  Let $k$ be a field, $A$ a finitely generated associative $k$-algebra and
$\operatorname{Rep}_A[n]$ the functor $\operatorname{Fields}_k\to
\operatorname{Sets}$, which sends a field $K$ containing $k$ to the set of
isomorphism classes of representations of $A_K$ of dimension at most $n$. We
study the asymptotic behavior of the essential dimension of this functor, i.e.,
the function $r_A(n) := \operatorname{ed}_k(\operatorname{Rep}_A[n])$, as
$n\to\infty$. In particular, we show that the rate of growth of $r_A(n)$
determines the representation type of $A$. That is, $r_A(n)$ is bounded from
above if $A$ is of finite representation type, grows linearly if $A$ is of tame
representation type and grows quadratically if A is of wild representation
type. Moreover, $r_A(n)$ is a finer invariant of A, which allows us to
distinguish among algebras of the same representation type.
