Hicksian Demand and Compensated Price Changes
Downward sloping Marshallian demand curves show the effect of price changes on quantity demanded. As the price of a good rises, presumably the quantity of that good demanded will fall, holding wealth and other prices constant. However, this price changes due to both the income effect and the substitution effect. The substitution effect is a price change that alters the slope of the budget constraint but leaves the consumer on the same indifference curve (i.e., at the same level of utility.) By this effect, the consumer is posited to substitute toward the good that becomes comparatively less expensive. If the good in question is a normal good, then the income effect from the rise in purchasing power from a price fall reinforces the substitution effect. If the good is an inferior good, then the income effect will offset in some degree the substitution effect.
The Hicksian demand function is also downward sloping, but isolated the substitution effect by supposing the consumer is compensated exactly enough to purchase some bundle on the same indifference curve. Hicksian demand illustrates the consumer's new consumption basket after the price change while being compensated as to allow the consumer to be as happy as previously (to stay at the same level of utility). If the Hicksian demand function is "steeper" than Walrasian demand, the good is a normal good; otherwise, the good is inferior.
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