- Chapter 3: Consumer Behavior PART II PRODUCERS, CONSUMERS, AND COMPETITIVE MARKETS CHAPTER 3 CONSUMER BEHAVIOR EXERCISES 1. In this chapter, consumer preferences for various commodities did not change during the analysis. Yet in some situations, preferences do change as consumption occurs. Discuss why and how preferences might change over time with consumption of these two commodities: a. cigarettes The assumption that preferences do not change is a reasonable one if choices are independent across time. It does not hold, however, when “habit-forming” or addictive behavior is involved, as in the case of cigarettes: the consumption of cigarettes in one period influences their consumption in the next period. b. dinner for the first time at a restaurant with a special cuisine This example is parallel to examples of adventure seeking. For some, a new dining experience creates enthusiasm to seek out more exciting and different cuisines and dishes. For others, they develop a fondness for regularity and consistency or fear of the new and unknown. In either of these cases, choices change as consumption occurs. 2. Draw indifference curves that represent the following individuals’ preferences for hamburgers and soft drinks. Indicate the direction in which the individuals’ satisfaction (or utility) is increasing. a. Joe has convex preferences and dislikes both hamburgers and soft drinks. Since Joe dislikes both goods, his set of indifference curves will be bowed inwards towards the origin instead of outwards, as in the normal case where more is preferred to less. Given he dislikes both goods, his satisfaction is increasing in the direction of the origin. Convexity of preferences implies his indifference curves will have the normal shape in that they are bowed towards the direction of increasing satisfaction. Convexity also implies that given any two bundles between which the consumer is indifferent, the “average” of the two bundles will be in the preferred set, or will leave him at least as well off. h amb urg er soft dr in k 23
- Chapter 3: Consumer Behavior b. Jane loves hamburgers and dislikes soft drinks. If she is served a soft drink, she will pour it down the drain rather than drink it. Since Jane can freely dispose of the soft drink if it is given to her, she considers it to be a neutral good. This means she does not care about soft drinks one way or the other. With hamburgers on the vertical axis, her indifference curves are horizontal lines. Her satisfaction increases in the upward direction. h amb urg er soft dr in k c. Bob loves hamburgers and dislikes soft drinks. If he is served a soft drink, he will drink it to be polite. Since Bob will drink the soft drink in order to be polite, it can be thought of as a “bad”. When served another soft drink, he will require more hamburgers at the same time in order to keep his satisfaction constant. More soft drinks without more hamburgers will worsen his utility. More hamburgers and fewer soft drinks will increase his utility. h amb urg er soft dr in k d. Molly loves hamburgers and soft drinks, but insists on consuming exactly one soft drink for every two hamburgers that she eats. Molly wants to consume the two goods in a fixed proportion so her indifference curves are L-shaped. For any given amount of one good, she gets no extra satisfaction from having more of the other good. She will only increase her satisfaction if she has more of both goods. 24
- Chapter 3: Consumer Behavior h amb urg er soft dr in k e. Bill likes hamburgers, but neither likes nor dislikes soft drinks. Like Jane, Bill considers soft drinks to be a neutral good. Since he does not care about soft drinks one way or the other we can assume that no matter how many he has, his utility will be the same. His level of satisfaction depends entirely on how many hamburgers he has. h amb urg er soft dr in k f. Mary always gets twice as much satisfaction from an extra hamburger as she does from an extra soft drink. How much extra satisfaction Mary gains from an extra hamburger or soft drink tells us something about the marginal utilities of the two goods, or about her MRS. If she always receives twice the satisfaction from an extra hamburger then her marginal utility from consuming an extra hamburger is twice her marginal utility from consuming an extra soft drink. Her MRS, with hamburgers on the vertical axis, is 1/2. Her indifference curves are straight lines with a slope of 1/2. h amb urg er soft dr in k 25
- Chapter 3: Consumer Behavior 3. If Jane is currently willing to trade 4 movie tickets for 1 basketball ticket then she must like basketball better than movies. True or false? Explain. This statement is not necessarily true. If she is always willing to trade 4 movie tickets for 1 basketball ticket then yes she likes basketball better because she will always gain the same satisfaction from 4 movie tickets as she does from 1 basketball ticket. However, it could be that she has convex preferences (diminishing marginal rate of substitution) and is at a bundle where she has a lot of movie tickets relative to basketball tickets. This would make her willing to give up more movie tickets to get another basketball ticket. It would not mean though that she liked basketball better. Her willingness to give up a good would in this case depend on the quantity of each good in her current basket. 4. Janelle and Brian each plan to spend $20,000 on the styling and gas mileage features of a new car. They can each choose all styling, all gas mileage, or some combination of the two. Janelle does not care at all about styling and wants the best gas mileage possible. Brian likes both equally and wants to spend an equal amount on the two features. Using indifference curves and budget lines, illustrate the choice that each person will make. Assume styling is on the vertical axis and gas mileage is on the horizontal axis. Janelle has indifference curves that are vertical. If the styling is there she will take it, but she otherwise does not care about it. As her indifference curves move over to the right, she gains more gas mileage and more satisfaction. She will spend all $20,000 on gas mileage. Brian has indifference curves that are L- shaped. He will not spend more on one feature than on the other feature. He will spend $10,000 on styling and $10,000 on gas mileage. 5. Suppose that Bridget and Erin spend their income on two goods, food (F) and clothing (C). Bridget’s preferences are represented by the utility function U(F,C) = 10FC, while Erin’s preferences are represented by the utility function U(F,C ) = .20F 2 C 2 . a. On a graph, with food on the horizontal axis and clothing on the vertical axis, identify the set of points that give Bridget the same level of utility as the bundle (10,5). Do the same for Erin on a separate graph. Bridget receives a utility of 10*10*5=500 from this bundle. The indifference curve is represented by the equation 10FC=500 or FC=50. Some bundles on this indifference curve are (5,10), (10,5), (25,2), and (2,25). Erin receives a utility of .2*10*10*5*5=500 from the bundle (10,5). Her indifference curve is 2 2 represented by the equation 500= .2F C , or 50=FC. This is the same indifference curve as Bridget. Both indifference curves have the normal, convex shape. b. On the same two graphs, identify the set of bundles that give Bridget and Erin the same level of utility as the bundle (15,8). For each person, plug in F=15 and C=8 into their respective utility functions. For Bridget, this gives her a utility of 1200, so her indifference curve is given by 26
- Chapter 3: Consumer Behavior the equation 10FC=1200, or FC=120. Some bundles on this indifference curve are (12,10), (10,12), (3,40), and (40,3). For Erin, this bundle gives her a utility 2 2 of 2880, so her indifference curve is given by the equation 2880= .2F C , or FC=120. This is the same indifference curve as Bridget. c. Do you think Bridget and Erin have the same preferences or different preferences? Explain. They have the same preferences because for any given bundle they have the same level of utility. This means that they will rank all bundles in the same order. Note however, that it is not necessary that they receive the same level of utility to have the same set of preferences. All that is necessary is that they rank the bundles in the same order. 6. Suppose that Jones and Smith have each decided to allocate $1,000 per year to an entertainment budget in the form of hockey games or rock concerts. They both like hockey games and rock concerts and will choose to consume positive quantities of both goods. However, they differ substantially in their preferences for these two forms of entertainment. Jones prefers hockey games to rock concerts, while Smith prefers rock concerts to hockey games. a. Draw a set of indifference curves for Jones and a second set for Smith. Given they each like both goods and they will each choose to consume positive quantities of both goods, we can assume their indifference curves have the normal convex shape. However since Jones has an overall preference for hockey and Smith has an overall preference for rock concerts, their two sets of indifference curves will have different slopes. Suppose that we place rock concerts on the vertical axis and hockey games on the horizontal axis, Jones will have a larger MRS than Smith. Jones is willing to give up more rock concerts in exchange for a hockey game since he prefers hockey games. The indifference curves for Jones will be steeper. b. Using the concept of marginal rate of substitution, explain why the two sets of curves are different from each other. At any combination of hockey games and rock concerts, Jones is willing to give up more rock concerts for an additional hockey game, whereas, Smith is willing to give up fewer rock concerts for an additional hockey game. Since the MRS is a measure of how many of one good (rock concerts) an individual is willing to give up for an additional unit of the other good (hockey games), then the MRS, and hence the slope of the indifference curves, will be different for the two individuals. 7. The price of DVDs (D) is $20 and the price of CDs (C) is $10. Philip has a budget of $100 to spend on the two goods. Suppose that he has already bought one DVD and one CD. In addition there are 3 more DVDs and 5 more CDs that he would really like to buy. a. Given the above prices and income, draw his budget line on a graph with CDs on the horizontal axis. His budget line is PD D + PCC = I , or 20D+10C=100. If he spends his entire income on DVD’s he could afford to buy 5. If he spends his entire income on CD’s he could afford to buy 10. 27
- Chapter 3: Consumer Behavior b. Considering what he has already purchased, and what he still wants to purchase, identify the three different bundles of CDs and DVDs that he could choose. Assume that he cannot purchase fractional units for this part of the question. Given he has already purchased one of each, for a total of $30, he has $70 left. Since he wants 3 more DVD’s he can buy these for $60 and spend his remaining $10 on 1 CD. This is the first bundle below. He could also choose to buy only 2 DVD’s for $40 and spend the remaining $30 on 3 CD’s. He can choose the following bundles: Purchased Quantities Total Quantities D C D C 3 1 2 6 2 3 3 4 1 5 4 2 8. Anne has a job that requires her to travel three out of every four weeks. She has an annual travel budget and can either travel by train or by plane. The airline she typically flies with has a frequent traveler program that reduces the cost of her tickets depending on the number of miles she has flown in a given year. When she reaches 25,000 miles the airline will reduce the price of her tickets by 25% for the remainder of the year. When she reached 50,000 miles, the airline will reduce the price of her tickets by 50% for the remainder of the year. Graph Anne’s budget line, with train miles on the vertical axis and plane miles on the horizontal axis. The typical budget line is linear (with a constant slope) because the prices of the two goods do not change as the consumer buys more or less of a particular good. In this case, the price of airline miles will change depending on how many miles she purchases. As the price changes, the slope of the budget line will change. Since there are three prices, there will be three slopes, or two kinks, to the budget line. Since the price falls as she flies more miles, the budget line will become flatter with every price change. See the graph in the problem below. 9. Debra usually buys a soft drink when she goes to a movie theater, where she has a choice of three sizes: the 8 ounce drink costs $1.50, the 12 ounce drink, $2.00, and the 16 ounce drink, $2.25. Describe the budget constraint that Debra faces when deciding how many ounces of the drink to purchase. (Assume that Debra can costlessly dispose of any of the soft drink that she does not want. First notice that as the size of the drink increases, the price per ounce decreases. $1.50 When she buys the 8-ounce soft drink she pays = $0.19 per oz. When 8 oz she buys the 12-ounce size she pays $0.17 per ounce, and when she buys the 16- ounce size, she pays $0.14 per ounce. Given that there are three different prices per ounce of soft drink, the budget line will have two kinks in it, as illustrated below. Notice that at each kink, the slope of the budget line gets flatter (due to the decreasing cost per ounce relative to the “other good” on the vertical axis). 28
- Chapter 3: Consumer Behavior 8 12 16 Ounces of Soft Drink 10. Antonio buys 5 new college textbooks during his first year at school at a cost of $80 each. Used books cost only $50 each. When the bookstore announces that there will be a 10% increase in the price of new books and a 5% increase in the price of used books, Antonio’s father offers him $40 extra. a. What happens to Antonio’s budget line? Illustrate the change with new books on the vertical axis. In the first year he spends $80 each on 5 new books for a total of $400. For the same amount of money he could have bought 8 used textbooks. His budget line is therefore 80*New+50*Used=400. After the price change, new books cost $88, used books cost $52.5, and he has an income of $440. If he spends all of his income on new books, he can still afford to buy 5 new books, but can now afford to buy 8.4 used books if he buys only used books. The new budget line is 88*New+52.5*Used=440. The budget line has changed its slope and become flatter if we place used books on the horizontal axis. b. Is Antonio worse or better off after the price change? Explain. The first year he bought 5 books at a cost of $80 each for a total of $400. The new price of books is $88 and the cost of 5 new books is now $440. The $40 extra income will cover the price increase. Antonio is definitely not worse off since he can still afford the same number of new books. He may in fact be better off if he decides to switch to used books. 11. Consumers in Georgia pay twice as much for avocados as they do for peaches. However, avocados and peaches are equally priced in California. If consumers in both states maximize utility, will the marginal rate of substitution of peaches for avocados be the same for consumers in both states? If not, which will be higher? The marginal rate of substitution of peaches for avocados is the amount of avocados that a person is willing to give up to obtain one additional peach. When consumers maximize utility, they set their marginal rate of substitution equal to the 29
- Chapter 3: Consumer Behavior Ppeach price ratio, which in this case is . In Georgia, Pavocado = 2 Ppeach , which Pavocado Ppeach 1 means that when consumers are maximizing utility, MRS = = . In Pavocado 2 California, Pavocado = Ppeach , which means that when consumers are maximizing Ppeach 1 utility, MRS = = . The marginal rate of substitution is therefore not the Pavocado 1 same in both states, and will be higher in California. 12. Ben allocates his lunch budget between two goods, pizza and burritos. a. Illustrate Ben’s optimal bundle on a graph with pizza on the horizontal axis. This is the standard graph, where Ben’s budget line is linear and he consumes at the point where his indifference curve is tangent to his budget line. This places him on the highest possible indifference curve. b. Suppose now that pizza is taxed, causing the price to increase by 20%. Illustrate Ben’s new optimal bundle. When the price of pizza increases, the budget line will pivot inwards. This will shrink the size of Ben’s budget set and he will no longer be able to afford his old bundle. His new optimal bundle is where the indifference curve is tangent to his new budget line and this indifference curve is below his original indifference curve. c. Suppose instead that pizza is rationed at a quantity less than Ben’s desired quantity. Illustrate Ben’s new optimal bundle. Rationing the quantity of pizza that can be purchased will result in Ben not being able to choose his optimal bundle. He will have to choose a bundle on the budget line that is above his original bundle. This new bundle will have a lower level of utility. bur rit o ra t ioned bun dle origin al b un dle pizza 13. Brenda wants to buy a new car and has a budget of $25,000. She has just found a magazine that assigns each car an index for styling and an index for gas mileage. Each index runs from 1-10, with 10 representing either the most styling or the best gas mileage. 30
- Chapter 3: Consumer Behavior While looking at the list of cars, Brenda observes that on average, as the style index rises by one unit, the price of the car increases by $5,000. She also observes that as the gas mileage index rises by one unit, the price of the car increases by $2,500. a. Illustrate the various combinations of style (S) and gas mileage (G) that Brenda could select with her $25,000 budget. Place gas mileage on the horizontal axis. For every $5,000 she spends on style the index rises by one so the most she can achieve is a car with a style index of 5. For every $2,500 she spends on gas mileage, the index rises by one so the most she can achieve is a car with a gas mileage index of 10. The slope of her “budget line” is -1/2. b. Suppose Brenda’s preferences are such that she always receives three times as much satisfaction from an extra unit of styling as she does from gas mileage. What type of car will Brenda choose? If Brenda always receives three times as much satisfaction from an extra unit of styling as she does from an extra unit of gas mileage then she is willing to trade one unit of styling for three units of gas mileage, and still maintain the same level of satisfaction. This is her MRS or the slope of her indifference curves, which is constant. Since the MRS is 1/3 and the slope of her budget line is -1/2, Brenda will choose all styling. You can also compute the marginal utility per dollar for styling and gas mileage and note that styling will be higher. In the graph below, she will move up to the highest possible indifference curve where she chooses all styling and no gas mileage. st yling gas m ile age c. Suppose that Brenda’s marginal rate of substitution (of gas mileage for styling) was S equal to . What value of each index would she like to have in her car? 4G To find the optimal value of each index, set MRS equal to the price ratio of 1/2 and cross multiply to get S=2G. Now substitute into the budget 5000S+2500G=25000 to get G=2 and S=4. d. Suppose that Brenda’s marginal rate of substitution (of gas mileage for styling) was 3S equal to . What value of each index would she like to have in her car? G To find the optimal value of each index set MRS equal to the price ratio of 1/2 and cross multiply to get G=6S. Now substitute into the budget 5000S+2500G=25000 to get G=7.5 and S=1.25. 14. Connie has a monthly income of $200, which she allocates between two goods: meat and potatoes. 31
- Chapter 3: Consumer Behavior a. Suppose meat costs $4 per pound and potatoes cost $2 per pound. Draw her budget constraint. Let M = meat and P = potatoes. Connie’s budget constraint is $200 = 4M + 2P, or M = 50 - 0.5P. As shown in the figure below, with M on the vertical axis, the vertical intercept is 50. The horizontal intercept may be found by setting M = 0 and solving for P. Mea t 100 75 Bu dget Con st r a in t 50 a n d Ut ilit y Fu n ct ion 25 U = 100 P ot a t oes 25 50 75 100 125 b. Suppose also that her utility function is given by the equation u(M, P) = 2M + P. What combination of meat and potatoes should she buy to maximize her utility? (Hint: Meat and potatoes are perfect substitutes.) When the two goods are perfect substitutes, the indifference curves are linear. To find the slope of the indifference curve, choose a level of utility and find the equation for a representative indifference curve. Suppose u=50, then 2M+P=50, or M=25-0.5P. Therefore, Connie’s budget line and her indifference curves have the same slope. Connie’s utility is equal to 100 when she buys 50 pounds of meat and no potatoes or no meat and 100 pounds of potatoes. The indifference curve for U = 100 coincides with her budget constraint. Any combination of meat and potatoes along this line will provide her with maximum utility. c. Connie’s supermarket has a special promotion. If she buys 20 pounds of potatoes (at $2 per pound), she gets the next 10 pounds for free. This offer applies only to the first 20 pounds she buys. All potatoes in excess of the first 20 pounds (excluding bonus potatoes) are still $2 per pound. Draw her budget constraint. Assume that potatoes are on the horizontal axis. Connie’s budget constraint has a slope of –1/2 until Connie has purchased twenty pounds of potatoes, is then flat from 20 to 30 pounds of potatoes, since the ten next pounds of potatoes are free, and then has a slope of –1/2 until it intercepts the potato axis at 110. d. An outbreak of potato rot raises the price of potatoes to $4 per pound. The supermarket ends its promotion. What does her budget constraint look like now? What combination of meat and potatoes maximizes her utility? 32
- Chapter 3: Consumer Behavior With the price of potatoes at $4, Connie may buy either 50 pounds of meat or 50 pounds of potatoes, or some combination in between. See Figure 3.14.d. She maximizes utility at U = 100 at point A when she consumes 50 pounds of meat and no potatoes. This is a corner solution. Mea t 100 75 A Bu dget Con st r a in t 50 In differ en ce Cu r ve for U = 100 25 P ot a t oes 25 50 75 100 125 Figure 3.14.d 15. Jane receives utility from days spent traveling on vacation domestically (D) and days spent traveling on vacation in a foreign country (F), as given by the utility function U(D,F) =10DF. In addition, the price of a day spent traveling domestically is $100, the price of a day spent traveling in a foreign country is $400, and Jane’s annual travel budget is $4,000. a. Illustrate the indifference curve associated with a utility of 800 and the indifference curve associated with a utility of 1200. The indifference curve with a utility of 800 has the equation 10DF=800, or DF=80. Choose combinations of D and F whose product is 80 to find a few bundles. The indifference curve with a utility of 1200 has the equation 10DF=1200, or DF=120. Choose combinations of D and F whose product is 120 to find a few bundles. b. Graph Jane’s budget line on the same graph. If Jane spends all of her budget on domestic travel she can afford 40 days. If she spends all of her budget on foreign travel she can afford 10 days. c. Can Jane afford any of the bundles that give her a utility of 800? What about a utility of 1200? Yes she can afford some of the bundles that give her a utility of 800 as part of this indifference curve lies below the budget line. She cannot afford any of the bundles that give her a utility of 1200 as this whole indifference curve lies above the budget line. 33
- Chapter 3: Consumer Behavior d. Find Jane’s utility maximizing choice of days spent traveling domestically and days spent in a foreign country. The optimal bundle is where the slope of the indifference curve is equal to the slope of the budget line, and Jane is spending her entire income. The slope of the budget line is PD 1 − =− . PF 4 The slope of the indifference curve is MU D 10F F MRS = − =− =− . MU F 10D D Setting the two equal we get: F 1 = D 4 4F = D. We now have two equations and two unknowns: 4F = D 100D + 400F = 4000. Solving the above two equations gives D=20 and F=5. Utility is 1000. This bundle is on an indifference curve between the two you had previously drawn. 16. Julio receives utility from consuming food (F) and clothing (C) as given by the utility function U(F,C) = FC . In addition, the price of food is $2 per unit, the price of clothing is $10 per unit, and Julio’s weekly income is $50. a. What is Julio’s marginal rate of substitution of food for clothing when utility is maximized? Explain. Utility is maximized when MRS (food for clothing) equals PC/PF, the price ratio. Given that clothing is on the horizontal axis and food is on the vertical axis, then the price ratio is the slope of the budget line, which is price of clothing divided by the price of food or -5. b. Suppose instead that Julio is consuming a bundle with more food and less clothing than his utility maximizing bundle. Would his marginal rate of substitution of food for clothing be greater than or less than your answer in part a? Explain. In absolute value terms, the slope of his indifference curve at this non-optimal bundle is greater than the slope of his budget line. He is willing to give up more food than he has to at market prices to obtain one more unit of clothing. He will therefore find it optimal to give up some food in exchange for clothing. 34
- Chapter 3: Consumer Behavior food cu rr en t bu ndle opt im al b un dle clot h ing 17. The utility that Meredith receives by consuming food F and clothing C is given by u(F,C) = FC. Suppose that Meredith’s income in 1990 is $1,200 and the prices of food and clothing are $1 per unit for each. However, by 1995 the price of food has increased to $2 and the price of clothing to $3. Let 100 represent the cost of living index for 1990. Calculate the ideal and the Laspeyres cost-of-living index for Meredith for 1995. (Hint: Meredith will spend equal amounts on food and clothing with these preferences.) First, we need to calculate F and C, which make up the bundle of food and clothing which maximizes Meredith’s utility given 1990 prices and her income in 1990. Use the hint to simplify the problem: Since she spends equal amounts on both goods, PFF = PCC. Or, you can derive this same equation mathematically: With this utility function, MUC = ΔU/ΔC = F, and MUF = ΔU/ΔF = C. To maximize utility, Meredith chooses a consumption bundle such that MUF/MUC = PF/PC, which again yields PFF = PCC. From the budget constraint, we also know that: PF F +PC C = Y. Combining these two equations and substituting the values for the 1990 prices and income yields the system of equations: C = F and C + F = 1,200. Solving these two equations, we find that: C = 600 and F = 600. Laspeyres Index The Laspeyres index represents how much more Meredith would have to spend in 1995 versus 1990 if she consumed the same amounts of food and clothing in 1995 as she did in 1990. That is, the Laspeyres index for 1995 (L) is given by: L = 100 (Y′)/Y where Y’ represents the amount Meredith would spend at 1995 prices consuming the same amount of food and clothing as in 1990. In 1995, 600 clothing and 600 food would cost ($3)(600)+($2)(600)=$3000. Therefore, the Laspeyres cost-of-living index is: L = 100($3000/$1200) = 250. Ideal Index 35
- Chapter 3: Consumer Behavior The ideal index represents how much Meredith would have to spend on food and clothing in 1995 to get the same amount of utility as she had in 1990. That is, the ideal index for 1995 (I) is given by: I = 100(Y'')/Y, where Y'' = P'FF' + P'CC' = 2F' + 3C' where F' and C' are the amount of food and clothing that give Meredith the same utility as she had in 1990. F' and C' must also be such that Meredith spends the least amount of money at 1995 prices to attain the 1990 utility level. The bundle (F',C') will be on the same indifference curve as (F,C) so F'C'=FC=360,000 in utility. If Meredith’s income is adjusted in 1995 so that the bundle (F',C') is maximizing her utility given her income, then the indifference curve at this point will be tangent to the budget line with slope -(P'F/P'C), where P'F and P'C are the prices of food and clothing in 1995. Using MUF'/MUC' = PF'/PC' we know that 2F' = 3C'. We now have two equations: F'C'=360,000 and 2F' = 3C'. Solving for F' yields: F'[(2/3)F'] = 360,000 or F' = [( 3 / 2 ) 360 , 000 )] = 734.8. From this, we obtain C': C' = (2/3)F' = (2/3)734.8 = 489.9. In 1995, the bundle of 734.8 food and 489.9 clothing would cost $2939.60 and Meredith would still get 360,000 in utility. We can now calculate the ideal index: I = 100($2939.60/$1200) = 244.9. 36