You shouldn't just shut up after identifying yourself either, you should explicitly state that you are exercising your 5th amendment rights and then shut up. Talking afterwards can be taken as rescinding your 5th amendment assertion.
Famously, a judge once ruled that saying "Yo, I want a lawyer, dawg" was actually not a 5th amendment assertion, and that the suspect was genuinely requesting a dog who practices law.
Not only that, but it likely significantly stimulates the local economy. People with no money buy nothing, meanwhile people with an excess of money don't buy much extra.