Question about the Law of Supply
The law of supply holds under fairly general conditions. Essentially, it states that &quot;quantities respond in the same direction as price changes.&quot; Formally,
$$(p-p')(q-q')\geq 0,$$
where $p$ is price, $q$ is quantity and primed and unprimed reflect two different states. You see that the inequality is weak such that a constant range is not excluded. However, a decreasing supply curve would violate the law of supply.
Moreover, your argument appears to be a bit fuzzy. Sure enough, it implies that for a given price-quantity pair $(p,q)$ that $S(p) = S(p-\epsilon)=q$, when $\epsilon$ price changes are not drastic. However, then consider price-quantity pair $(p-\epsilon,q)$ and another non-drastic price drop. Your argument appears to imply $S(p-\epsilon)=S(p-2\epsilon)=q$ and so on culminating in a constant demand function, which --it seems-- you do not want to apply.
It seems more reasonable to suggest that a marginal price drop also has a marginal effect on supply such that $S(p)=q$ and $S(p-\epsilon) = q - \varepsilon$, where both $\epsilon$ and $\varepsilon$ are tiny such that a &quot;non-drastic price drop&quot; implies a &quot;non-drastic quantity reduction.&quot;