$\displaystyle P1 = k * A * V^3$
where P1 is the initial power for across sectional area of the jet A and velocity and k is the constant of proportionality.
If area is halved and velocity is doubled, then:
$\displaystyle P2=k * (\frac{1}{2}*A)*(2*V)^3$
$\displaystyle P2=4 * k*A*V^3$
$\displaystyle P2=4 * P1$
The factor is 4.