The figure provided by Mr Bridges is the same as cited by Contact Energy but less than the 3.6 per cent Genesis and Meridian say clients will face.
Genesis head Albert Brantley said three-quarters of that was down to higher transmission and lines fees, with the rest being an increase in his company's charges.
Mr Shearer later said Mr Bridges' claim of a 2.4 per cent average increase was "laughable".
"Households around the country have received electricity bills with increases of much more than that in just the last week. Customers in Wellington are being charged three times that figure," he said.
Some Kiwis are already bracing for the reality of bigger power bills.
Hastings resident Darrin Crombie said his power bill cost $20 per week in summer but during the winter it could swing to $120 a week.
Meanwhile, energy company annual reports show Dennis Barnes, head of Contact Energy, is the industry's highest-paid chief executive. He received remuneration of almost $1.6 million in the past financial year, putting him ahead of Mark Binns, of Meridian, who was paid just over $1 million, and Mighty River's Doug Heffernan and Mr Brantley of Genesis, who were both paid about $1.3 million.