And after 2140 there will be no reward to maintain the network then why would anyone bother doing it?
Long before 2140, miners' income will be mainly determined by transaction fees. If there are no transactions, their income will drastically decline, which will reduce difficulty. The bet is that transaction volume will be large enough to compensate them enough to keep their machines running. One thing is certain: In the transaction-fee era, a block reward will be orders of magnitude more volatile than it is today.
If the mining difficulty reduces its a very appealing time for new miners to
start up because the hardware needed would be more affordable in order to
make a return.
Would it be right to say that the transaction fees would also drop which
could result in more movement of coins?