The optimal supply of rail and bus in low density areas is studied by calibrating a demand and supply model with three modes (car, bus and rail) to an existing low density corridor. Varying the length of the network, the frequencies and the size of the populations, allows to study the trade-off between the consumer surplus losses of the public transport users and the transit operation and maintenance costs savings. We find that for an existing rail network, the optimization of frequency is the prime source of welfare gains. The rail network is marginally beneficial in the sense that keeping the network is welfare improving as long as there is no major repair or replacement investment needed. When population in the smaller towns decreases strongly, it becomes welfare improving to close the existing rail network but a bus service remains beneficial for at least part of the network. © 2020 The Authors