I was told when I bought my house a year and a half ago that I should get
a roof membrane that my extend the life of my roof. I have a flat rof,
concrete. How effective is a roof membrane? How cost efficient is it?
Whenever there is a heavy downpour, water seems to be entering a light
fixture in my kitchen. Would a membrane help? I am in distress!

yes, a rubber membrane roof is likely your answer.

Single ply roof ing is common and works well when applied carefully.
Detail at edge of membrane is important.
Choose a contractor with good references.
TB

I have a flat roof and it has been replaced with a membrane (bitumen
fired down), which after it's applied is a full piece of rubber on the
roof.

It costs about $200/square to rip out the old stuff and install this
one. If you have a flat roof, you're going to have problems, and this
only helps put off the inevitable, so it's cost efficient.

good luck,
tim1198