Their income is irrelevant. If they consume fewer kWh of electricity than the average power company customer, they will get a net benefit. They might pay a $25 tax, but get a $40 benefit. Meanwhile the large factory might pay $5,000 but they still get the same $40 rebate the pensioner gets.
Given that large corporations who consume huge amounts of electricity are in the pool, it's almost impossible that the pensioner could consume more than the average.
Businesses will use orders of magnitude more than the pensioners. The fact that a pensioner might use more per capita than a young person doesn't matter. When the young person leaves the home for work, they're just going to a different building that is also consuming electricity, generating more pollution tax. Plus, there are more people per household in a young home because of children.
Given that large corporations who consume huge amounts of electricity are in the pool, it's almost impossible that the pensioner could consume more than the average.