Refer to the graph below: Units of good Y 30 14 0 A 24 B U₂ 40 Units of good X The price of X is $30 and the price of Y is $60. If U₁ is the highest level of utility the consumer can achieve, what is the consumer's income?
Refer to the graph below: Units of good Y 30 14 0 A 24 B U₂ 40 Units of good X The price of X is $30 and the price of Y is $60. If U₁ is the highest level of utility the consumer can achieve, what is the consumer's income?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![### Graph Explanation
The graph presents two axes labeled X and Y, representing "Units of good X" and "Units of good Y" respectively. The X-axis ranges from 0 to 40 units, while the Y-axis ranges from 0 to 30 units.
#### Key Elements of the Graph:
- **Budget Line**: The straight line with endpoints touching the axes, indicating the combinations of goods X and Y that the consumer can purchase given their income. The slope of this line represents the trade-off between the two goods.
- **Indifference Curves (U₁ and U₂)**:
- **U₁**: An indifference curve showing a lower level of utility that the consumer can achieve.
- **U₂**: A higher indifference curve that is unattainable given the current budget constraint.
- **Points A and B**:
- **Point A**: Lies on the indifference curve U₁ and the budget line, indicating the optimal choice of goods that the consumer can afford while maximizing utility at this level.
- **Point B**: Lies on the higher indifference curve U₂ but outside the budget line, indicating a combination of goods that provides more utility but is unaffordable given the consumer's income.
- **Specific Values**:
- At point A, the consumer can afford 24 units of good X and 14 units of good Y.
### Problem Statement
Given the prices:
- Good X: $30 per unit
- Good Y: $60 per unit
If U₁ is the highest level of utility the consumer can achieve, determine the consumer's income.
### Calculating Consumer's Income
The consumer’s budget is spent entirely on a combination of goods X and Y at point A (24 units of X and 14 units of Y).
**Income Calculation Formula**:
\[ \text{Income} = (\text{Units of good X} \times \text{Price of X}) + (\text{Units of good Y} \times \text{Price of Y}) \]
Plug the values into the formula:
\[ \text{Income} = (24 \times 30) + (14 \times 60) \]
\[ \text{Income} = 720 + 840 \]
\[ \text{Income} = 1560 \]
Thus, the consumer's income is $1,560.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcb0f4bab-4f32-4fca-9ced-04b298ae980f%2F460029b3-818a-4dd8-a8c2-e2abdfb08ab8%2Fzc9l5tr_processed.png&w=3840&q=75)
Transcribed Image Text:### Graph Explanation
The graph presents two axes labeled X and Y, representing "Units of good X" and "Units of good Y" respectively. The X-axis ranges from 0 to 40 units, while the Y-axis ranges from 0 to 30 units.
#### Key Elements of the Graph:
- **Budget Line**: The straight line with endpoints touching the axes, indicating the combinations of goods X and Y that the consumer can purchase given their income. The slope of this line represents the trade-off between the two goods.
- **Indifference Curves (U₁ and U₂)**:
- **U₁**: An indifference curve showing a lower level of utility that the consumer can achieve.
- **U₂**: A higher indifference curve that is unattainable given the current budget constraint.
- **Points A and B**:
- **Point A**: Lies on the indifference curve U₁ and the budget line, indicating the optimal choice of goods that the consumer can afford while maximizing utility at this level.
- **Point B**: Lies on the higher indifference curve U₂ but outside the budget line, indicating a combination of goods that provides more utility but is unaffordable given the consumer's income.
- **Specific Values**:
- At point A, the consumer can afford 24 units of good X and 14 units of good Y.
### Problem Statement
Given the prices:
- Good X: $30 per unit
- Good Y: $60 per unit
If U₁ is the highest level of utility the consumer can achieve, determine the consumer's income.
### Calculating Consumer's Income
The consumer’s budget is spent entirely on a combination of goods X and Y at point A (24 units of X and 14 units of Y).
**Income Calculation Formula**:
\[ \text{Income} = (\text{Units of good X} \times \text{Price of X}) + (\text{Units of good Y} \times \text{Price of Y}) \]
Plug the values into the formula:
\[ \text{Income} = (24 \times 30) + (14 \times 60) \]
\[ \text{Income} = 720 + 840 \]
\[ \text{Income} = 1560 \]
Thus, the consumer's income is $1,560.
Expert Solution
Step 1
The budget line depicts the combination of X and Y that a consumer can afford under a given budget.
Budget line equation:
X *Px + Y*Py = M
Where
X is the quantity of X
Px is the price of X
Y is the quantity of Y
Py is the price of Y
M is income to spend
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