Municipalities have begun demanding that private developers pay an increased share of the costs of expanding the current road networks, sewer systems and other public services to accommodate new development projects.


a. demanding that private developers pay an increased share of the costs of expanding
demanding ...pay---proper usage of subjunctive mood

b. demanding that private developers to pay for an increased share of the costs of expanding
demanding that....to pay....wrong construction -violates subjunctive mood..

c. demanding payment by private developers for an increased share of the costs of expanding
Unnecessarily uses passive voice

d. to demand that private developers pay for an increased share of the costs to expand
IMO we can't use infinitive after past participle

e. to demand that private developers should pay for an increased share of the costs to expand
IMO we can't use infinitive after past participle

Hence A

Just to add: Idiomatically, we say the "cost OF" something, so we can eliminate (D) and (E).