Chapter 6 Demand This is a very important chapter, since it unifies all the material in the previous chapter. It is also the chapter that separates the sheep from the goats. If the student has been paying attention for the previous 5 chapters and has been religiously doing the homework, then it is fairly easy to handle this chapter. Alas have often found that students have developed a false sense of confidence after eeing budget constraints, drift through the discussions of preference and utility and come crashing down to earth at Chapter 6. So, the first thing to do is to get them to review the previous chapters Emphasize how each chapter builds on the previous chapters, and how Chapter 6 represents a culmination of this building. In turn Chapter 6 is a foundation for further analysis, and must be mastered in order to continue. Part of the problem is that there is a large number of new concepts in this chapter: offer curves, demand curves, Engel curves, inferior goods, Giffen goods etc. A list of these ideas along with their definitions and page references is often helpful just for getting the concepts down pat If you are doing a calculus-based course, the material in the appendix on quasilinear preferences is quite important. We will refer to this treatment later on when we discuss consumer's surplus, so it is a good idea to go through it carefully now Students usually have a rough time with the workbook problems. In part, I think that this is due to the fact that we have now got a critical mass of ideas, and that it has to percolate a bit before they can start brewing some new ideas A few words of encouragement help a lot here, as well as drawing links with the earlier chapters. Most students will go back on their own and see what they missed on first reading, if you indicate that is a good thing to do. Remember he point of the workbook problems is to show the students what they don 't give them a pat on the back, pat on the back. The role of the professor is to understand, not to give them or a nudge in the behind, whichever seems more appropriat A. Demand functions - relate prices and income to choices
16 Chapter Highlights Chapter 6 Demand This is a very important chapter, since it unifies all the material in the previous chapter. It is also the chapter that separates the sheep from the goats. If the student has been paying attention for the previous 5 chapters and has been religiously doing the homework, then it is fairly easy to handle this chapter. Alas, I have often found that students have developed a false sense of confidence after seeing budget constraints, drift through the discussions of preference and utility, and come crashing down to earth at Chapter 6. So, the first thing to do is to get them to review the previous chapters. Emphasize how each chapter builds on the previous chapters, and how Chapter 6 represents a culmination of this building. In turn Chapter 6 is a foundation for further analysis, and must be mastered in order to continue. Part of the problem is that there is a large number of new concepts in this chapter: offer curves, demand curves, Engel curves, inferior goods, Giffen goods, etc. A list of these ideas along with their definitions and page references is often helpful just for getting the concepts down pat. If you are doing a calculus-based course, the material in the appendix on quasilinear preferences is quite important. We will refer to this treatment later on when we discuss consumer’s surplus, so it is a good idea to go through it carefully now. Students usually have a rough time with the workbook problems. In part, I think that this is due to the fact that we have now got a critical mass of ideas, and that it has to percolate a bit before they can start brewing some new ideas. A few words of encouragement help a lot here, as well as drawing links with the earlier chapters. Most students will go back on their own and see what they missed on first reading, if you indicate that is a good thing to do. Remember: the point of the workbook problems is to show the students what they don’t understand, not to give them a pat on the back. The role of the professor is to give them a pat on the back, or a nudge in the behind, whichever seems more appropriate. Demand A. Demand functions — relate prices and income to choices
B. How do choices change as economic environment changes? changes in income a) this is a parallel shift out of the budget line b) increase in income increases demand- normal good. Figure 6.1 c)increase in income decreases demand --inferior good. Figure 6.2 d)as income changes, the optimal choice moves along the income expan- sion path e)the relationship between the optimal choice and income, with prices fixed, is called the Engel curve. Figure 6.3 2. changes in price a) this is a tilt or pivot of the budget line b) decrease in price increases demand -ordinary good. Figure 6.9. c) decrease in price decreases demand- Giffen good. Figure 6.10 e) the relationship between the optimal choice and a price, with income d the other price fixed, is called the demand curve C. Examples 1. perfect substitutes. Figure 6. 12 2. perfect complements. Figure 6.13 3. discrete good. Figure 6.14. a)reservation price - price where consumer is just indifferent between consuming next unit of good and not consuming it b)a(0,m)=u(1,m-r1) c) special case: quasilinear preferences d)v(0) v(1)+m that v(0)=0 f)then r1=v(1) g) similarly, r2=v(2)-v(1) D. Substitutes and complements 1. increase in p2 increases demand for T1- substitutes 2. increase in p2 decreases demand for I1-complements E. Inverse demand sually think of demand curve as measuring quantity as a function of price but can also think of price as a function of quantity 2. this is the inverse demand curve 3. same relationship, just represented differently
Chapter 6 17 B. How do choices change as economic environment changes? 1. changes in income a) this is a parallel shift out of the budget line b) increase in income increases demand — normal good. Figure 6.1. c) increase in income decreases demand — inferior good. Figure 6.2. d) as income changes, the optimal choice moves along the income expansion path e) the relationship between the optimal choice and income, with prices fixed, is called the Engel curve. Figure 6.3. 2. changes in price a) this is a tilt or pivot of the budget line b) decrease in price increases demand — ordinary good. Figure 6.9. c) decrease in price decreases demand — Giffen good. Figure 6.10. d) as price changes the optimal choice moves along the offer curve e) the relationship between the optimal choice and a price, with income and the other price fixed, is called the demand curve C. Examples 1. perfect substitutes. Figure 6.12. 2. perfect complements. Figure 6.13. 3. discrete good. Figure 6.14. a) reservation price — price where consumer is just indifferent between consuming next unit of good and not consuming it b) u(0, m) = u(1, m − r1) c) special case: quasilinear preferences d) v(0) + m = v(1) + m − r1 e) assume that v(0) = 0 f) then r1 = v(1) g) similarly, r2 = v(2) − v(1) h) reservation prices just measure marginal utilities D. Substitutes and complements 1. increase in p2 increases demand for x1 — substitutes 2. increase in p2 decreases demand for x1 — complements E. Inverse demand curve 1. usually think of demand curve as measuring quantity as a function of price — but can also think of price as a function of quantity 2. this is the inverse demand curve 3. same relationship, just represented differently
Chapter 7 Revealed preference This is a big change of pace, and usually a welcome one. The basic idea of revealed preference, as described in Section 7.1, is a very intuitive one. All I want to do in this chapter is give the students the tools to express that intuition I think that the material in Section 7.3, on recovering preferences, is very exciting. Start out with the idea of indirect revealed preference, as depicted in Figure 7. 2. Point out that the optimization model allows us to predict how this person would behave when faced with a choice between(1, I2)and(21, 22),even ough we have never observed the person when faced with this choice! This is a big idea, and a very important one. Again, drive home how the economic model of optimization allows us to make strong predictions about behavior Figure 7.3 is the natural extension of this line of reasoning. Given the idea of revealed preference, and more importantly the idea of indirect revealed preference, we can determine the shape of underlying indifference curves from looking at choice data. I motivate this in terms of benefit-cost issues, but you could also choose to think about forecasting demand for products in a marketing survey, or similar application Once students understand the idea of revealed preference, they can usually understand the Weak Axiom right away. However, they generally have difficult in actually checking whether the Weak Axiom is satisfied by some real numbers I added Section 7. 5 for this reason; it just outlines one systematic way to check WARP. The students can omit this in their first reading, but they might want to come back to it when they start to do the exercises. If your students know a little computer programming, you might ask them to think about how to write a computer program to check WARP. The same comments go for the treatment of the Strong Axiom and checking SARP. This is probably overkill, but I found that students couldn't really handle problem 7.5 in the workbook without some guidance about how to systematically check SARP. Speaking of the workbook, the problems in this section are really fun. I am especially fond of 7.6 and 7.7. Problem 7.9 had some wrong numbers in it in early printings of Workouts, so people with old books should be warned Finally, the material on index numbers is very worthwhile. Students here bout price indices and cost-of-living indices all the time, so it's nice to describe he theory that lies behind these ideas
18 Chapter Highlights Chapter 7 Revealed Preference This is a big change of pace, and usually a welcome one. The basic idea of revealed preference, as described in Section 7.1, is a very intuitive one. All I want to do in this chapter is give the students the tools to express that intuition algebraically. I think that the material in Section 7.3, on recovering preferences, is very exciting. Start out with the idea of indirect revealed preference, as depicted in Figure 7.2. Point out that the optimization model allows us to predict how this person would behave when faced with a choice between (x1, x2) and (z1, z2), even though we have never observed the person when faced with this choice! This is a big idea, and a very important one. Again, drive home how the economic model of optimization allows us to make strong predictions about behavior. Figure 7.3 is the natural extension of this line of reasoning. Given the idea of revealed preference, and more importantly the idea of indirect revealed preference, we can determine the shape of underlying indifference curves from looking at choice data. I motivate this in terms of benefit-cost issues, but you could also choose to think about forecasting demand for products in a marketing survey, or similar applications. Once students understand the idea of revealed preference, they can usually understand the Weak Axiom right away. However, they generally have difficulty in actually checking whether the Weak Axiom is satisfied by some real numbers. I added Section 7.5 for this reason; it just outlines one systematic way to check WARP. The students can omit this in their first reading, but they might want to come back to it when they start to do the exercises. If your students know a little computer programming, you might ask them to think about how to write a computer program to check WARP. The same comments go for the treatment of the Strong Axiom and checking SARP. This is probably overkill, but I found that students couldn’t really handle problem 7.5 in the workbook without some guidance about how to systematically check SARP. Speaking of the workbook, the problems in this section are really fun. I am especially fond of 7.6 and 7.7. Problem 7.9 had some wrong numbers in it in early printings of Workouts, so people with old books should be warned. Finally, the material on index numbers is very worthwhile. Students here about price indices and cost-of-living indices all the time, so it’s nice to describe the theory that lies behind these ideas
Revealed prefe 1. up until now we've started with preference and then described behavior 2. revealed preference is "working backwards"- start with behavior and describe preferences 3. recovering preferences how to use observed choices to "estimate"the difference curves B. Basic idea 1. if(a1, I2)is chosen when(y1, y2)is affordable, then we know that(a1, r2) at least as good as(y1, 32) 2. in equations: if(31, I2)is chosen when prices are(p1, P2)and p1T1+p22 P191+p2 2, then(a1, I2)>(91, y2) 4. if P121+ p222> P191+ P232, we say that (r1, r2) is directly revealed rred to(1, g2) 5. if X is directly revealed preferred to Y, and y is directly revealed preferred to Z(etc ) then we say that X is indirectly revealed preferred to Z. See Figure 7.2 6. the "chains"of revealed preference can give us a lot of information about the preferences. See Figure 7.3 7. the information revealed about tastes by choices can be used in formulating economic policy C. Weak Axiom of Revealed Preference 1. recovering preferences makes sense only if consumer is actually maximizing 2. what if we observed a case like Figure 7.4 3. in this case X is revealed preferred to Y and Y is als ealed preferred to XI 4. in symbols, we have(a1, I2)purchased at prices (p1, p2) and(y1, 32 purchased at prices(q1, 92)and p151+p2I2>p1g+p2y2 and q191+9232> 1x1+q2x2 5. this kind of behavior is inconsistent with the optimizing model of consumer 6. the Weak Axiom of Revealed Preference(WARP) rules out this kind of 7. WARP: if (I1, T2) is directly revealed preferred to(y1, y2), then(y1, y2) cannot be directly revealed preferred to(a1, I2) 8. WARP: if P1T1+p22> P1g1+p292, then it must happen that q191+929 2< q11+q2x2 9. this condition can be checked by hand or by computer D. Strong Axiom of Revealed Preference 1. WARP is only a necessary condition for behavior to be consistent with 2. Strong Axiom of Revealed Preference(SARP): if (r1, I2) is directly or indirectly revealed preferred to(y1, y2), then(y, y2) cannot be directly or 3. SARP is a necessary and sufficient condition for utility maximization 4. this means that if the consumer is maximizing utility, then his behavior must be consistent with SARP 5. furthermore if his observed behavior is consistent with SARP, then we can lways find a utility function that explains the behavior of the consumer mizing behavior
Chapter 7 19 Revealed Preference A. Motivation 1. up until now we’ve started with preference and then described behavior 2. revealed preference is “working backwards” — start with behavior and describe preferences 3. recovering preferences — how to use observed choices to “estimate” the indifference curves B. Basic idea 1. if (x1, x2) is chosen when (y1, y2) is affordable, then we know that (x1, x2) is at least as good as (y1, y2) 2. in equations: if (x1, x2) is chosen when prices are (p1, p2) and p1x1+p2x2 ≥ p1y1 + p2y2, then (x1, x2) (y1, y2) 3. see Figure 7.1. 4. if p1x1 + p2x2 ≥ p1y1 + p2y2, we say that (x1, x2) is directly revealed preferred to (y1, y2) 5. if X is directly revealed preferred to Y , and Y is directly revealed preferred to Z (etc.), then we say that X is indirectly revealed preferred to Z. See Figure 7.2. 6. the “chains” of revealed preference can give us a lot of information about the preferences. See Figure 7.3. 7. the information revealed about tastes by choices can be used in formulating economic policy C. Weak Axiom of Revealed Preference 1. recovering preferences makes sense only if consumer is actually maximizing 2. what if we observed a case like Figure 7.4. 3. in this case X is revealed preferred to Y and Y is also revealed preferred to X! 4. in symbols, we have (x1, x2) purchased at prices (p1, p2) and (y1, y2) purchased at prices (q1, q2) and p1x1+p2x2 > p1y1+p2y2 and q1y1+q2y2 > q1x1 + q2x2 5. this kind of behavior is inconsistent with the optimizing model of consumer choice 6. the Weak Axiom of Revealed Preference (WARP) rules out this kind of behavior 7. WARP: if (x1, x2) is directly revealed preferred to (y1, y2), then (y1, y2) cannot be directly revealed preferred to (x1, x2) 8. WARP: if p1x1+p2x2 ≥ p1y1+p2y2, then it must happen that q1y1+q2y2 ≤ q1x1 + q2x2 9. this condition can be checked by hand or by computer D. Strong Axiom of Revealed Preference 1. WARP is only a necessary condition for behavior to be consistent with utility maximization 2. Strong Axiom of Revealed Preference (SARP): if (x1, x2) is directly or indirectly revealed preferred to (y1, y2), then (y1, y2) cannot be directly or indirectly revealed preferred to (x1, x2) 3. SARP is a necessary and sufficient condition for utility maximization 4. this means that if the consumer is maximizing utility, then his behavior must be consistent with SARP 5. furthermore if his observed behavior is consistent with SARP, then we can always find a utility function that explains the behavior of the consumer as maximizing behavior
6. can also be tested by a computer E. Index numbers 1. given consumption and prices in 2 years, base year b and some other year t 2. how does consumption in year t compare with base year consumption? 3. general form of a consumption index: 4. natural to use prices as weights 5. get two indices depending on whether you use period t or period b prices 6. Paasche index uses period t(current period) weight Pit 7. Laspeyres index uses period b(base period) weight pia 8. note connection with revealed preference: if Paasche index is greater than 1, then period t must be better than period b: pirl +p? 十>1 n+n2>内+鸡 c) so period t is revealed preferred to period b 9. same sort of thing can be done with Laspeyres index-if Laspeyres index is less than 1. consumer is worse off
20 Chapter Highlights 6. can also be tested by a computer E. Index numbers 1. given consumption and prices in 2 years, base year b and some other year t 2. how does consumption in year t compare with base year consumption? 3. general form of a consumption index: w1xt 1 + w2xt 2 w1xb 1 + w2xb 2 4. natural to use prices as weights 5. get two indices depending on whether you use period t or period b prices 6. Paasche index uses period t (current period) weights: pt 1xt 1 + pt 2xt 2 pt 1xb 1 + pt 2xb 2 7. Laspeyres index uses period b (base period) weights: pb 1xt 1 + pb 2xt 2 pb 1xb 1 + pb 2xb 2 8. note connection with revealed preference: if Paasche index is greater than 1, then period t must be better than period b: a) pt 1xt 1 + pt 2xt 2 pt 1xb 1 + pt 2xb 2 > 1 b) pt 1xt 1 + pt 2xt 2 > pt 1xb 1 + pt 2xb 2 c) so period t is revealed preferred to period b 9. same sort of thing can be done with Laspeyres index — if Laspeyres index is less than 1, consumer is worse off