Explaining why Hicksian demand is more inelastic to intermediate micro student 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.
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.