The total cost of a duo test and a trio test is about the same (for the same level of accuracy). It’s simply that the costs are in different places.
A duo test uses less chemicals and equipment time. However, analyzing the results of a duo test requires far more computer and people time in order to obtain the same level of accuracy in the absence of the mother’s DNA. Forensic scientists are expensive!
Some labs report duo tests at lower accuracy in order to advertise a low priced “loss-leader”. The AABB only requires 99.1% probability of paternity for non-exclusions. This means that there is nearly a 1 in 100 men match and would not be excluded.
We require our labs to provide a minimum of 99.99% probability of paternity. This greatly lowers the probability to 1 in 10,000. We require our labs to test additional loci or even to perform expensive micro-array SNP testing at no additional cost to you if necessary to hit that number. So there is no savings to be had in duo testing.
A trio test is clearly superior and so one should insist that the mother participate unless she is deceased or refuses to cooperate.