What is the maximum amount of x and y one can consume in BL1?

a.

x = 9; y = 27/13

b.

x = 9; y = 13

c.

x = 13; y = 3

d.

x = 13; y = 9

e.

x = 27/13; y = 9

To find the maximum amount of \( x \) and \( y \) that one can consume on the budget line BL1, we need to determine the intercepts of the budget line with the axes.

### Step 1: Find the x-intercept
The x-intercept occurs when \( y = 0 \). Substitute \( y = 0 \) into the equation of BL1:

\[
3x + 13(0) = 27
\]
\[
3x = 27
\]
\[
x = \frac{27}{3} = 9
\]

So, the x-intercept is \( x = 9 \).

### Step 2: Find the y-intercept
The y-intercept occurs when \( x = 0 \). Substitute \( x = 0 \) into the equation of BL1:

\[
3(0) + 13y = 27
\]
\[
13y = 27
\]
\[
y = \frac{27}{13}
\]

So, the y-intercept is \( y = \frac{27}{13} \).

### Conclusion:
The maximum values that can be consumed on the budget line BL1 are \( x = 9 \) and \( y = \frac{27}{13} \).

The correct answer is:

**a. \( x = 9; y = \frac{27}{13} \)**

Would you like further details or have any questions? Here are some related questions to expand your understanding:

1. How do the intercepts of BL2 compare to those of BL1?
2. What would happen to the intercepts if the budget increased?
3. What is the slope-intercept form of BL2?
4. How would an increase in the price of \( y \) affect the maximum \( x \) and \( y \)?
5. If \( x = 4 \), how much of \( y \) can be consumed?

**Tip:** The intercepts of a budget line help determine the maximum quantity of each good that can be consumed if all income is spent on just one good.

Discover the maximum amount of x and y that can be consumed on budget line BL1. Learn how to calculate intercepts and understand budget constraints in economics. Suitable for high school students and economics enthusiasts.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation