  We consider the cones of curves and divisors on the moduli space of stable
pointed rational curves,M_n, and on the quotient by the symmetric group, Q_n,
which is a moduli space of pairs. We find generators for contractible extremal
rays of the cone of curves NE_1(M_n), and for the cone of divisors NE^1(Q_n).
This second cone turns out to be simplicial. We give complete descriptions of
NE_1(M_n) and NE_1(Q_n) for small n (< 8 in the first case, < 11 in the
second). We also have results of independent interest on when curves in a
divisor generate the cone of curves of the ambient variety.
