Step 1: Write the wind power formula and identify the variables.
The power available in wind passing through a rotor is \[ P_a = \frac{1}{2} \rho A V^3 \] where the swept area is \( A = \frac{\pi d^2}{4} \), so the power is proportional to \( d^2 V^3 \).
Step 2: Apply the given changes to each variable separately.
Doubling the diameter multiplies the swept area term by \( 2^2 = 4 \). Halving the wind speed multiplies the velocity term by \( (0.5)^3 = 0.125 \), that is, one eighth.
Step 3: Combine the two factors to get the net change.
\[ \frac{P_{new}}{P_{old}} = 4 \times \frac{1}{8} = \frac{1}{2} \] So the new available wind power is exactly half of the original power, since the cubic dependence on wind speed dominates the squared dependence on diameter.
\[ \boxed{\text{Reduced to half}} \]