2. A certain product at the same price underwent 2 price adjustments in 3 stores. Store A first decreased the price by a percentage of $a$, then increased it by a percentage of $b$; Store B first decreased the price by a percentage of $\frac{a+b}{2}$, then increased it by a percentage of $\frac{a+b}{2}$; Store C first decreased the price by a percentage of $b$, then increased it by a percentage of $a(0<b<a<1)$. After the 2 price adjustments, the store that sold the product at the lowest price is ( ).
(A) A (B) B (C) C (D) Cannot be determined
2.A.

Let the original price of this commodity be 1. After 2 price adjustments, the prices of this commodity in stores A, B, and C are respectively
$$
\begin{array}{l}
M_{\text {A }}=(1-a)(1+b)=1-a+b-a b ; \\
M_{\text {B }}=\left(1-\frac{a+b}{2}\right)\left(1+\frac{a+b}{2}\right)=1-\left(\frac{a+b}{2}\right)^{2} ; \\
M_{\text {C }}=(1-b)(1+a)=1-b+a-a b .
\end{array}
$$

Since $M_{\text {A }}-M_{\text {C }}=2(b-a)<0$,
$$
\begin{array}{l}
M_{\text {A }}-M_{\text {B }}=-a+b-a b+\frac{(a+b)^{2}}{4} \\
=\frac{1}{4}\left[(a-b)^{2}-4(a-b)+4-4\right] \\
=\frac{1}{4}\left[(a-b-2)^{2}-4\right]<0,
\end{array}
$$

Therefore, $M_{\text {A }}<M_{\text {C }}, M_{\text {A }}<M_{\text {B }}$.
Thus, after 2 price adjustments, store A sells the commodity at the lowest price.