The difference between a “normal” price demand curve and an income compensated one is that the income compensated one has been constructed in such a way so as to exclude the income effect of a change in price. Thus the Hicks-compensated demand curve shows how quantity demanded varies with price, assuming that as price changes, consumers are compensated with enough income to keep them on their initial indifference curve . The two different demand curves and the way they are derived are presented below.
In the above diagram we see how we construct a Hicks compensated demand curve using the concept of compensated variations. On the left hand graph we see that as the price of good A declines our budget constraint becomes flatter thus enabling us to reach a higher indifference curve moving us from point A to point B. At point B we see that we consume more of good A due to the price signal sent by the price reduction but we also consume more of other goods because of our increase in real income. However, point B doesn’t show us real demand for A because the change in price also created an increase in real income so we can’t determine the extent to which a reduction in price for good A would lead to a substitution of other goods for good A. By drawing a budget constraint parallel to BC1 that is tangent to our new indifference curve (compensated variations are illustrated by the movement on the income axis) we get the real substitution effect of the change in price. In other words we see the effect in price b ecause now we consume the same quantity of good B as before because we have cancelled out the income effect. As seen in the above figure, the Hicks compensated demand curve is relatively steeper than the Marshallian one because when the good is normal the income and substitution effects reinforce each other thus making the slope of the Marshallian demand curve flatter. However, this wouldn’t happen for an inferior good when the income and substitution effects are opposite and thus make the Marshallian demand curve relatively steeper. Even though Hicks compensated demand curves are more accurate measures of the price effect we prefer Marshallian ones because they are easier to construct since often we lack the data to estimate how the quantity demanded changes with money income. Also the Marshallian demand curve only gives you an estimate of consumer surplus because it includes consumer surplus gain or loss due to the income effect whereas the Hicks compensated one doesn’t, since income in real terms must rem ain fixed so that our focus is only on the effect of price on quantity demanded. Thus the Hicks-compensated demand curve also gives us a more accurate measurement of consumer surplus.