in class so that people can see how to do them and, more importantly, that the MRS doesn’t change as you change the representation of utility. The example at the end of the chapter, on commuting behavior, is a very nice one. If you present it right, it will convince your students that utility is an operational concept. Talk about how the same methods can be used in marketing surveys, surveys of college admissions, etc. The exercises in the workbook for this chapter are very important since they drive home the ideas. A lot of times, students think that they understand some point, but they don’t, and these exercises will point that out to them. It is a good idea to let the students discover for themselves that a sure-fire way to tell whether one utility function represents the same preferences as another is to compute the two marginal rate of substitution functions. If they don’t get this idea on their own, you can pose it as a question and lead them to the answer. Utility A. Two ways of viewing utility 1. old way a) measures how “satisfied” you are 1) not operational 2) many other problems 2. new way a) summarizes preferences b) a utility function assigns a number to each bundle of goods so that more preferred bundles get higher numbers c) that is, u(x1, x2) > u(y1, y2) if and only if (x1, x2)  (y1, y2) d) only the ordering of bundles counts, so this is a theory of ordinal utility e) advantages 1) operational 2) gives a complete theory of demand B. Utility functions are not unique 1. if u(x1, x2) is a utility function that represents some preferences, and f(·) is any increasing function, then f(u(x1, x2)) represents the same preferences 2. why? Because u(x1, x2) > u(y1, y2) only if f(u(x1, x2)) > f(u(y1, y2)) 3. so if u(x1, x2) is a utility function then any positive monotonic transfor￾mation of it is also a utility function that represents the same preferences C. Constructing a utility function 1. can do it mechanically using the indifference curves. Figure 4.2. 2. can do it using the “meaning” of the preferences D. Examples 1. utility to indifference curves a) easy — just plot all points where the utility is constant 2. indifference curves to utility 3. examples a) perfect substitutes — all that matters is total number of pencils, so u(x1, x2) = x1 + x2 does the trick