The BBC has made a new comedy about itself.

It's called W1A and there's a great moment in the first episode when a group of producers try to explain their idea for a new show to Carol Vorderman (Claire Balding has dropped out because of her commitments to How Big is My Dog?). "The new show is like Countryfile meets Bake Off," says one of the producers. "With a bit of The One Show thrown in just in case."

It's a nice little joke, aimed at the timidity of programme commissioning and how much at the BBC is a bit like the thing before that, which was a bit like the thing before that. But it is a joke that holds hands with the truth.

There are plenty of other jokes like it in the first episode, which re-introduces us to Ian Fletcher, the head of branding at the London Olympics in 2012. Fletcher (Hugh Bonneville) is now head of values at the BBC and is in charge of dealing with the corporation's learning opportunities (problems).

He also chairs the Way Ahead Taskforce which, in the words of the wonderfully sarcastic narrator David Tennant, is there to clarify the role of the BBC in a digital age. "With renewal of the charter due in 2016," he says, "finding an answer to the question 'what is the BBC for?' before then could potentially be important."

It's a nice line, and funny, but it has the same mix of amusing and true as the rest of the programme. It is also awkward for the BBC because the corporation really does need to clarify its role in the digital age and really does need to find answer to the question "what is the BBC for?"

Some answers have started to emerge in the past few days: answers that challenge the structures of the organisation, and how it is paid for, and signal the beginnings of a realisation that things cannot go on as they are. The decision to make BBC3 online-only, for example, was criticised by a few comedians but there are rapid changes going on in the television landscape, so rapid in fact that the BBC said in October it would not consider closing a channel before announcing in March that it would: a volte-face worthy of W1A.

It was also the right decision and a logical response to the fact television has escaped from the box in the corner of the room and, for young people in particular, exists largely on tablet computers, which also raises the even bigger question of how the BBC is funded.

One suggestion the other day, by Culture Secretary Maria Miller, was that refusing to pay the licence fee should be decriminalised but the Government should go further and abolish the fee. It was created when announcers wore dinner jackets and the programmes were in black and white, but the world is multi-channel and digital now and the BBC is one choice among many options, paid for by advertising and subscription.

Beloved as it is by some, the BBC should be subject to the same rules and pay for itself through subscription or adverts. If you watch the BBC, you pay for it; if you don't watch it, you don't pay. That doesn't make for a good joke for W1A but it's the only logical, fair position and the internet has made it irresistible.

W1A, BBC 2, March 19, 10pm