Multistage Compressor: Power Distribution

[gfd43tg]

Hello,

When using a multistage compressor that is assumed to be isentropic with no interstage temperature increases, is it assumed each stage does the same amount of power?

 

[Baluncore]

Each stage increases the pressure while decreasing the volume and should be designed for maximum efficiency.
For an inlet pressure P1 and an outlet pressure P3, can you find the intermediate pressure P2 that would maximise the efficiency of the whole process = product of all stage efficiencies.