Answer
2:1.
Work Step by Step
Let the long, thick conductor be called number 1, and the short, thin conductor be called number 2.
Note that $\mathcal{l}_1=2\mathcal{l}_2$ and $A_1=4A_2$.
The power dissipated by a resistor is $P=V^2/R$. The voltages are identical.
$$\frac{P_1}{P_2}=\frac{V^2/R_1}{V^2/R_2}=\frac{R_2}{R_1}$$
$$R_2=\rho\frac{\mathcal{l}_2}{A_2}=\rho\frac{0.5\mathcal{l}_1}{A_1/4}=2\rho\frac{\mathcal{l}_1}{A_1}=2R_1$$
$$\frac{P_1}{P_2}=\frac{R_2}{R_1}=2$$
