NEW YORK—Verizon Communications, Inc. announced a new service package for its wireless and residential customers that would charge them widely varying, but always high, fees every month depending how the communications giant feels at the time. "Our Charge-At-Whim packages offer the same mediocre quality and insufferable level of customer service you’ve come to expect," a Verizon spokesman said Tuesday. "But it adds an unjustified, arbitrary and, if you’ll allow us to boast, frankly unjustifiable method of determining just how much you’ll pay for them." Packages start at "oh, $69.99 a month, let’s say?" and went into effect about three or four months ago.