Questions: Budget Constraint and Purchasing Power

Question 1

The price of coffee (good 1) rises while the price of tea (good 2) and consumer income remain unchanged. What happens to the budget constraint?

• A. The line rotates inward — the coffee-axis intercept falls, but the tea-axis intercept is unchanged
• B. The line shifts inward in parallel — all bundles of coffee and tea become less affordable
• C. The line rotates outward — consumers substitute toward tea, expanding the feasible set
• D. The slope becomes shallower — coffee is now relatively more expensive than tea

Answer: (A)

A price change for one good rotates the budget line around the intercept of the unchanged good. If P₁ (coffee) rises, the maximum coffee affordable (I/P₁) falls, so that intercept moves inward. But since P₂ and I are unchanged, the tea intercept (I/P₂) stays fixed — the line pivots. A parallel inward shift (option B) would require income to fall or both prices to rise proportionally. This geometric distinction between rotation and parallel shift is the key insight of this topic. Note also that option D gets the direction wrong: if coffee becomes more expensive, the slope −P₁/P₂ becomes steeper in magnitude, not shallower.

Question 2

Consumer income doubles while all prices remain unchanged. What is the effect on the budget constraint?

• A. The line shifts outward parallel to its original position — the slope is unchanged because relative prices have not changed
• B. The line rotates outward — higher income raises purchasing power of good 1 more than good 2
• C. The slope steepens — doubling income changes the relative price ratio
• D. Both intercepts double but the slope also changes to reflect higher purchasing power

Answer: (A)

Income affects both intercepts equally: if I doubles, both I/P₁ and I/P₂ double, shifting both intercepts out by the same factor. The slope (−P₁/P₂) is unchanged because neither price changed — only income. The result is a parallel outward shift. The slope encodes only relative prices; income determines how far out along the slope you can reach, not the slope itself. Options B–D incorrectly suggest that income changes the slope.

Question 3

An increase in the price of good 1 and a decrease in income have the same effect on the budget constraint — both shift the line inward in parallel.

• T. True
• F. False

Answer: False

This is the key asymmetry the topic is designed to teach. An income decrease shifts the line inward in parallel — both intercepts fall by the same proportion, so the slope is unchanged. A price increase for good 1 rotates the line inward around the good 2 intercept — only the good 1 intercept changes, so the slope changes. They both reduce affordability, but in geometrically distinct ways with different implications: income changes affect the feasible set uniformly, while price changes alter relative trade-offs.

Question 4

The slope of the budget line represents the opportunity cost of good 1 in terms of good 2 — how many units of good 2 must be given up to buy one more unit of good 1.

• T. True
• F. False

Answer: True

The slope is −P₁/P₂, the relative price ratio. If good 1 costs $4 and good 2 costs $2, the slope is −2: buying one more unit of good 1 requires forgoing 2 units of good 2. This is exactly the opportunity cost of good 1 expressed in units of good 2. The slope thus encodes the market's forced trade-off independently of income — which is why a price change alters the slope and an income change does not.

Question 5

Explain why a price increase for one good rotates the budget line rather than shifting it in parallel. What does this rotation convey that a parallel shift would not?

Model answer: When only P₁ rises, the maximum quantity of good 1 affordable (I/P₁) falls, but the maximum of good 2 (I/P₂) is unchanged — so only one intercept moves, producing a rotation around the good 2 intercept. A parallel shift would move both intercepts equally, which happens when income changes. The rotation conveys that relative prices have changed: good 1 is now more expensive relative to good 2. The slope steepens, meaning the opportunity cost of good 1 in terms of good 2 has increased. A parallel shift preserves relative prices; a rotation does not.

The geometric distinction between rotation and parallel shift encodes an economically meaningful difference. After a parallel shift from an income change, the consumer faces the same relative trade-offs at a different scale. After a rotation from a price change, the trade-offs themselves have changed — the consumer must give up more of good 2 per unit of good 1. This difference matters for consumer behavior: pure income changes produce income effects; price changes produce both income and substitution effects.