How does the budget line change if the price of good 2 decreases by a rupee but the price of good 1 and the consumer’s income remain unchanged?
When the price of good 2 decreases by a rupee (from Rs 5 to Rs 4), while the price of good 1 (Rs 4) and the consumer's income (Rs 20) remain unchanged, the budget line pivots outward around the horizontal intercept.
The vertical intercept increases from 4 units (20÷5) to 5 units (20÷4) of good 2, as the consumer can now buy more of good 2 with the same income. The horizontal intercept remains unchanged at 5 units (20÷4) of good 1, since the price of good 1 and income have not changed.
The slope of the budget line changes from -4/5 to -4/4 = -1. The absolute value of the slope increases, making the budget line steeper. The budget set expands as more bundles become affordable for the consumer.
Explanation
This question tests understanding of how the budget line changes when only one price changes. From the context, when the price of one commodity changes while the other price and income remain constant, the budget line pivots around the intercept of the unchanged good. The intercept on the axis of the good whose price decreased increases (consumer can buy more), while the other intercept stays the same. The context explains this pivoting mechanism for price changes of good 1, and the same logic applies to good 2.
Solution Steps
Step 1: Identify original intercepts - Vertical intercept = M/p₂ = 20/5 = 4 units of good 2; Horizontal intercept = M/p₁ = 20/4 = 5 units of good 1
Step 2: Calculate new vertical intercept after price decrease - New vertical intercept = M/p₂' = 20/4 = 5 units of good 2
Step 3: Note that horizontal intercept remains unchanged at 5 units of good 1
Step 4: Conclude that the budget line pivots outward around the horizontal intercept, becoming steeper as the vertical intercept increases.