No, I would not. The price of life should not be an others life. The moral death that would follow that incident would not be worth living with. There's also the use of taxpayers money that would be keeping me alive for many years, even though I did nothing to deserve it. Murder for the sake of living is nothing to live with.
I know yours is the morally correct answer, but I would, if my two options were limited to just those specified in the question (which would never be true). Because if I lived in a world where people, both collectively and individually, didn't care enough about me that they were willing for me to slowly starve to death, I would owe them nothing. That said, I could/would never actually kill someone - I don't even kill insects (excluding wasps - we have an ongoing feud).
Thanks for the clarification. When I was five, my older brother told me to catch a 'hoverfly' in a jar, from outside their nest at the base of a tree. I learned two things that day. 1) My brother is not an expert in flora and fauna. 2) Wasps are not to be trusted and must be eliminated on sight. To clarify, this stance only applies to the 'standard' wasp found in the UK.