I have set up a private block chain. I started to mine on this network. Now the number of ethers in the coinbase account is continuously increasing. How is it getting ethers? Do the blockchain generate new ethers to reward the miner? If so wouldn't it result in the inflation.
Mining is rewarded, even in a private blockchain, 5 Eth for each block.
In your case, you are the only miner, so you get 5 ETH almost continuously...
For more information concerning the minig :
In Ethereum you get 5 Ether as reward if you are the one who first solves the puzzle and, consequently, you are the one who adds the new block to the blockchain.
This happens on any network, be it private or public, since it is part of the Ethereum protocol and code.
Inflation does not take place because the Ether gathered on a private network can only be spent on gas in that private network and cannot be exchanged for real money. Only the ether from the public network has real world value.
If we talk about inflation on the public network, it doesn't happen since the demand for ether is bigger than the rate with which is produced.
The Ether is a reward for mining, on any chain, the system always works the same. It does not matter whether you mine a private, a testnet or the public network chain.
However, the mined Ether on a testnet or private blockchain can not be used on the public blockchain. So, to answer your question, no: this does not increase inflation, because to mine real Ether, you would have to mine the main network.