On an idle instance, why does setting max memory to 256mb cause %CPU to jump Five 2012 instances on a 2-node cluster using AVGs. Two of them doing nothing yet, no user databases or users.  Customer insists on specific max mem settings while waiting for additional memory approval.  We lowered max mem from 1gb to 256mb on both and each instances CPU usage jumped to 20% and stayed there. Raising it to 512mb brought it back down to basically nothing. Regardless of mem setting each instances memory usage stayed right around 200mb.

Any ideas?  I'm still doing research for the technical answer they are requesting.
If the Page Life Expectancy performance counter is at a decent value, this can be due to constant (re) compilation : because of the low amount of memory available, plans get evicted quite quickly from the cache, and need to be compiled every time thier corresponding query is submitted to SQL Server.