Two toy models are considered within the framework of noncommutative
differential geometry. In the first one, the Einstein action of the Levi-Civita
connection is computed for the algebra of matrix valued functions on a torus.
It is shown that, assuming some constraints on the metric, this action splits
into a classical-like, a quantum-like and a mixed term. In the second model, an
analogue of the Palatini method of variation is applied to obtain critical
points of the Einstein action functional for $M\sb 4(R)$. It is pointed out
that a solution to the Palatini variational problem is not necessarily a
Levi-Civita connection. In this model, no additional assumptions regarding
metrics are made.