Question

Define budget line.

Hint:

The budget line shows the trade-off between two goods based on the consumer’s income and the prices of the goods. Changes in income or prices shift or rotate the budget line.

Answer 1

A budget line represents the different combinations of two goods that a consumer can purchase given their income and the prices of the goods. It shows the trade-off between the two goods that a consumer faces when deciding how to allocate their income. The budget line is defined by the following equation: \[ P_1 \cdot X + P_2 \cdot Y = I \] where: - \(P_1\) and \(P_2\) are the prices of goods \(X\) and \(Y\),
- \(X\) and \(Y\) are the quantities of goods \(X\) and \(Y\) that the consumer can buy,
- \(I\) is the consumer's income.

Step 1: Slope of the Budget Line.
The slope of the budget line represents the opportunity cost of consuming one good over the other. The opportunity cost is the amount of one good that must be forgone to consume an additional unit of the other good. The slope of the budget line is given by: \[ \text{Slope} = -\frac{P_1}{P_2} \] This indicates how many units of \(Y\) the consumer must give up to consume one additional unit of \(X\).

Step 2: Shifts in the Budget Line.
- Change in Income: If the consumer’s income increases, the budget line shifts outward, allowing the consumer to buy more of both goods. If income decreases, the budget line shifts inward, reducing the consumer's purchasing power. - Change in Prices: If the price of one of the goods changes, the budget line will rotate. An increase in the price of \(X\) causes the budget line to rotate inward around the \(Y\)-axis, reducing the amount of \(X\) the consumer can purchase. Similarly, a decrease in the price of \(Y\) would rotate the line around the \(X\)-axis.

Step 3: Conclusion.
The budget line is a graphical representation of the combinations of two goods a consumer can afford given their income and the prices of the goods. It illustrates the constraints the consumer faces when making consumption decisions.