14.7. 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.

ENGR.ECONOMIC ANALYSIS
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Chapter1: Making Economics Decisions
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i know you guys have a policy for answering 4 parts only so so B, C, D, E for me

**Section 4.3: Other Household Decisions**

---

**Figure 4.16: Income and Substitution Effects**

The diagram presents a graphical representation of income and substitution effects using a typical budget constraint and indifference curve analysis. 

### Explanation of the Diagram:

- **Axes:**
  - The vertical axis (\(y\)) represents the quantity of one good.
  - The horizontal axis (\(x\)) represents the quantity of another good.

- **Budget Lines:**
  - Initial budget line \(b_A\) intersects the vertical axis at \(y_A\) and the horizontal axis at \(x_A\).
  - Point \(A\) indicates the consumer's initial consumption bundle on budget line \(b_A\).
  - The new budget line \(b_B\) shows a parallel shift, reflecting a change in income or prices leading to point \(B\).
  - Budget line \(b_C\) is the final budget line, indicating another shift in either income or prices, with consumption point \(C\).

- **Indifference Curves:**
  - Indifference curves are shown curving inward, representing different levels of utility.
  - Each curve illustrates the consumer's preference given their budget constraints.

### Key Insights:

- **Income Effect:**
  - Observed when a change in income shifts the consumption point from \(A\) to \(B\).

- **Substitution Effect:**
  - Represented in the movement from \(B\) to \(C\), showing changes in consumption given an alteration in relative prices.

---

**Question (i):**

True or false: Since Ann and Bob have the same income level, they also must have the same level of consumer surplus.

---

This educational content specifically explores the dynamics of consumer choices through income and substitution effects, using graphical analysis to illustrate these economic concepts.
Transcribed Image Text:**Section 4.3: Other Household Decisions** --- **Figure 4.16: Income and Substitution Effects** The diagram presents a graphical representation of income and substitution effects using a typical budget constraint and indifference curve analysis. ### Explanation of the Diagram: - **Axes:** - The vertical axis (\(y\)) represents the quantity of one good. - The horizontal axis (\(x\)) represents the quantity of another good. - **Budget Lines:** - Initial budget line \(b_A\) intersects the vertical axis at \(y_A\) and the horizontal axis at \(x_A\). - Point \(A\) indicates the consumer's initial consumption bundle on budget line \(b_A\). - The new budget line \(b_B\) shows a parallel shift, reflecting a change in income or prices leading to point \(B\). - Budget line \(b_C\) is the final budget line, indicating another shift in either income or prices, with consumption point \(C\). - **Indifference Curves:** - Indifference curves are shown curving inward, representing different levels of utility. - Each curve illustrates the consumer's preference given their budget constraints. ### Key Insights: - **Income Effect:** - Observed when a change in income shifts the consumption point from \(A\) to \(B\). - **Substitution Effect:** - Represented in the movement from \(B\) to \(C\), showing changes in consumption given an alteration in relative prices. --- **Question (i):** True or false: Since Ann and Bob have the same income level, they also must have the same level of consumer surplus. --- This educational content specifically explores the dynamics of consumer choices through income and substitution effects, using graphical analysis to illustrate these economic concepts.
### 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 Marginal Rate of Substitution (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
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 Marginal Rate of Substitution (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
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