I didn't fully understand the concept so i have a question,
What I have understood so far is the market makers have a stock inventory and they make quotes about bid and ask price to provide liquidity.
Can a market maker offer less shares(than have in his inventory) for sell to push the stock price up?
Price moves up and down because of supply and demand. Market makers often trade for their own accounts so their volume is variable. However, market makers are regulated and they are required to continually quote prices and volumes at which they are willing to buy and sell and there are precedence rules for other market participants.
Is it possible for market makers to move price on his own? Yes but that requires an illiquid stock (no individual is going to move AAPL, GOOG, etc. on their own) as well as willing counterparties to take the other side of the trade. However, it's not feasible to assume because one drives price up somewhat that one can easily benefit because in order to realize that profit, you must sell and that drives price down.
Note that the market maker isn't a monolithic market participant who controls the market unilaterally. If the B/A is $10.00 x $10.25 and you offer to buy for $10.05, the quote becomes $10.05 x $10.25 and you are now the market on one side. The market maker doesn't control the auction. He's only one of the participants.
