The trial will see free parking city-wide with Mr Olliver saying retailers should help by encouraging their staff not to park in front of their, or their neighbours', shops.
While parking would be free at all council metered car parks on November 5, 12, 19 and 26, parking wardens would still be enforcing all other infringements, including registrations and warrants.
Council staff would monitor car park use and turnover during the trial.
Mr Olliver said much of the perceived problem was caused by people not displaying a valid pay-and-display coupon on their car dashboard.
Government legislation states a $40 fine must be applied for people with no coupon. People with a coupon and who have parked longer than their time limit allowed would receive the standard fine of $10.
"Signage on all machines also makes this very clear," Mr Olliver said.
Car parking in the city would remain free from midday Saturday and all day Sunday.
However, councillor Dave Donaldson said if people could not understand how pay-and-display worked, they shouldn't be driving a car.
"I can't fathom how people can use that as an excuse for incurring a $40 fine. If they can't get it through their heads they should have no right to drive a motor vehicle.
"What we are trying to achieve is either blow some myths out of the water or see if this perceived problem actually exists," he said.
Councillor Maggie Bentley said the council was an easy target for retailers who were already struggling to make ends meet.
Councillor Charles Sturt said central city rents were astronomical and a lot of retailers had moved out of the central city because of this.
Councillor Glenys Searancke said she didn't see how free parking would help retailers.
"The fact is people won't go shopping if they don't have the dollars in their pockets," she said.
McLeods Booksellers manager Fraser Newman said he applauded the council for showing some initiative but said they had missed the mark. "It's fantastic they have listened to what retailers have been saying all along but people are just going to park there all day.
"With no time limit, workers could take advantage of that.
"Good on them for trying, but the cynical side of me says they have set this up to fail," he said.