From Billy Del Cook's spartan, unadorned office in the Municipal Center, the outlook for the District of Columbia's fiscal future is promising.

Cook, associate director of the Department of Finance and Revenue, is in charge of estimating tax revenues for the District government; his charts project a steady rise in sales and income tax receipts for the next five years, reflecting a healthy economy and a tax structure that benefits from inflation.

From Edward G. Winner's spacious District Building office, festooned with baseball photographs, the outlook for the city's fiscal future is ominous. Winner, the assistant city administrator for financial management, envisions a relentless, continuing rise in the cost of supplies and services.

His numbers are going up faster than Cook's, and therein lies much of the explanation for the budgetary vise that is squeezing the city government. The numbers embody the paradox of a city that looks prosperous and is often described as recession-proof, but is actually less able to sustain itself with each passing month.

"The cost curve is going up geometrically," Winner said. "The gap between revenues and costs is widening like the mouth of a horn. We have to get those lines into parallel."

That horn-shaped gap, according to city officials and their private financial advisers, has been in existence, and widening for some years. The current crisis atmosphere results from Mayor Marion Barry's recognition of that gap and mounting pressure on him to close it before it becomes unbridgeable.

Barry has already said that he does not plan to ask for any further tax increases for the next two years and therefore the income-expenditure gap will have to be closed mostly by slashing city services and payrolls.

Winner said the mayor's long-range financial plan, to be unveiled July 21, "will identify the services that will be cut in the future if any anticipated revenues fail to come in.

About two-thirds of the money that finances the city's budget comes from local taxes, and it is Cook's job to calculate what those revenues are likely to be.

He acknowledged in an interview that doing so is "an art, not a science" because of the inherent difficulty of determining what retail sales, personal incomes and property tax assessments will be several years in the future.

Sales and income tax receipts are particularly sensitive to overall economic conditions, Cook said -- propelled upward by inflation, driven downward by recession and unemployment -- and he often resorts to the "WAG system" of estimating them. The initials stand for "wildassed guess."

"We look at history and we study everything and we listen to everybody, but finally we have to put down a bottom-line number," Cook said. He and his staff have a reputation for accuracy, but he said that "any tax estimator is high half the time, low half the time. It's a very humbling experience."

Cook recently submitted to Barry his estimates of the city's probable income from taxes through the 1985 fiscal year. After a decline for the rest of this recession year, they show a steady, long-term rise in revenues from all taxes and especially from the big three -- sales, personal income and property.

The District's total tax revenue is projected to increase from $828.3 million in the current fiscal year, 1980, to $1.21 billion in fiscal 1985.

That includes an anticipated increases in property tax revenue from $184.1 million this year to $300 million in 1985; in sales tax revenues from $185.4 million this year to $258.6 million in 1985; and in personal income tax revenue from $252.4 million to $398.8 million in 1985.

And yet, Cook, Winner and other analysts of the District's fiscal affairs agree, those steady gains will not be nearly sufficient to sustain the present level of city services for several reasons.

The District's income tax revenues are growing more slowly than those of other metropolitan area jurisdictions, they said, because the personal income of the city's residents is far lower.

One recent report showed that median household income in the District was just two-thirds of the area-wide average and that more than half of all families in the metropolitan area with incomes below $5,000 a year live in the District.

Earning less and paying less in taxes, the District's low-income population creates a correspondingly heavier demand for city services in health, welfare and recreation.

The number of persons in the District's labor force who are potential taxpayers, has actually declined; and demographers have surmised that while the city is attracting prosperous young professionals, their total taxable incomes are less than those of the middle-class blacks moving to the suburbs.

As a result, Winner said, the projected rise in tax receipts will not keep pace with the rising costs of fuel and energy, Medicaid payments, or supplies and equipment. The rate of growth, he said, is lower than the cost of borrowing money for capital projects and lower even than the rate at which city salaries are rising.

A freeze on hiring and the layoffs of some city workers, he said, eliminates only workers at the low end of the pay scale; those with more seniority, and higher salaries, remain, and pay increase granted on a percentage basis are correspondingly higher.

A glance at the mayor's proposed 1981 budget demonstrates Winner's point.

The Recreation Department budget, for example, calls a staff reduction of one, from 492 to 491, but a rise in total expenditures over 1980 of more than $1 million. A cut of $112,000 for "supplies and materials," such as pool-cleaning equipment, is more than matched by an increase of $800,000 in the budget for "energy, communications and building rent."

Overall, the mayor's revised 1981 budget provides for about $3,000 fewer employes than were on the payroll in 1979. But total outlays will still be higher, $1.52 billion against $1.39 billion, the difference, $130 million, is more than twice the increase in tax revenues over the same period.