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CHAPTER 3
CONSUMER BEHAVIOR
EXERCISES
2. Draw the indifference curves for the following individuals’ preferences for two goods: hamburgers and beer.
a. Al likes beer but hates hamburgers. He always prefers more beer no matter how many hamburgers he has. For Al, hamburgers are a “bad.” His indifference curves slope upward and to the right rather than downward and to the left. For Al, U 1 is preferred to U 2 and U 2 is preferred to U 3. See figure 3.2a. If you instead assumed that hamburgers were a neutral good, then the indifference curves would be vertical and utility is increasing to the right as more beer is consumed.
b. Betty is indifferent between bundles of either three beers or two hamburgers. Her preferences do not change as she consumes any more of either food. Since Betty is indifferent between three beers and two burgers, an indifference curve connects these two points. Betty’s indifference curves are a series of parallel lines with slope of − 2 3. See figure 3.2b.
c. Chris eats one hamburger and washes it down with one beer. He will not consume an additional unit of one item without an additional unit of the other. For Chris, hamburgers and beer are perfect complements, i.e., he always wants to consume the goods in fixed proportions to each other. The indifference curves are L - shaped, with corners on a 45-degree line out of the origin. See figure 3.2c.
Hamburgers
Beer
U 3
U 2
U 1
Figure 3.2.a
Hamburgers
Beer
U 1 U 2 U 3
Figure 3.2.b
d. Doreen loves beer but is allergic to beef. Every time she eats a hamburger she breaks out in hives. For Doreen, hamburgers are not considered a “good” but rather a “bad,” and thus her preferred position is not upwards and to the right, but rather downward and to the right. For Doreen, U 1 is preferred to U 2 and U 2 is preferred to U 3. See figure 3.2d.
Hamburgers
Beer
U 1
U 2
U 3
Figure 3.2.c
First notice that as the size of the drink increases, the price eper ounce decreases.
When she buys the 8 ounce soft drink she pays
8 oz
= $0.19 per oz. When 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 in figure 3.4.
O unces of
Soft D rink
Figure 3.
5. Suppose Bill views butter and margarine as perfectly substitutable for each other.
a. Draw a set of indifference curves that describes Bill’s preferences for butter and margarine.
Butter
Margarine
U 1 U 2 U 3
Figure 3.5.a
b. Are these indifference curves convex? Why?
Convexity implies that a line segment connecting any two points on a curve lies above
the curve, i.e., the curve is “bowed inward.” Because the consumer considers butter and
margarine to be perfect substitutes, there is no diminishing marginal utility, and the resultant indifference curves are straight lines. Straight-line indifference curves are not strictly convex.
c. If butter costs $2 per package, while margarine costs only $1, and Bill has a $ budget to spend for the month, which butter-margarine market basket will he choose? Can you show this graphically? Let Bill’s income be represented by Y , the price of butter by PB , the quantity of butter by B , the price of margarine by PM , and the quantity of margarine by M. Then the general form of the budget constraint is: Y = PB B + PM M.
Substituting for the given values of Y , PB , and PM , we obtain the specific representation of Bill’s budget constraint: 20 = 2 B + 1 M , or B = 10 - 0.5 M. Because Bill is indifferent between butter and margarine, and the price of butter is greater than the price of margarine, Bill will only buy margarine. This is a corner solution , because the optimal choice occurs on an axis. In Figure 3.5.c Bill’s utility maximizing bundle is point A.
Butter
Margarine
U 1 U 2
U 3
L 1
A
Figure 3.5.c
6. Suppose that Jones and Smith have decided to allocate $1,000 per year on liquid refreshments in the form of alcoholic or nonalcoholic drinks. Jones and Smith differ substantially in their preferences for these two forms of refreshment. Jones prefers alcoholic to nonalcoholic drinks, while Smith prefers the nonalcoholic option.
a. Draw a set of indifference curves for Jones and a second set for Smith.
(1) If new and used texts are not substitutes for Antonio ( L -shaped indifference curves), then Antonio will be just as well off when the price of new texts rises and his father gives him $80 (= (60 - 50)8). (2) If he chooses to buy a few used texts in response to the relative price increase (given the extra $80), he will move to a higher indifference curve and will therefore be better off. See Figures 3.9.a and 3.9.b.
New Texts
All Other Goods (Including Used Texts)
U 1
L 1
L 2 L 1 reflects the price increase for texts and the extra $80.
Figure 3.9.a
New Texts
All Other Goods (Including Used Texts)
U 1
L 2 L 1
U 2
B
A
Figure 3.9.b
10. Suppose that Samantha and Jason both spend $24 per week on video and movie entertainment. When the prices of videos and movies are both $4, they both rent 3 videos and buy 3 movie tickets. Following a video price war and an increased cost of movie tickets, the video price falls to $2 and the movie ticket increases to $6. Samantha now rents 6 videos and buys 2 movie tickets; Jason, however, buys 1 movie ticket and rents 9 videos.
a. Is Samantha better off or worse off after the price change?
Samantha’s original point of utility maximization may be represented by point A on U 1 in Figure 3.10.a. With the new prices, Samantha could still afford to choose bundle A :
$24 = $2(3 videos) + $6 (3 movies). The fact that she chose bundle B reveals she has obtained a higher level of utility, U 2. See Figure 3.10.a.
Videos
Movies
B
A
U 1
U 2
L 2
L 1
Figure 3.10.a
b. Is Jason better off or worse off?
Similarly, Jason must also be better off.
11. Connie Consumer has a monthly income of $200 which she allocates among two goods: meat and potatoes.
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 = 4 M + 2 P , or M = 50 - 0.5 P. As shown in Figure 3.11.a, 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. Meat
Potatoes
U = 100
Budget Constraint and Utility Function
The indifference curves are convex.
b. Suppose that food costs $1 a unit, clothing costs $3 a unit, and Jane has $12 to spend on food and clothing. Graph the budget line that she faces. The budget constraint is: Y = PF F + PC C , or
12 = 1 F + 3 C , or C = 4 −
1 3
F.
See Figure 3.12.a.
Clothing
Food
U = 12
U = 24
Figure 3.12.a
c. What is the utility-maximizing choice of food and clothing? (Hint: Solve the problem graphically.) The highest level of satisfaction occurs where the budget line is tangent to the highest indifference curve. In Figure 3.12.a this is at the point F = 6 and C = 2. To check this answer, note that it exhausts Jane’s income, 12 = 6 PF + 2 PC. Also, this bundle yields a satisfaction of 12, as (6)(2) = 12. See Figure 3.12.a.
d. What is the marginal rate of substitution of food for clothing when utility is maximized? At the utility-maximizing level of consumption, the slope of the indifference curve is equal to the slope of the budget constraint. Since the MRS is equal to the negative slope of the indifference curve, the MRS in this problem is equal to one-third. Thus, Jane would be willing to give up one-third of a unit of clothing for one unit of food.
e. Suppose that Jane buys 3 units of food and 3 units of clothing with her $12 budget. Would her marginal rate of substitution of food for clothing be greater or less than 1/3? Explain. If Jane buys 3 units of food for $1.00 per unit and 3 units of clothing for $3.00 per unit, she would spend all her income. However, she would obtain a level of satisfaction of only 9, which represents a sub-optimal choice. At this point, the MRS is greater than one-third, and thus, at the prices she faces, she would welcome the opportunity to give up clothing to get more food. She is willing to trade clothing for food until her MRS is equal to the ratio of prices. See Figure 3.12.e.
Clothing
Food
U = 12
U = 9
Figure 3.12.e
