Source: Seminar Practice Questions, Chapters 5 & 6 | Microeconomic Theory, Texas A&M University
Tags: Engel curve, inferior good, Giffen good, income effect, substitution effect, Paasche Index, CPI substitution bias, indifference curves, price change decomposition, consumer choice
Chapter 5 covers how consumers respond to changes in income and prices. The core task is decomposing a price change into its substitution effect (movement along an indifference curve) and income effect (shift to a new indifference curve), then understanding how these interact for normal goods, inferior goods, and Giffen goods. The chapter also examines how price indices like the CPI and Paasche Index can over- or undercompensate consumers for inflation.
Engel curve
A graph showing the relationship between income and the quantity demanded of a good, holding prices constant. Upward-sloping for normal goods, backward-bending when a good transitions from normal to inferior at higher income levels.
Normal good
A good for which quantity demanded increases as income rises. Has a positive income elasticity and an upward-sloping Engel curve.
Inferior good
A good for which quantity demanded falls as income rises. Exhibits a negative income elasticity. The Engel curve slopes downward (or bends backward) in the inferior range.
Giffen good
A special case of an inferior good where the income effect is so large that it overwhelms the substitution effect. When the price of a Giffen good rises, quantity demanded also rises, violating the usual law of demand.
Substitution effect
The change in quantity demanded resulting solely from a change in relative prices, holding utility constant. Always moves in the opposite direction to the price change (price up, quantity down).
Income effect
The change in quantity demanded resulting from the change in purchasing power caused by a price change, holding prices constant at their new level.
Paasche Index (Paasche Price Index)
A price index that uses the current period's consumption bundle as the basket of goods. Tends to understate inflation relative to the consumer's actual welfare loss, because it credits consumers for substitution they have already made.
CPI (Consumer Price Index)
A Laspeyres-type price index that uses a fixed base-period basket. Tends to overstate the cost of living because it ignores consumers' ability to substitute towards cheaper goods (substitution bias).
Substitution bias
The systematic overstatement of inflation in a fixed-basket price index (like the CPI) because it does not account for consumers switching to relatively cheaper substitutes when prices change.
The shape of the Engel curve tells you how demand responds to income:
Upward-sloping: normal good (more income, more demand)
Downward-sloping: inferior good (more income, less demand)
Backward-bending: the good starts as normal, then becomes inferior beyond a certain income level
A backward-bending Engel curve means the consumer initially buys more as income rises, then switches to a preferred alternative at higher incomes (e.g., home improvements on a current house, then upgrading to a bigger house instead)
All Giffen goods are inferior goods, but not all inferior goods are Giffen goods
An inferior good simply has falling demand as income rises (negative income elasticity)
A Giffen good requires the income effect to be both negative and larger in magnitude than the substitution effect
When the price of a Giffen good increases:
The substitution effect says "buy less" (positive substitution effect in standard notation, meaning it pushes away from the now-expensive good)
The income effect says "buy more" (because the consumer is effectively poorer and this is an inferior good they rely on heavily)
The income effect dominates, so quantity demanded rises with price
The substitution effect isolates the impact of the relative price change by holding utility constant (sliding along the original indifference curve to reflect new price ratios)
The income effect isolates the impact of the change in purchasing power by holding prices constant at their new level (shifting to a different indifference curve)
Key distinction: the substitution effect holds utility constant; the income effect holds prices constant
The Paasche Index uses the new (current) consumption bundle as its reference basket
It undercompensates consumers for inflation
The consumer ends up at a lower utility level than before the price change
This happens because the index only pays enough to buy the new (already-substituted) bundle at old prices, not enough to restore original utility
The CPI (Laspeyres-type) uses the old (base-period) bundle as its reference basket
It overcompensates consumers for inflation
The consumer could achieve higher utility than before, because the CPI gives enough income to buy the original bundle, but the consumer can then substitute towards cheaper goods and end up better off
Substitution bias disappears only when consumers cannot or do not substitute between goods
L-shaped indifference curves (perfect complements) mean the consumer always buys goods in fixed proportions regardless of price
No substitution is possible, so no substitution bias exists
Linear indifference curves (perfect substitutes) and convex indifference curves both allow substitution, so the CPI will overstate inflation in those cases
Engel curve: plot income (vertical axis) against quantity demanded (horizontal axis). Slope and shape reveal normal, inferior, or transitional status.
Slutsky decomposition: Total effect = Substitution effect + Income effect. The substitution effect is found by rotating the budget line around the original indifference curve; the income effect is the parallel shift from the compensated to the new budget line.
Paasche Index: uses current-period quantities as weights. Understates cost of maintaining original utility.
Laspeyres / CPI: uses base-period quantities as weights. Overstates cost of maintaining original utility.
⚠️ The backward-bending Engel curve is a common exam question. It describes a good that is normal at low incomes and inferior at high incomes, not a good that is always inferior.
⚠️ For Giffen goods, all three conditions hold simultaneously: negative income effect, positive substitution effect (away from the good), and the income effect larger than the substitution effect. "All of the above" is often the correct framing.
⚠️ The substitution effect holds utility constant; the income effect holds prices constant. Getting these reversed is the most common error in decomposition questions.
⚠️ Paasche undercompensates; CPI (Laspeyres) overcompensates. Students frequently mix these up. Remember: Paasche uses new weights and assumes substitution has already happened, so it pays too little.
⚠️ No substitution bias only with L-shaped (perfect complement) indifference curves. Linear indifference curves still allow substitution (in fact, they allow complete switching), so they do generate bias.
Q: Joyce and Larry initially spend more on home improvements as income rises, then reduce spending on home improvements when income rises further. What shape is their Engel curve?
A: Backward bending. The good is initially normal (upward-sloping Engel curve) but becomes inferior at higher income levels, so the curve bends back.
Q: What does an inferior good exhibit?
A: A decline in quantity demanded as income rises. It has a negative income elasticity and a downward-sloping (or backward-bending) Engel curve.
Q: When the price of a Giffen good increases, what happens to the income and substitution effects?
A: The income effect is negative (consumer is poorer and buys more of the inferior good), the substitution effect is positive (pushes away from the more expensive good), and the income effect is larger than the substitution effect, so overall quantity demanded rises.
Q: What is the primary difference between the substitution effect and the income effect?
A: The substitution effect holds utility constant and the income effect holds prices constant. The substitution effect captures the response to changed relative prices; the income effect captures the response to changed purchasing power.
Q: If the Paasche Index is used to adjust wages for inflation, will the worker be over- or undercompensated?
A: Undercompensated. The Paasche Index uses the new consumption bundle as its reference, so it only provides enough income for the consumer to buy the substituted basket, leaving them at a lower utility level than before the inflation.
Q: Under what condition is there no substitution bias in the CPI?
A: When indifference curves are L-shaped (perfect complements). In that case, consumers buy goods in fixed proportions and never substitute, so a fixed-basket index does not overstate inflation.
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