4.7. Ann and Bob. Ann and Bob have the same income level and 4.3. OTHER HOUSEHOLD DECISIONS 161 face the same prices of goods x and y. The price of x is 4 and the price of y is 8. (a) At the current consumption level, Ann's MRS is equal to 1. In order to improve her situation, should Ann increase or decrease her consumption of x? (b) At the current consumption level, Bob's MRS is equal to 0.5. Is Bob's current consumption bundle optimal or suboptimal? (c) Suppose that, after adjusting their consumption levels, both Ann and Bob choose their optimal levels of x and y. Ann chooses x = 5 and Bob chooses x = 4. True or false: Ann and Bob have the same MRS at their current consumption levels. (d) Continuing with the assumptions of the previous question. True or false: If Ann exchanges 1 unit of x for 2 units of y, then both Ann and Bob become better off. (e) Bob's income increased and his consumption of x changed from 4 to 4.5. True or false: x is an inferior good for Bob. (f) Suppose Bob's consumption choices are always optimal. We observe that, when the price of x increased from 4 to 6, Bob's consumption of x decreased from x = 4 to x = 3. True or false: The income effect of the price increase is necessarily negative. Suppose Ann's consumption choices are always optimal. We observe that, when the price of x increased from 4 to 6, Ann's consumption of x increased from x = 5 to x = 6. True or false: Ann's behavior necessarily contradicts economic theory. (h) Suppose Ann's consumption choices are always optimal. We observe that, when the price of x increased from 4 to 6, Ann's consumption of x increased from x = 5 to x = 6. True or false: The income effect of the price change on Ann's consumption of x must be positive.
4.7. Ann and Bob. Ann and Bob have the same income level and 4.3. OTHER HOUSEHOLD DECISIONS 161 face the same prices of goods x and y. The price of x is 4 and the price of y is 8. (a) At the current consumption level, Ann's MRS is equal to 1. In order to improve her situation, should Ann increase or decrease her consumption of x? (b) At the current consumption level, Bob's MRS is equal to 0.5. Is Bob's current consumption bundle optimal or suboptimal? (c) Suppose that, after adjusting their consumption levels, both Ann and Bob choose their optimal levels of x and y. Ann chooses x = 5 and Bob chooses x = 4. True or false: Ann and Bob have the same MRS at their current consumption levels. (d) Continuing with the assumptions of the previous question. True or false: If Ann exchanges 1 unit of x for 2 units of y, then both Ann and Bob become better off. (e) Bob's income increased and his consumption of x changed from 4 to 4.5. True or false: x is an inferior good for Bob. (f) Suppose Bob's consumption choices are always optimal. We observe that, when the price of x increased from 4 to 6, Bob's consumption of x decreased from x = 4 to x = 3. True or false: The income effect of the price increase is necessarily negative. Suppose Ann's consumption choices are always optimal. We observe that, when the price of x increased from 4 to 6, Ann's consumption of x increased from x = 5 to x = 6. True or false: Ann's behavior necessarily contradicts economic theory. (h) Suppose Ann's consumption choices are always optimal. We observe that, when the price of x increased from 4 to 6, Ann's consumption of x increased from x = 5 to x = 6. True or false: The income effect of the price change on Ann's consumption of x must be positive.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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i know you guys have a policy of only answering 4 parts per question so do F, G, H, I
Transcribed Image Text:**4.7. Ann and Bob**
Ann and Bob have the same income level and face the same prices of goods \( x \) and \( y \). The price of \( x \) is 4 and the price of \( y \) is 8.
(a) At the current consumption level, Ann’s MRS is equal to 1. In order to improve her situation, should Ann increase or decrease her consumption of \( x \)?
(b) At the current consumption level, Bob’s MRS is equal to 0.5. Is Bob’s current consumption bundle optimal or suboptimal?
(c) Suppose that, after adjusting their consumption levels, both Ann and Bob choose their optimal levels of \( x \) and \( y \). Ann chooses \( x = 5 \) and Bob chooses \( x = 4 \). True or false: Ann and Bob have the same MRS at their current consumption levels.
(d) Continuing with the assumptions of the previous question. True or false: If Ann exchanges 1 unit of \( x \) for 2 units of \( y \), then both Ann and Bob become better off.
(e) Bob’s income increased and his consumption of \( x \) changed from 4 to 4.5. True or false: \( x \) is an inferior good for Bob.
(f) Suppose Bob’s consumption choices are always optimal. We observe that, when the price of \( x \) increased from 4 to 6, Bob’s consumption of \( x \) decreased from \( x = 4 \) to \( x = 3 \). True or false: The income effect of the price increase is necessarily negative.
(g) Suppose Ann’s consumption choices are always optimal. We observe that, when the price of \( x \) increased from 4 to 6, Ann’s consumption of \( x \) increased from \( x = 5 \) to \( x = 6 \). True or false: Ann’s behavior necessarily contradicts economic theory.
(h) Suppose Ann’s consumption choices are always optimal. We observe that, when the price of \( x \) increased from 4 to 6, Ann’s consumption of \( x \) increased from \( x = 5 \) to \( x = 6 \). True or false: The income effect of the price change on Ann’s consumption of \( x \) must be positive.
![### 4.3. Other Household Decisions
#### Figure 4.16: Income and Substitution Effects
The image contains a graph illustrating the concepts of income and substitution effects with respect to consumer choices. The graph is set in a typical x-y coordinate plane.
- **Axes**:
- The x-axis represents the quantity of good x.
- The y-axis represents the quantity of good y.
- **Budget Lines**:
- The graph includes three budget lines:
- \( b_A \)
- \( b_B \)
- \( b_C \)
These lines represent different levels of affordability for a consumer given changes in income or prices.
- **Indifference Curves**:
- There are indifference curves intersecting with the budget lines at points \( A \), \( B \), and \( C \).
- Indifference curves represent combinations of goods that provide the consumer the same level of satisfaction or utility.
- **Points of Interest**:
- **Point A**: The initial consumption bundle where the consumer starts.
- **Point B**: The consumption bundle after a price change, showing how the consumer substitutes one good for the other.
- **Point C**: The consumption bundle after an income change, showing the new level of utility.
- **Vertical Lines**:
- These lines illustrate different quantities of x and y chosen at the intersections with budget lines and indifference curves:
- \( x_A \), \( x_B \), \( x_C \)
- \( y_A \), \( y_B \)
**Question for Analysis**:
(i) True or false: Since Ann and Bob have the same income level, they also must have the same level of consumer surplus.
[Analysis of consumer behavior through this graph can provide insight into how consumers adjust their consumption in response to changes in prices and income, reflecting the income and substitution effects in microeconomic theory.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F29484458-c49a-4784-8582-6da2b7d9fbab%2F9018f9b6-a921-43db-ad6b-76cc2516d378%2F0715q5i_processed.png&w=3840&q=75)
Transcribed Image Text:### 4.3. Other Household Decisions
#### Figure 4.16: Income and Substitution Effects
The image contains a graph illustrating the concepts of income and substitution effects with respect to consumer choices. The graph is set in a typical x-y coordinate plane.
- **Axes**:
- The x-axis represents the quantity of good x.
- The y-axis represents the quantity of good y.
- **Budget Lines**:
- The graph includes three budget lines:
- \( b_A \)
- \( b_B \)
- \( b_C \)
These lines represent different levels of affordability for a consumer given changes in income or prices.
- **Indifference Curves**:
- There are indifference curves intersecting with the budget lines at points \( A \), \( B \), and \( C \).
- Indifference curves represent combinations of goods that provide the consumer the same level of satisfaction or utility.
- **Points of Interest**:
- **Point A**: The initial consumption bundle where the consumer starts.
- **Point B**: The consumption bundle after a price change, showing how the consumer substitutes one good for the other.
- **Point C**: The consumption bundle after an income change, showing the new level of utility.
- **Vertical Lines**:
- These lines illustrate different quantities of x and y chosen at the intersections with budget lines and indifference curves:
- \( x_A \), \( x_B \), \( x_C \)
- \( y_A \), \( y_B \)
**Question for Analysis**:
(i) True or false: Since Ann and Bob have the same income level, they also must have the same level of consumer surplus.
[Analysis of consumer behavior through this graph can provide insight into how consumers adjust their consumption in response to changes in prices and income, reflecting the income and substitution effects in microeconomic theory.]
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VIEWStep 3: g. Determine whether Ann behavior necessarily contradict economic theory
VIEWStep 4: h. Determine whether the income effect of Ann's consumption choices are positive.
VIEWStep 5: i. Determine whether Ann and Bob will have similar consumer surplus
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