Appendix: Indifference Curves Chapter APPENDIX CHECKLIST The appendix uses indifference curves and budget lines to derive a demand curve. Indifference curves An indifference curve is a line that shows combinations of goods among which a consumer is indifferent. All combinations above the indifference curve are preferred to those on the indifference curve and all combinations on the indifference curve are preferred to those below the indifference curve. The marginal rate of substitution, MRS, is the rate at which the consumer will give up the good y (the good measured on the y axis) to get more of the good x (the good measured on the x axis) and at the same time remain on the same indifference curve. The magnitude of the slope of the indifference curve equals the marginal rate of substitution. The marginal rate of substitution diminishes as the consumer moves along an indifference curve, increasing consumption of the good measured on the x axis and decreasing consumption of the good measured on the y axis. The consumer equilibrium is at the best affordable point so that the consumer is on the budget line, is on the highest attainable indifference curve, and has a marginal rate of substitution equal to the relative price of the two goods. We can use the indifference curve model to generate a demand curve. CHECKPOINT 1 Indifference curves. Additional Practice Problems 1 1. Figure A12.1 shows one of Maria s indifference curves between ice cream cones and milkshakes. Lightly shade combinations of cones and milkshakes that are more preferred to those on the indifference curve. More heavily shade combinations that are less preferred to those on the indifference curve. 2. In Figure A12.1, what is Maria s marginal rate of substitution when she is consuming 4 ice cream cones and 2 milkshakes?
186 Part 4. A CLOSER LOOK AT DECISION MAKERS through the combination of 4 ice cream cones and 2 milkshakes and touches the indifference curve at only that point. The magnitude of the slope of this line is 1/2 of a milkshake per ice cream cone, so Maria s marginal rate of substitution is 1/2 of a milkshake per ice cream cone. This marginal rate of substitution means that when Maria is consuming 4 ice cream cones and 2 milkshakes, she is willing to give up only 1/2 of a milkshake in order to get another ice cream cone. 3. Figure A12.2 shows Maria s budget line and several of her indifference curves. a. What is Maria s best affordable point? b. If Maria consumed 3 milkshakes and 2 ice creams, how would her marginal rate of substitution between cones and shakes compare to the relative price of cones and shakes? Solutions to Additional Practice Problems 1 1. Figure A12.3 shows that all combinations above the indifference curve are more preferred to those on it and all combinations below the indifference curve are less preferred to those on it. 2. Maria s marginal rate of substitution equals the magnitude of the slope of the indifference curve. Use the straight line that goes 3a. Figure A12.4 shows Maria s best affordable point. This point is on Maria s budget line and also on the highest attainable indifference curve, I3. At this point, Maria s marginal rate of substitution between cones and shakes equals the relative price of cones and shakes. 3b. If Maria consumed 3 milkshakes and 2 ice cream cones, she would be on indifference curve I3. The slope of this indifference curve at that point equals Maria s marginal rate of substitution. So Maria s marginal rate of substitution between cones and shakes at this consumption possibility is greater than the relative price of cones and shakes. Self Test 1 Fill in the blanks An is a curve that shows combinations of goods among which a consumer is indifferent. A consumer prefers being on a (lower;
Appendix 12. Indifference Curves 187 higher) indifference curve. The magnitude of the slope of an indifference curve equals the. If an indifference curve is steep, the marginal rate of substitution is (high; low). The best affordable point occurs at the point on the budget line where the magnitude of the slope of the budget line (is greater than; equals; is less than) the marginal rate of substitution. True or false 1. A consumer is indifferent among combinations of goods that are on his or her indifference curve. 2. A consumer is indifferent among combinations on different indifference curves. 3. The marginal rate of substitution is the rate at which a person will give up the good measured on the y axis to get more of the good measured on the x axis and at the same time remain indifferent. 4. The only requirement for a consumer to be at his best affordable point is that the consumer be on the budget line. 5. Along a demand curve that is derived using indifference curves, the quantity of the good demanded increases when the price rises. Multiple choice 1. An indifference curve is a line that shows combinations of goods among which a consumer a. prefers one over the other. b. places no value on any of the items. c. can afford to buy all the combinations. d. is indifferent. e. believes that all combinations have the same marginal rate of substitution. 2. What is the difference between a budget line and an indifference curve? a. One is measured in dollars while the other is measured in units of goods. b. One shows what is possible while the other shows what is preferred. c. One shows a positive relationship and the other shows a negative relationship. d. The budget line is bowed in toward the origin and the indifference curves are linear. e. There is no difference. 3. In a preference map, consumption combinations on higher indifference curves a. always cost more than any combination on a lower indifference curve. b. always are preferred to combinations on lower indifference curves. c. always cost less than any combination on a lower indifference curve. d. always are less preferred than combinations on lower indifference curves. e. are sometimes more preferred, sometimes less preferred, and sometimes equally preferred than any combination on a lower indifference curve. 4. The marginal rate of substitution for the good on the horizontal axis is a. the consumer surplus. b. the same as the consumer s budget line. c. equal to the magnitude of the slope of the indifference curve. d. equal to the magnitude of the slope of the consumer surplus curve. e. equal to 1.0 if the indifference curves are linear.
188 Part 4. A CLOSER LOOK AT DECISION MAKERS 17. When the consumer whose indifference curve is illustrated in the figure consumes more tacos, the marginal rate of substitution is of slices of pizza for tacos a. stays the same. b. increases. c. decreases. d. changes randomly. e. More information is needed about the consumer s budget line to determine how the marginal rate of substitution changes. 5. When the consumer whose indifference curve is illustrated in the figure above is consuming 3 slices of pizza and 3 tacos per week, the marginal rate of substitution is of pizza per taco a. 3 slices b. 9 slices c. 0 slices d. 1 slice e. More information is needed about the consumer s budget line to determine the marginal rate of substitution. 6. When the consumer whose indifference curve is illustrated in the figure above is consuming 1½ slices of pizza and 6 tacos per week, the marginal rate of substitution is of pizza per taco a. 6 slices b. 1½ of a slice c. 1/4 of a slice d. 1 slice e. More information is needed about the consumer s budget line to determine the marginal rate of substitution. 18. At her best affordable point, Kris i. is on her budget line. ii. is on the highest attainable indifference curve. iii. has a marginal rate of substitution equal to the relative price of the goods. a. i only. b. ii only. c. iii only. d. i, and ii. e. i, ii, and iii. 19. When Bo is at his best affordable consumption point, his marginal rate of substitution is a. greater than the relative price. b. equal to the relative price. c. less than the relative price. d. is equal to one. e. maximized. 10. To derive a demand curve using the indifference curve model, you must change the a. consumer s preferences. b. consumer s income. c. price of one good, holding the price of the other good and income constant. d. price of both goods simultaneously but by different amounts. e. price of both goods simultaneously but by the same percentage.
Appendix 12. Indifference Curves 189 Complete the graph a. Initially, the price of a movie is $10 and the price of a DVD is also $10. Brent s income is $40 per month. Draw Brent s budget line in Figure A12.7. How many DVDs does Brent buy per month? b. DVDs fall in price to $5. Brent s income remains at $40 and the price of a movie remains at $10. Draw Brent s new budget line in Figure A12.7. How many DVDs does Brent now buy per month? 1. For entertainment, Laura goes to the movies and buys magazines. Laura devotes a monthly budget of $24 per month for entertainment. The price of a movie is $8 and the price of a magazine is $4. a. In Figure A12.6, draw Laura s budget line and label it BL1. b. Suppose magazines rise in price to $6. Draw Laura s new budget line in Figure A12.6 and label it BL2. c. Finally suppose that magazines fall in price to $3. Draw Laura s new budget line in Figure A12.6 and label it BL3. 2. Brent goes to the movies and buys DVDs. Figure A12.7 shows two of his indifference curves. c. You have two points on Brent s demand curve for DVDs. What are these two points? Assuming Brent s demand curve is linear, plot these points in Figure A12.8 and draw his demand curve. How does a fall in the price of a DVD affect the quantity of DVDs Brent buys? Short answer and numeric questions 1. What is the defining characteristic of the points on an indifference curve? 2. If Alberto s marginal rate of substitution between shirts and pants is 2 shirts per pair of pants, what does this number mean? As Alberto obtains more pants, what happens to his marginal rate of substitution? 3. What is the difference between an indifference curve and a demand curve?
190 Part 4. A CLOSER LOOK AT DECISION MAKERS SELF TEST ANSWERS CHECKPOINT 1 Fill in the blanks An indifference curve is a curve that shows combinations of goods among which a consumer is indifferent. A consumer prefers being on a higher indifference curve. The magnitude of the slope of an indifference curve equals the marginal rate of substitution. If an indifference curve is steep, the marginal rate of substitution is high. The best affordable point occurs at the point on the budget line where the magnitude of the slope of the budget line equals the marginal rate of substitution. True or false 1. True; page 313 2. False; page 313 3. True; page 314 4. False; page 315 5. False; page 317 Multiple choice 11. d; page 313 12. b; page 313 13. b; page 313 14. c; page 314 15. d; page 315 16. c; page 315 17. c; page 314 18. e; page 315 19. b; page 316 10. c; page 317 1. a. Figure A12.10 shows the budget line. Brent buys 2 DVDs a month; page 316. b. Figure A12.10 shows the new budget line. Brent now buys 4 DVDs a month; page 316. Complete the graph 1. a. Figure A12.9 shows the budget line;. page 317. b. Figure A12.9 shows the budget line;. page 317. c. Figure A12.9 shows the budget line;. page 317.
Appendix 12. Indifference Curves 191 c. One point on Brent s demand curve is from part (a). When the price of a DVD rental is $10, the quantity of DVDs Brent buys is 2 a month. The other point is from part (b). When the price of a DVD is $5, Brent buys 4 DVDs a month. Figure A12.11 plots these two points and draws Brent s demand curve. A fall in the price of a DVD increases the quantity of DVDs Brent buys; page 317. Short answer and numeric questions 1. The defining characteristic of points on an indifference curve is that the consumer is indifferent about which combination he or she consumes. Of all the possible combinations on an indifference curve, the consumer does not care which combination he or she receives; page 313. 2. The marginal rate of 2 shirts per pair of pants means that Alberto is willing to give up 2 shirts in order to get another pair of pants. As Alberto obtains more pants, his marginal rate of substitution decreases; page 314. 3. An indifference curve and a demand curve are quite different. An indifference curve shows combinations of goods among which a consumer is indifferent. A demand curve shows the relationship between the price of a good and the quantity demanded. An indifference curve, along with a budget line, can be used to derive a demand curve. Hence the demand curve can be viewed as a result of using an indifference curve; pages 313 and 317.