How is it possible to achieve strong production in the city?

After all, with every industrial district that is built, future ones become more expensive. Is there anything to counteract this price increase?

You can't counteract the scaling, however, if you're choosing all builder cultures, your district cost should stay down to about 3-4 turns/per. 

Another thing is that there are some discounts to certain district types in the civics. For example 50% discount to religious districts - that includes EQs. Also 50% discount to garrison or common quarters. So if you choose one of those cultures, make sure you choose the civic first. 

Next, there is the Great Pyramids - permanent 25% discount which really adds up once things start scaling.

Lastly, Mississippians give a 50% discount to adjacent districts when you build their EQ.

All of these stack so you could end up with some really cheap district costs.