How do I respond to a price increase and try to negotiate?

Price increase with what? Please give more detail.

Well, I manage a café and the coffee roaster wants to increase their beans prices

If they won't negotiate with prices, go with someone else.

Well, first what I would do is research. Try and find another place that sells for the price you are looking for. After that talk to the company that you have been buying from and say that their prices have been a little too high for you lately and ask if they can lower it to X amount or in your range. If they say they can't do anything about it I would tell them that you did find another business that sells for X amount on their coffee beans and if they can't do anything about it you would have to take your business elsewhere. If this is a company that you like and have used for a while and don't really want to change tell them you value their business as well. However, if you don't really care about sticking with them if you do find another business I would just switch to them :P.

If you can't find another business that sells in your range I would just try your best to try to work them down working with their managers and etc.. Tell them that they may lose your business because of the price increase.