Australian Prime Minister Robert Hawke, capitalizing on his longstanding popularity and the country's booming economy, has taken a Reagan-size lead in the opinion polls as the national election campaign enters its final two weeks.

Andrew Peacock, a former foreign minister who is leader of the Liberal Party, has seen his own approval rating hit a record low of 32 percent against 68 percent for Hawke, while his conservative coalition of Liberals and the Rural National Party trails Hawke's Labor Party by 15 percentage points.

Peacock, who assumed leadership of the conservatives 20 months ago when Hawke, a hero of the labor union movement, ousted Malcolm Fraser from the premiership in a surprise election, acknowledges that he needs every minute of television time and every headline he can get to have a chance of closing the gap before the Dec. 1 vote.

Complicating that task, and casting a shadow over the final stretch of the campaign, is a national scare over acquired immune deficiency syndrome (AIDS), which has caused the death of three babies in a northern state and is implicated in the deaths of several adults, all of whom contracted it by receiving transfusions of tainted blood or plasma.

Only one political leader has attempted to make any political capital out of the scare. Ian Sinclair, the leader of the National Party, accused the Labor Party, which has extended many welfare benefits to individual homosexuals and to homosexual couples, of encouraging "a situation which can prejudice future generations of children and where diseases such as AIDS can become more common."

AIDS, which is believed to be transmitted by intimate contact, primarily strikes homosexuals. It can also be contracted via blood or blood plasma transfusions from AIDS-affected donors.

In his campaign, Hawke has concentrated on a direct appeal to voters and on extending the rapport he developed with the electorate during the past decade when he was president of the Australian Council of Trade Unions (the much more powerful counterpart of the AFL-CIO) and later in politics.

A policy speech last week marked his shift from most of the high-spending promises he made during the 1983 election campaign, with his proposed course of economic management so conservative that he was warmly applauded by big business, the traditional enemy of Labor in Australia.

As the campaign began last month, Hawke broke down at a press conference when he started talking about his family.

His wife, Hazel, later went on national television to explain the reason -- their married daughter Rosslyn and her husband Matt Dillon were heroin addicts undergoing treatment and that Rosslyn was so badly affected by the drug that her lower limbs were wasting and her life expectancy had been shortened. The end result of the disclosure has been to neutralize it as an issue and to engender sympathy for Hawke.

The prime minister's campaign promises have been vague.

On tax reform, in a country where the average wage earner is now paying 47 cents of every dollar for income tax and which has a huge underground cash economy, he has promised a massive review next year ending in a "summit" of all organizations interested in reform.

Since March 1983, when the Hawke government was elected, unemployment has dropped from nearly 11 percent to about eight percent. More than a quarter of a million new jobs have been created and inflation has been slashed from 11.5 to 3.2 percent.

Using the terms and attitudes that have dominated conservative party thinking Down Under for generations and until now were despised by Labor, Hawke promised that taxation would not increase in real terms during his next three-year government and that the government deficit would not increase as a percentage of gross domestic product.

Peacock's fight to establish a credible alternative to Hawke's charisma and newly conservative policies has been tough. His approach has been to push his party's policies further to the right.

In addition to pledging to abolish an assets test instituted by Hawke aimed at preventing the rich from getting old-age pensions, Peacock has promised to reform the taxation system along American lines.

He also said his government would not impose a capital gains tax -- there is none in Australia except on assets sold for a profit within 12 months of acquisition -- or other wealth taxes.