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How would you best explain to a student in intermediate micro class that the Hicksian demand for a normal good is more inelastic than the Walrasian demand without heavy differential calculus?

When I mean inelastic, I mean specifically being less responsive to price changes, a picture similar to MWG Figure 3.I.3.

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  • $\begingroup$ You mean less elastic? $\endgroup$
    – Michael Greinecker
    Sep 28 '17 at 9:49
  • $\begingroup$ @MichaelGreinecker No, I mean more elastic, more sensitive to price changes thus steeper slope than the Marshallian. See the answer below. $\endgroup$
    – Frank Swanton
    Sep 28 '17 at 11:45
  • $\begingroup$ From your question: "I mean specifically being more responsive to price changes," From the answer below: "So Hicksian demand changes less with prices." $\endgroup$
    – Michael Greinecker
    Sep 28 '17 at 11:47
  • $\begingroup$ @MichaelGreinecker You're right. Now I am confused. Let me read the answer more carefully. $\endgroup$
    – Frank Swanton
    Sep 28 '17 at 11:49
  • $\begingroup$ @MichaelGreinecker I was putting the axis incorrectly and talking about the unconventional demand graph. In the inverse demand function picture, which is what we do, put P on y-axis, Q on x, then steeper does mean more inelastic. I was unclear on this. $\endgroup$
    – Frank Swanton
    Sep 28 '17 at 11:59
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Here's a "no maths" explanation (including the inferior goods case, because I think it helps to understand what's going on):

Suppose we have a normal good, $x$, and we increase its price. Marshallian demand decreases thanks to two effects (i) consumers substitute away from $x$ towards cheaper alternatives; (ii) because prices are higher, consumers can afford less stuff, so it's as if their income were lower. Both of these effects point towards lower demand for $X$.

Now consider Hicksian demand, which shows the effect of a price change after we compensate consumers to eliminate the income effect. Instead of having two effects (income and substitution) pointing in the direction of lower demand, now there is only one (substitution). So Hicksian demand changes less with prices.

Note that on p83 of MWG, the authors note that the figure is drawn for the case of normal goods.

But let's look at the case of an inferior good. By definition, when the price of an inferior good increases Marshallian demand tends to fall due to the substitution effect, but increase due to the income effect. In other words, there is one negative effect and one positive effect on demand. These two effects cancel each other out to some extent, so that the overall effect of price on Marshallian demand is muted.

Hicksian demand eliminates the (positive) income effect, so that the only remaining effect is the unambiguously negative substitution effect. Thus, Hicksian demand for an inferior good is more sensitive to price that Marshallian demand.

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  • $\begingroup$ Thanks for the answer. Now, when you say "Hicksian demand, which shows the effect of a price change after we compensate consumers to eliminate the income effect", how do you mean? $\endgroup$
    – Frank Swanton
    Sep 28 '17 at 11:50
  • $\begingroup$ For infinitesimal price changes, I understand that the following Slutsky equation holds, thus Hicksian and Marshallian are virtually no different. $\frac{\partial X_i}{\partial P_j}+\frac{\partial X_i}{\partial W}X_i = \frac{\partial H_i}{\partial P_j}$ $\endgroup$
    – Frank Swanton
    Sep 28 '17 at 11:56
  • $\begingroup$ I am having hard time explaining (perhaps understanding) is that for large price changes, how they become different, and that translates into the inverse demand function we see, as you explained MWG p83 picture, where the Marshallian is less steep and Hicksian is relatively steeper. $\endgroup$
    – Frank Swanton
    Sep 28 '17 at 11:57
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    $\begingroup$ @FrankSwanton The way i would explain this is with the help of an indifference curve diagram. If the price of a good rises then the budget constraint rotates and the old IC is no longer attainable. The Marshallian demand curve tells me what will demand be with the new price. The Hicksian curve tells me what will demand be with the new price if, additionally, I give the consumer enough money to make the old IC affordable again. If You draw this diagram then it will be obvious that $h$ and $x$ differ because of the income effect. Such figures are in most introductory textbooks. $\endgroup$
    – Ubiquitous
    Oct 1 '17 at 7:58
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    $\begingroup$ @FrankSwanton Example diagram: image.slidesharecdn.com/me4-130715104506-phpapp02/95/… $\endgroup$
    – Ubiquitous
    Oct 1 '17 at 7:58

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