Asteroid mining modules cost 60 Duranium + 60 Corundium each with the cost of the rest of the ships systems on top of that, while automines cost 120 Duranium + 120 Corundium. So it make sense to make them when you have an acute Corundium or Duranium shortage as you get twice the number of mines out of your stockpile.
As an example one of my old asteroid miners(though with fairly high armour tech so low tech ships would have a higher Duranium cost).
Extractor class Asteroid Miner 28,200 tons 593 Crew 863.5 BP TCS 564 TH 300 EM 0
531 km/s Armour 1-82 Shields 0-0 Sensors 1/1/0/0 Damage Control Rating 1 PPV 0
MSP 19 Max Repair 120 MSP
Asteroid Miner: 5 module(s) producing 50 tons per mineral per annum
Civilian Ion Engine (2) Power 150 Fuel Use 7% Signature 150 Armour 0 Exp 1%
Fuel Capacity 50,000 Litres Range 45.5 billion km (992 days at full power)
This design is classed as a Commercial Vessel for maintenance purposes
Costs 424 Duranium, 300 Corundium, 27.5 Neutronium, 5 Corbomite, 50 Mercassium, 57 Gallicite. Total 863.5
5 Automines would cost 600 Duranium, 600 Corundium. Total 1200
As a note, when designing asteroid miners it may be a good idea to go with older cheaper engines as they are going to be spending most of their time sitting still with only occasional need to move, so no need for a high speed. Also personally I wouldn't go with putting cargo space on a miner to transport the mass driver as it is just wasted space for most of the time. Just have a freighter ship one to your next intended asteroid just before your current mine is exhausted.