He got 11 per cent market share and lost his money.
These days Morgan is better known as a multimillionaire philanthropist with a flair for blunt talking, good causes and skilful self-promotion. He built his success on his economic forecasting firm Infometrics (founded in 1982, just after the racing fiasco) and now runs an investment advisory firm named after him.
In 2006 he collected $47 million from his stake in Trade Me - the company started by his son Sam and sold for $700 million to Fairfax - which he promptly announced he would give away to charity.
Since then the Wellington-based economist has rarely been out of the headlines for long, touring the world by motorbike with his wife Jo and friends, co-writing a book on climate change, trying to save the troubled Phoenix soccer club and paying for a satellite transmitter to trace Happy Feet the penguin's journey home.
And 30 years on from that early attempt to beat the TAB, he has another grand economic solution to an even bigger national dilemma.
Morgan's latest proposal, the Big Kahuna, is to replace the entire tax and welfare system with an annual payment of $11,000 to every adult, a flat tax rate of 30 per cent and a comprehensive capital tax on buildings and property, including the family home.
He predicts this would end our confusing and unfair system of targeted social welfare, which hands out money to families earning $100,000 a year but has to top up a minimum wage too low to live on.
He openly admits it would also slash the incomes of superannuitants and halve average payments of the Domestic Purposes Benefit. Many pensioners would gradually lose ownership of their homes to pay the capital tax, which could depress the value of all our houses (Morgan sees this as a good thing as it would help young people to buy). Many solo parents on benefits would have to either move into cheaper housing or share with other adults to make ends meet.
Yet despite the harsh implications for beneficiaries, Morgan argues strongly that we should not blame people for their own poverty. Instead he takes aim at our whole economic system, claiming we have lost the plot because we have ignored moral values and allowed market forces to run unchecked.
In his new book and a series of articles in the Business Herald, Morgan and co-author Susan Guthrie call for the rich to pay a greater share of taxes to support the poor and an end to welfare debate centred on accusations of bludging.
Morgan even quotes Adam Smith - generally regarded as the father of laissez-faire capitalism - as realising later in life that the "trickle-down effect" did not work because the factory owners captured all the wealth for themselves. His apparent change of heart has infuriated some conservative commentators and puzzled those who remember him as a cheerleader for Rogernomics in the 1980s. Has the arch-capitalist undergone an Adam Smith-style transformation too?
"No, I've always had that view that there was an excess. I mean I got painted pretty starkly as you know, sort of market-mad or whatever. But I think that was quite a big misinterpretation of what I was saying."
Morgan sketched out the original idea that became the Big Kahuna on the back of an Air New Zealand sickbag on his way to a meeting of the Tax Working Group in December 2009.
By his own admission, the idea bombed with the rest of the group, which had been asked by the Government to look for long-term answers. So he tried again, with the help of Guthrie, a former Consumer magazine financial writer who had worked with him at Infometrics in the 1980s.
Guthrie did the research, says Morgan, and challenged him every step of the way. "I was going to exempt the family home. She said, 'what the hell would you do that for? That's the biggest tax dodge there is'."
He plans to run a conference next year, as he did with his climate change book, and invite economists from around the world to come and criticise the plan. There's been plenty of criticism already, starting with the $11,000 unconditional basic income, which is designed to support unpaid work but could just as easily be used for an extended surfing holiday.
Morgan says this won't happen because $11,000 is not much to live on and people will have more incentive to work because the payment will not be reduced (unlike current benefits). Solo parents on the DPB, who currently get about $20,000 to $30,000 a year depending on allowances and the number of children, would lose out badly.
Morgan argues the state cannot afford to support a single person as if he or she was a two-parent household. He suggests a range of possible answers - including compulsory life insurance and direct financial help from absent partners - but the main message is that people need incentives to make better choices.
Economist and Child Poverty Action Group member Susan St John says this ignores the fact that struggling to survive on the DPB already gives solo parents more than enough financial incentive to cut their costs. Many families do share houses, she says, which can lead to dangerous overcrowding.
She likes Morgan's overall idea to redistribute income from the old and rich to the young and poor but thinks it could be achieved less radically, perhaps through higher taxes on superannuation.
Morgan is forthright about cutting payments to superannuitants - "they get too bloody much anyway" - despite huge political backlashes against previous governments who have dared to tamper with the pension scheme. He suggests using money from the Cullen fund, which was created to pay for future superannuation needs, to smooth the transition. As for the impact of a comprehensive capital tax, elderly people who own their own homes could deduct the payments from the value of their houses. There wouldn't be much inheritance left for the family, of course, but at least they wouldn't have to find any extra money.
So how does he rate his chances of political success?
High, says Morgan, but radical change like this is a slow-burner. "I see in five years this still being very much the subject of debate. I don't see it at all as featuring in election manifestos this year."
The Big Kahuna
Gareth Morgan's vision for our tax and welfare system
1 An annual, tax-free payment of $11,000 to every adult, whether they do any paid work or not. This replaces virtually all benefits, including superannuation.
2 A flat tax rate of 30 per cent on all income.
3 A capital tax of 1.8 per cent on all buildings and property, including the family home. It would not cover deposits and shares.