Business confidence, whatever that is, is lacking and administration officials. Wall Street investors and Federal Reserve Board chairman Arthur F. Burns are among those who voice concern over its absence.

It is this lack of confidence, coupled with a low level of profits, that keeps businessmen from investing enough in plant and equipment to sustain the economic expansion at a level high enough to bring down unemployment. Burns said in a speech last week.

Burns told the Carter administration that it was partially to blame for the uncertainty that contributed to the low-level of business confidence that threatens the strength of the recovery.

The administration, for its part, is not only worried, but apparently perplexed about the state of affairs.

Treasury Secretary W. Michael Blumenthal, in a speech designed to assuage business distress, told bankers last month that the Carter administration would soon be offering "prudent" economic policies that tilted toward increasing the role of the private sector in the economy.

But Blumenthal said that the administration was puzzled that there should be so much unease at a time when the economy is 32 months into an economic expansion and prospects for the future look pretty good.

Jimmy Carter, himself a small businessman, is not the first, nor is he likely to be the last, President to be accused of failing to instill confidence in the hearts and spines of businessmen.

Former Presidents Nixon and Ford, whose appreciation of the role of the private sector was rarely questioned, also faced crises of business confidence. In those days executives liked to say that they could not be sure of the future because there was the threat that wage and price controls might be reimposed at any time.

In his quest to restore business confidence President Carter is likely to discover that business confidence is elusive and that any action he takes to restore it in one sector will shatter confidence in another.

One group complains that the worry is whether demand can be sustained and calls for a tax cut. Another group frets that inflation is the threat and that actions taken to stimulate demand will make the economy worse.

Businessmen who were concerned last year about the long-run availability of energy supplies find the Carter-Congress confrontation over an enery policy equally worrisome.

The same businesses that complain loudly about the uncertainty government creates when it interferes in the economy are often the ones that ask the government to interfere in the economy by restraining imports.

Even Burns who in one breath told the administration that it had put forward so many policy initiatives that businesses were confused and uncertain, called on Carter in the next breath to end business uncertainty by coming up with a "bold" new proposal to enhance business profitability.

But Carter, or any president can only do so much to alleviate business uncertainty. Supposedly it is the willingness of business to deal with uncertainty that generates profits.

As businesses have discovered - along with other groups - bold new confidence-creating moves often are accompanied by side-effects that sap more strength than they impart.

Wage and price controls were hailed in 1971 as an antidote to inflation and were viewed by business as a means of holding down wage increases. Prices and wages were rising at a faster clip in 1974 when the last controls were removed that in 1971 when they were imposed.

Northeast oil consumers who fought oil import curbs in 1971 in order to have access to cheaper foreign oil, were surprised to find by 1974 that Arab crude cost more than the Texas variety.

"There are billions of dollars of approved, but unfunded projects sitting in the boardrooms of major American corporations," one major corporate director said. "The operating people and the managers want to get going right away. But the board of directors is holding back."

They are afraid of the ever present risk, and there is little a President - Democratic or Republican - can do to change that state of affairs.