The Carter administration has drafted its alternative to Ronald Reagan's new tax-cut plan for business, calling for a moderate speedup in depreciation writeoffs at less long-run cost to the Treasury than Reagan proposes.

The new plan would provide an estimated $4.5 to $5 billion in tax reductions for business in 1981 and up to $13 billion by 1985, compared with $4 billion in 1981 and a huge $57 billion by 1985 in the Reagan proposal.

Although the administration's proposal has not been approved formally by either the president or his Cabinet-level Economic Policy Group, it has been given the green light by Treasury Secretary G. William Miller and approved informally by other officials.

Treasury tax experts, who have been shaping the proposal since the middle of last year, now "have things fairly well worked out," Miller said yesterday.

The new administration proposal would be timed to take effect in 1981. Miller reiterated that the president still strongly opposes action on a tax bill -- particularly involving a complex business tax cut -- before the November election.

Miller declined to provide any of the plan's details, which were obtained from other sources. However, he said the speedup in depreciation -- the time in which businesses can recover the cost of capital outlays -- was needed to spur investment.

He said the administration's plan would "tilt the economy, without shaking it," toward increased investment. Most economists believe the United States need more investment to spur productivity.

The new administration proposal presumably will be discussed with members of congressional tax-writing committees when the lawmakers return from recess. Both panels plan hearings on a tax bill the week of July 20.

Administration strategists are hoping that their proposal will be adopted by Senate Finance Committee Chairman Russell B. Long (D-La.), who last week criticized the Reagan plan as too expensive.

Reagan has proposed replacing the depreciation system with a simplified plan that would enable business to deduct the cost of buildings in 10 years, outlays for equipment in five years and spending on trucks and cars in three.

However, Miller and other administration officials have criticized the Reagan plan on three grounds -- that it is too costly, too generous in it writeoffs for real estate, and "inequitable" in favoring certain industries over others.

Depreciation, the administration's alternative, is the expense a business claims each year as its capital assets -- such as trucks, machines and plant buildings -- gradually wear out.

Depreciation allowances now are tied to the original cost of an asset and its expected "useful life," which is set arbitrarily by the Internal Revenue Service. In some cases, businesses can speed up these writeoffs somewhat.

The administration's proposal would reduce the current number of about 100 categories of assets, each of which has a separately calculated useful life, to only 30, compared to the three Reagan has proposed.

It also would set the useful life of an asset, and thus the speed at which the cost of an investment could be written off, according to three broad classes:

Relatively short-lived equipment, such as autos, trucks, office furnishings and the like.

Other assets and equipment, in which "useful lives" are determined by the industry in which an asset is used -- in agriculture, trade and services, and so forth.

Buildings, with separate categories for farm and industrial structures.

Sources said it was likely the administration would seek to phase in the speedup plan, beginning in early 1981, with the reduction not fully in effect until later.

Miller said the administration's new proposal would "have some balance . . . among different kinds of industries" -- unlike Reagan's so-called 10-5-3 plan, which he said would favor industries like steel whose equpiment lasts for many years.