Increasing returns to scale

[VanHelsing]

Can someone please help me with this question ?

If production function is such that there is IRS, then

a. Perfect competition is inconsistent.
b. Production wise efficient number of firms is 1.
c. P=LAC  at long run equilibrium
d. All of the ABOVE

Since there is IRS, I know both the LAC and LMC curves are downward sloping continuously, and the LMC is below the LAC always. This enables me to eliminate options c and d. But how to eliminate either of options a and b ?

[Econenthusiast]

a can be ruled out on the grounds that with an IRS production fn, perfect competition results in losses as price is below average cost. Like you said c can be ruled out as well, I'm not sure about b. What is the correct answer that's given for the question ?

[VanHelsing]

The correct answer given is b.

If we are able to eliminate a, as well as c and d, then we can arrive at b as the correct answer through elimination. The reason I was hesitating about eliminating a was that I felt that, since with an IRS production function firms will continuously be making losses, they will exit from the market, reducing market size, thus there will not be the 'infinite' number of firms that are required for perfect competition.

[Econenthusiast]

If the firms have identical cost curves, I guess then all firms would exit the market since they all make losses with MC below the AC as well as AVC here, so they the supply on a whole ceases to exist I guess.

I'm wondering how b can be proved, cant oligopolists with IRS production co-exist ?