Why is the equilibrium price not anything between \$0 and \$200?
Varian is indeed wrong here in that there is a critical omission: He should have specified whether there in a 27th person and what this person's reservation price is.


If there is no 27th person, then the set of possible equilibrium prices is $[\$0,\$200]$, as you correctly point out. Explanation:


At each $p\in(\$0,\$200)$, we have $S(p)=26$ and $D(p)=26$, so that there is a possible equilibrium.

At $p=\$200$, we have $S(p)=26$ and $D(p)=\{25,26\}$, so that there is a possible equilibrium.

At $p=\$0$, we have $S(p)=\{0,1,\dots,26\}$ and $D(p)=26$, so that there is a possible equilibrium.

At any $p&gt;\$200$, we have $S(p)=26$ and $D(p)\leq25$, so that there is no possible equilibrium.


If there is a 27th person and her reservation price is $k&lt;\$200$, then the set of possible equilibrium prices is $[k,\$200]$. Explanation:


At each $p\in(\$k,\$200)$, we have $S(p)=26$ and $D(p)=26$, so that there is a possible equilibrium.

At $p=\$k$, we have $S(p)=26$ and $D(p)=\{26,27\}$, so that there is a possible equilibrium.

At $0&lt;p&lt;k$, we have $S(p)=26$ and $D(p)=27$, so that there is no possible equilibrium.

At $p=\$0$, we have $S(p)=\{0,1,\dots,26\}$ and $D(p)=27$, so that there is a possible equilibrium.

At any $p&gt;\$200$, we have $S(p)=26$ and $D(p)\leq25$, so that there is no possible equilibrium.



Notes.


I assume throughout, as I believe Varian has, that each apartment-owner's reservation price or willingness-to-accept is \$0. I also assume that negative prices are impossible.
Following usual practice in economics, I've been a little sloppy about whether the elements of the codomains of the supply and demand functions $S$ and $D$ are numbers or sets of numbers. (Technically and most generally, they should be sets. But so as not to confuse students, we usually and more simply say they are numbers.)