Question

Why does the budget line slope downward?

Hint:

The downward slope of the budget line shows the trade-off between two goods that a consumer faces given their income.

Answer 1

Step 1: Defining the Budget Line:
The budget line represents all possible combinations of two goods that a consumer can purchase given their income and the prices of the goods. It shows the trade-offs between two goods, given the consumer’s budget.
Step 2: The Slope of the Budget Line:
The budget line slopes downward because of the following reason: as a consumer spends more of their income on one good, they have less income available to spend on the other good. In order to maintain the same total expenditure (income), the consumer must reduce the quantity of one good as they increase the quantity of the other. This inverse relationship between the two goods creates the downward slope.
Step 3: Formula for the Budget Line:
The slope of the budget line is determined by the ratio of the prices of the two goods: \[ \text{Slope of the Budget Line} = -\frac{P_X}{P_Y} \] Where \(P_X\) is the price of good X, and \(P_Y\) is the price of good Y. This indicates the rate at which the consumer must give up one good in order to obtain more of the other.
Step 4: Final Conclusion:
The budget line slopes downward because as a consumer allocates more of their income to one good, they have to forgo some of the other good, reflecting the trade-off between the two goods.