"Doggone it -- if you're going to boycott this candy store ... then don't come in for any of it," Pierce told FoxNews.com.
In the letter, he ridiculed Villaraigosa for saying that the point of the boycott was to "send a message" by severing the "resources and ties" they share.
"I received your message; please receive mine. As a statewide elected member of the Arizona Corporation Commission overseeing Arizona's electric and water utilities, I too am keenly aware of the 'resources and ties' we share with the city of Los Angeles," Pierce wrote.
"If an economic boycott is truly what you desire, I will be happy to encourage Arizona utilities to renegotiate your power agreements so Los Angeles no longer receives any power from Arizona-based generation."
Appearing to tap into local frustration in Arizona over the raft of boycotts and threatened boycotts from cities across the country, including Los Angeles, Pierce warned that Arizona companies are willing and ready to fight boycott with boycott.
"I am confident that Arizona's utilities would be happy to take those electrons off your hands," Pierce wrote. "If, however, you find that the City Council lacks the strength of its convictions to turn off the lights in Los Angeles and boycott Arizona power, please reconsider the wisdom of attempting to harm Arizona's economy."