MARBLEHEAD – Selectmen have extended Swampscott restaurateur Paul Petersiel’s lease on the Devereux Beach concession stand known as Lime Rickey’s until 2016, with a $3,200 increase in rent.Petersiel, who owns the Red Rock Restaurant in Swampscott, paid the town $35,222 a year to use the beach food location for the past five years. Starting Dec. 1, when his new lease begins, the rent will be $38,425.Asked if he was happy with the agreement, Petersiel said, "Absolutely. If I weren’t I wouldn’t be here doing this (extending the lease)."First, he had to answer some questions about price increases in his latest menu and whether he still charges the "reasonable prices" he promised in 2006 for the casual beach food he serves.Selectman Judy Jacobi noted that the price of a peanut butter and jelly sandwich has more than doubled and prices for a number of other items have increased by 50 percent.Petersiel answered that food prices have gone up since 2006. As an example, he pointed to the $2.95 he charges for an all-beef, kosher hot dog, an overwhelming favorite in a taste test he supervised around the time he opened."I tried selling a cheaper hot dog for 98 cents," he said. "We didn’t sell very many. People didn’t want them."Erica Petersiel said she has been working with the Recreation and Parks Department to bring trash collection problems under control.Petersiel notified selectmen eight months ago that he was exercising an option to extend his lease five years.Town Counsel Marc Miller said he informed Petersiel that the extension was not automatic and as the expiration date approached the board would review all the circumstances.