Owner Adrian Nicholas said the aim was to make people think and act a different way.
"We do what we do - making the coffee - and then we gift it away. Then it's up to the customer, whether they'd like to give a gift themselves. I imagine it's creating a lot of commotion. People are thinking things through ... I guess it's about morals and ethics - wondering how much is fair to give."
The "gift economy" is an idea that has been around for years, but has succeeded only in parts of the United States and Australia.
A blackboard hanging over what would have been the cash register gives customers the Wikipedia explanation for the concept.
"We are changing to gift economy model ... (it's) where valuables are not sold, but given without explicit agreement for immediate or future rewards."
Mr Nicholas said customers were still trying to get their minds around the idea of "gifting" rather than paying a set price for their coffee, as well as the fact that they could easily just leave without paying.
"I don't think our customers do that. But there has been the odd guy who'll stand in the corner for a while and then slip out the door," he laughs.
"But the money we're getting is around the same we would get if we were to charge people."
That was a figure Mr Nicholas did not want to reveal.
The concept also means that customers are able to "gift" something other than money. This week, they received a bag of coffee beans, an offer to have Mr Nicholas' motorbike professionally cleaned and a camel - although that was apparently a joke.
One customer who stumbled on the place admitted he probably overpaid for his coffee - leaving a $5 note on the donation table.
He said: "I was standing behind a guy who had just paid $3 for his coffee ... and I didn't want to come off as being stingy."
The Espresso Coffee school offers courses throughout the year to those wanting to start a coffee business, young students and drinkers who just want to refine their coffee-making skills.
Dr David Mason, senior lecturer at Victoria University's School of Information Systems, said the main problem with the idea of the gift economy was the issue of legal liability.
"If you go into a shop and you don't think their coffee is worth very much and you burn yourself ... Does that make a difference?"
A similar situation arose a couple of years ago when an e-commerce website was asking people to donate unwanted electrical goods for low income families.
The concept was worthy but raised the question of "where does the liability lie" if one of the items caught fire.
"Our economy works on the basis of well-understood rules and principles - and if you go outside of them the laws have to be tweaked and so on."
Dr Mason said there was nothing wrong with the pay-for-what-it's-worth model if it was a straightforward service, "for buying something you can consume immediately".
But if it was something that could be used later and was later found to be deficient or inaccurate in any way it could create problems.
There were also unlikely to be any underground economy fears.
"There's no reason why it should be illegal assuming the person is above board, paying taxes and (having) their premises inspected as normal."
• For more about the gift economy idea see wiki.gifteconomy.org.
- Additional reporting by Andrew Koubaridis
