Chapter
Appendix:
Indifference
Curves
APPENDIX OUTLINE
1. Indifference curves
A. An Indifference Curve
B. Marginal Rate of Substitution
C. Consumer Equilibrium
D. Deriving the Demand Curve
APPENDIX ROADMAP
Where We Are
The appendix to Chapter 11 takes a different approach to explaining consumer behavior by using indifference curves. Instead of equating marginal utility per dollar spent across all goods, consumers achieve consumer equilibrium by de‐
ciding whether different combinations of goods make them better off, worse off, or leave them indifferent. The combina‐
tions among which consumers are indifferent lie along an indifference curve and the consumer equilibrium is the com‐
bination that is on the budget line and on the highest attain‐
able indifference curve. A downward‐sloping demand curve is derived using indifference curves and budget lines. Where We’ve Been
Chapter 11 used marginal utility theory to study the con‐
sumer’s equilibrium choice of goods and services as well as to derive a consumer’s downward‐sloping demand curve. Where We’re Going
The next chapter starts our examination of firms by studying their production and how production relates to costs. None 290
Part 4 . A CLOSER LOOK AT DECISION MARKERS
of the material in this appendix is used in Chapter 12 or any of the following chapters. IN THE CLASSROOM
Class Time Needed
Depending on your class’s mathematical sophistication, you might decide to make this appendix optional. If you cover it in class, you should spend between one to one and a half class sessions on it. Appendix 11 . Indifference Curves
291
CHAPTER LECTURE
A11.1 Indifference Curves
An Indifference Curve
•
An indifference curve is a line that shows combinations of goods among which a con‐
sumer is indifferent. The figure to right shows three of a person’s indifference curves between pizza and books. •
The consumer is indifferent among all the points on any particular in‐
difference curve. •
The consumer prefers points above any particular indifference curve to points on the curve. And the con‐
sumer prefers points on the indif‐
ference curve to points below the curve. So in the figure, the con‐
sumer prefers any point on indif‐
ference curve I2 to any point on I1 and any point on I1 to any point on I0. Marginal Rate of Substitution
•
The marginal rate of substitution, (MRS) is the rate at which a person will give up good y (the good measured on the y‐axis) to get an additional unit of good x (the good meas‐
ured on the x‐axis) and at the same time remaining indifferent (remain on the same indif‐
ference curve). •
•
The magnitude of the slope of the indifference curve at any point measures the mar‐
ginal rate of substitution between the goods. If the indifference curve is steep, the MRS is high; if the indifference curve is flat, the MRS is small. The diminishing marginal rate of substitution is the general tendency for a person mar‐
ginal rate of substitution to diminish (so that the consumer is willing to give up less of good y to get one unit of good x, and at the same time remain indifferent) moving down along the indifference curve, increasing consumption of the good measured on the x‐axis and decreasing consumption of the good measured on the y‐axis. Part 4 . A CLOSER LOOK AT DECISION MARKERS
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Consumer Equilibrium
•
•
•
•
The consumer’s goal is to buy the affordable combination of goods and services that make the consumer as well off as possible. A household’s consumption choices are constrained by its income and the prices of the goods and services available. The budget line describes the limits to its consumption choices. The consumer will select his or her best affordable point. This point • is on the budget line, • is on the highest attainable indif‐
ference curve, • has a marginal rate of substitution between the two goods equal to the relative price of the two goods. The figure shows the best affordable point using the budget line and the indifference curves in the previous figures. At the best affordable point, the person buys 3 books and 2 pizzas per month. Deriving the Demand Curve
•
•
When the price of the good on the x‐axis falls, the budget line rotates around the y‐axis intercept and becomes flatter. The person moves to a new consumption point. The new consumption bundle satisfies all three properties: It is on the new budget line, it is on the highest attainable indifference curve, and the MRS equals the slope of the new budget line. When the price of a good changes, tracking the change in the quantity of the good consumed reveals the demand curve for that good. The demand curve will slope downward, show‐
ing that an increase in the price of a good decreases the quantity the consumer demands. Many economists have studied the infamous potato famine in Ireland in the mid‐19th cen‐
tury in search of the elusive “upward‐sloping demand curve.” Indeed, when food became even scarcer than usual in that poverty stricken country, historical records indicate that Irish families consumed a greater quantity of potatoes as the market price of potatoes in‐
creased. Many economists were misled into thinking they had found historical evidence of the world’s first recorded positively‐sloped demand curve! However, they failed to re‐
member that it is the relative price of potatoes that is tracked on the demand curve for pota‐
toes, not the money price. The money price of potatoes rose more slowly than the prices of other foods. This change lowered the relative price of potatoes to Irish families and so the quantity they consumed increased, in accord with the law of demand. Appendix 11 . Indifference Curves
Lecture Launchers
1. Students need to be told why they are studying indifference curves. Indeed, many students think indifference curves impractical and so are less than eager to study them. Motivation is necessary! One way to motivate students is by pointing out that the material will be on their test. But that is perhaps not the best way. Launch your lecture on indifference curves by reminding students that economists are social scientists. As social scientists, we are in‐
terested in humans and their behavior. Tell your students that the indiffer‐
ence curve theory you will present is one way economists have of studying people’s behavior. Point out to them that indifference curves might not seem as “practical” as, say, elasticity, but not everything a scientist does has immediate practicality. 2. Emphasize to the students the meaning behind the tangency point between the indifference curve and the budget line: •
•
•
•
The marginal rate of substitution (MRS) shows the consumer’s willing‐
ness to give up one good to get more of the other good. The relative price of the two goods shows what the consumer must give up of one good to get more of the other good. When a consumer equates the marginal rate of substitution (MRS) with the relative price ratio, he or she leaves no unrealized gains from substi‐
tuting one good for another. The consumer is just willing to give up what he or she must give up, and there are no unrealized gains from substituting one good for an‐
other. Land Mines
1. The most dangerous error students can make in this appendix is to think that the indifference curve is the same as the demand curve. This error arises because both slope downward and both have the quantity of a good measured along the x‐axis. Be sure to stress that they are different. Point out that the indifference curve is truly more basic because we use indifference curves to derive the demand curve. Hence an indifference curve and a de‐
mand curve are quite different curves. 293
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ANSWERS TO APPENDIX CHECKPOINT EXERCISES
1a. The relative price of cola is ($3 a can of cola) ÷ ($3 a bag of popcorn), which is 1 bag of popcorn per can of cola. 1b. The opportunity cost of a can of cola is the same as its relative price, 1 bag of popcorn per can of cola. 1c. The budget line is in Figure A11.1. 1d. Sara buys 2 bags of popcorn and 2 cans of soda because that is the combination of popcorn and soda that is on her budget line and on the highest indifference curve. 1e. The marginal rate of substitution is equal to the slope of the budget line, 1 bag of popcorn per can of cola. 2a. Sara buys 1 bag of popcorn and 6 cans of soda because that is the combination of popcorn and soda that is on her budget line and on the highest indifference curve. 2b. One point on Sara’s demand curve is from the answer to exercise 1 part (d): when the price of a can of cola is $3, the quantity Sara demands is 2 cans. The other point on the demand curve comes from part (a) of this question, that when the price of a can of cola is $1.50, the quantity Sara demands is 6 cans. 3a. The relative price of a bottle of root beer is ($5 a bottle of root beer) ÷ ($10 a CD), which is 1/2 of a CD per bottle of root beer. 3b. The opportunity cost of a bottle of root beer is the same as its relative price, 1/2 of a CD per bottle of root beer. 3c. The budget line is in Figure A11.2. 3d. Marc buys 2 bottles of root beer and 1 CD because that is the combination that is on his budget line and on the highest indifference curve. 3e. The marginal rate of substitution is equal to the slope of the budget line, 2 bottles of root beer per CD. 4a. Marc now buys 3 CDs and 1 bottle of root beer. 4b. One point on Marc’s demand curve for CDs comes from the answer to exercise 3, part (d), Appendix 11 . Indifference Curves
that when the price of a CD is $10, the quantity Marc demands is 1 CD. An‐
other point come from the answer to part (a) of this question, that when the price of a CD is $5, the quantity Marc demands is 3 CDs. 5a. If the sales tax is replaced with a consumption tax, the relative price of food rises and the relative price of a haircut falls. 5b. Assuming the sales tax and consumption tax are the same rate, the budget line rotates inward around a fixed haircut intercept. The price of a haircut does not change but the price of a unit of food increases. 5c. If the relative price of food rises and the relative price of a haircut falls, most consumers buy more haircuts and less food. 5d. The type of tax that is best for the consumer depends on the consumer’s preferences. If the consumer prefers food to haircuts, the sales tax is better. If the consumer prefers haircuts, the consumption tax is better. 6a. An increase in income allows Jim to spend more money on all goods. As‐
suming all the goods Jim buys are normal goods, Jim buys more housing, food, and clothing. The fact that vacation travel rises in price makes Jim’s purchases of this good ambiguous. His higher income leads Jim to spend more on vacation travel but the higher relative price leads Jim to consume less vacation travel. 6b. Depending on his preferences, Jim might be better off, but we cannot say for sure. For instance, if prior to the changes Jim spent, say, $1 on vacation travel and the rest of his income on the other goods, almost certainly Jim is better off. But, if prior to the changes Jim spent $2,999 on vacation travel and the rest of his income on the other goods, than almost surely Jim is worse off. 6c. If all prices rise by 50 percent while Jim’s income increases by 33 percent, Jim’s budget line shifts inward and Jim decreases his purchases. Because his budget line shifted inward, signaling a decrease in Jim’s consumption possibilities, Jim is worse off. 6d. Your students’ answers will not be identical to the answer that follows, but they should be similar. Figure A11.3 divides Jim’s purchases into vacation travel and all other goods. (The slope of the budget line is arbitrary; your stu‐
dents’ budget lines will have different slopes.) The 50 percent increase in prices combined with only a 33 percent increase in income shifts Jim’s budget line inward. The slope does not change. Assuming that both goods are normal 295
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goods, the figure shows that Jim decreases his purchases of vacation travel and of the other goods as he moves from point A to point B. ADDITIONAL EXERCISES FOR ASSIGNMENT
Questions
Appendix: Indifference Curves
1. Why are both a budget line and an indifference curve required to determine the consumer’s equilibrium? 2. How does an increase in income affect the budget line? The indifference curves? 3. Suppose a poor person and rich person like lobster equally. How do their indifference curves differ? Why does the rich person consume more lobster than the poor person? Answers
Appendix: Indifference Curves
1. The budget line shows affordable combinations of goods and services. The indifference curves show the consumer’s preferences. The consumer will se‐
lect the affordable combination that he or she most prefers. Intuitively, a budget line is similar to a menu: it shows what is available. However, what a consumer chooses to consume from a menu depends on the consumer’s preferences. For instance, a restaurant might offer liver on the menu, but if a diner hates liver, the diner will not order it. It takes both the menu, which shows what is available, and the consumer’s preferences, which show what the consumer likes to determine what the consumer se‐
lects. 2. An increase in income shifts the budget line outward and does not change its slope. An increase in income has no effect on the indifference curves. Al‐
though the consumer moves to a new indifference curve, that indifference curve existed all along, but until the increase in income, had been unafford‐
able. 3. Indifference curves capture the consumer’s preferences. So if a poor person likes lobster as much as a rich person, their indifference curves are the same. The poor person buys less lobster than the rich person because their budget lines differ. It takes both preferences and the budget line to deter‐
mine what people consume.