Economics of 1-φ vs 3-φ delivery

For the same power, distance, line loss and maximum voltage, a 3-phase system needs less conductor material and so costs less.

Single-phase 2-wire line

Power $P$, voltage $V$ (between conductors), p.f. $\cos\phi$, length $l$, area $a_1$:

$$\begin{aligned} I_1 &= \frac{P}{V\cos\phi},\qquad W = 2I_1^2\frac{\rho l}{a_1} = \frac{2P^2\rho l}{a_1V^2\cos^2\phi}\\ a_1 &= \frac{2P^2\rho l}{WV^2\cos^2\phi},\qquad \text{Vol}_1 = 2a_1l = \frac{4P^2\rho l^2}{WV^2\cos^2\phi} \end{aligned}$$

Three-phase 3-wire line (line voltage $V$)

$$\begin{aligned} I_3 &= \frac{P}{\sqrt3V\cos\phi},\qquad W = 3I_3^2\frac{\rho l}{a_3} = \frac{P^2\rho l}{a_3V^2\cos^2\phi}\\ a_3 &= \frac{P^2\rho l}{WV^2\cos^2\phi},\qquad \text{Vol}_3 = 3a_3l = \frac{3P^2\rho l^2}{WV^2\cos^2\phi} \end{aligned}$$

Comparison

$$\frac{\text{Vol}_3}{\text{Vol}_1} = \frac{3}{4} = 0.75$$

So 3-phase 3-wire needs only 75 % of the conductor of 1-phase 2-wire (with the same voltage between conductors).

Other economic points

Hence 3-phase delivery is more economical for generation, transmission and distribution; 1-phase is only used for small loads tapped from the 3-phase system.