Question

The slope of the budget line is

• A. \( - \frac{P_x}{P_y} \)
• B. \( - \frac{P_y}{P_x} \)
• C. \( + \frac{P_x}{P_y} \)
• D. \( + \frac{P_y}{P_x} \)

Hint:

The slope of the budget line reflects the trade-off between the two goods, showing the opportunity cost of one good in terms of the other.

Answer 1

The Correct Option is A

Step 1: Understanding the Budget Line:
The budget line represents all the combinations of two goods that a consumer can purchase given their income and the prices of the goods. The slope of the budget line reflects the rate at which the consumer can trade one good for another, given their budget constraint.
Step 2: Formula for the Budget Line:
The equation for the budget line is: \[ P_x X + P_y Y = M \] Where:
- \( P_x \) is the price of good X
- \( P_y \) is the price of good Y
- \( X \) and \( Y \) are the quantities of the two goods
- \( M \) is the consumer’s income.
Step 3: Deriving the Slope:
To find the slope of the budget line, we rearrange the equation to isolate \( Y \) on one side: \[ Y = \frac{M}{P_y} - \frac{P_x}{P_y} X \] The slope of the budget line is \( - \frac{P_x}{P_y} \), which represents the rate at which the consumer must give up good Y to get one more unit of good X.
Step 4: Conclusion:
The slope of the budget line is \( - \frac{P_x}{P_y} \), showing how many units of good Y must be sacrificed to obtain an additional unit of good X.