To address your developers concern only (i.e. demonstrate memory isn't the problem), you could start by proving that the query isn't waiting on memory grants and that page life expectancy is at a comfortable figure.
Memory grants (from Glen Berry):
-- Shows the memory required by both running (non-null grant_time)
-- and waiting queries (null grant_time)
-- SQL Server 2008 version
SELECT DB_NAME(st.dbid) AS [DatabaseName], mg.requested_memory_kb, mg.ideal_memory_kb,
mg.request_time, mg.grant_time, mg.query_cost, mg.dop, st.[text]
FROM sys.dm_exec_query_memory_grants AS mg
CROSS APPLY sys.dm_exec_sql_text(plan_handle) AS st
ORDER BY mg.requested_memory_kb DESC;
Page Life Expectancy:
SELECT [object_name],
[counter_name],
[cntr_value]
FROM sys.dm_os_performance_counters
WHERE [object_name] LIKE '%Manager%'
AND [counter_name] = 'Page life expectancy'
From there, I'd follow the advice in the comments and identify what the actual problem is, rather than focusing on what the problem is not.
- Waits & Queues
- sp_whoisactivesp_whoisactive
- Post the execution plans on your question.
