Problem 16 Why does a change in income caus... [FREE SOLUTION]

Chapter 6: Problem 16

Why does a change in income cause a parallel shift in the budget constraint?

Short Answer

Expert verified

A change in income causes a parallel shift in the budget constraint because when income changes, both the intercepts of the budget constraint change, but the slope remains the same. This means that the new budget constraint line will be parallel to the initial one, with an increase in income shifting the constraint line outward and a decrease in income shifting it inward.

Step by step solution

Define the budget constraint

A budget constraint represents the combinations of two goods that can be consumed by an individual given their income and the prices of the goods. Mathematically, the budget constraint is represented as: \(I = P_1Q_1 + P_2Q_2\) Where: - \(I\) is the consumer's income - \(P_1\) is the price of good 1 - \(Q_1\) is the quantity of good 1 consumed - \(P_2\) is the price of good 2 - \(Q_2\) is the quantity of good 2 consumed The budget constraint can be rearranged to isolate \(Q_2\), giving: \(Q_2= \frac{I}{P_2} - \frac{P_1}{P_2}Q_1\)

Graph the budget constraint

The budget constraint can be graphed as a straight line with good 1 quantity (\(Q_1\)) on the x-axis and good 2 quantity (\(Q_2\)) on the y-axis. The intercepts and slope of the line are determined by the income and prices of the goods. - The intercept of good 2 on the y-axis is \(\frac{I}{P_2}\) (when \(Q_1=0\)) - The intercept of good 1 on the x-axis is \(\frac{I}{P_1}\) (when \(Q_2=0\)) - The slope of the budget constraint line is \(-\frac{P_1}{P_2}\)

Show the effect of a change in income

Now, let's consider a change in income, say, the income increases to \(I'\). The new budget constraint equation will be: \(I' = P_1Q_1 + P_2Q_2\) If we isolate \(Q_2\) again, we get: \(Q_2= \frac{I'}{P_2} - \frac{P_1}{P_2}Q_1\) Notably: - The slope of the new budget constraint line, \(-\frac{P_1}{P_2}\), remains the same - The intercept of good 2 on the y-axis increases to \(\frac{I'}{P_2}\) - The intercept of good 1 on the x-axis increases to \(\frac{I'}{P_1}\)

Explain the parallel shift

As we have seen from the equations, when income changes, both intercepts of the budget constraint change, but the slope remains the same. This implies that the new budget constraint line is parallel to the old budget constraint line. In other words, a change in income causes a parallel shift in the budget constraint line. An increase in income will shift the budget constraint line outwards, while a decrease in income will shift the budget constraint line inwards.