  We study two homogeneous supersymmetric extensions for the $f(R)$ modified
gravity model of Starobinsky with the FLRW metric. The actions are defined in
terms of a superfield $\mathcal{R}$ that contains the FLRW scalar curvature.
One model has N=1 local supersymmetry, and its bosonic sector is the
Starobinsky action; the other action has N=2, its bosonic sector contains, in
additional to Starobinsky, a massive scalar field without self-interaction. As
expected, the bosonic sectors of these models are consistent with cosmic
inflation, as we show by solving numerically the classical dynamics. Inflation
is driven by the $R^2$ term during the large curvature regime. In the N=2 case,
the additional scalar field remains in a low energy state during inflation.
Further, by means of an additional superfield, we write equivalent
tensor-scalar-like actions from which we can give the Hamiltonian formulation.
