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## Microeconomics Question from Walter E. Williams:Edit

What is an income-compensated demand curve? Carefully derive one graphically. How does it differ from an ordinary demand curve? For a normal good, which of the two curves is more elastic? Why? What might be an empirical use of an income-compensated demand curve?

An income-compensated (Hicksian) demand curve has been constructed in such a way so as to exclude the income effect of a change in price. This is done by holding real income verses nominal income constant. The effect of this is that a change in price will have a corresponding change in nominal income, with the result that the consumer stays on the same indifference curve. Changes in price thus only have substitution effects. Graphically this produces a demand curve that intersects the uncompensated demand curve at the current quantity and is less elastic than the uncompensated demand curve.

Graphically this would be constructed by having one indifference curve with a budget line at each price point being tangent to the indifference curve. Movement can only be along the indifference curve, as the nominal wage will adjust with the change in relative price to hold utility constant.

Since the Hicksian demand curve $\vec{x} = h(\vec{p}, u)$ is a function of utility, which is not observable, Hicksian demand curves are of little empirical use.