President Reagan's spending-cut speech last night was addressed to all the people. But it was aimed most intensely at a much narrower audience, Wall Street.

Stubbornly high interest rates and the evident unhappiness in the financial markets have spurred the administration search for new cuts, even as Congress has warned against them. Administration officials hope anxiously that the new proposal will bring spending back on the course Reagan set for it, cheer up investors and bring down the cost of money.

Two important economic question marks hang over this proposition. Will the $13 billion of additional spending cuts and $3 billion of extra revenues next year indeed lead to lower interest rates and an improved economy? And this second, clearly related question: will changes of this size really bring the federal deficit down to the $43 billion promised and insisted upon by Reagan?

Serious doubts remain over both. Few people believe that cuts of this size can make much practical difference in credit conditions or in the economy this year. In addition, much of the financial market worry this summer has focused on 1983 and 1984 and, although the administration made some more promises yesterday, there remain huge unspecified program cuts to be made for those years if spending is to stay on the president's course.

Nevertheless, Reagan officials argue, yesterday's package could have a critical psychological impact. If Congress accepts it, this would convince markets that the years of steady upward creep in successive budget estimates were over, they say, in that it would keep spending to $709 billion and thus very close to the July target.

Once convinced of this, the markets will lower their expectations of future inflation, the Reagan theory continues, and interest rates will fall, allowing faster economic growth.

But it is here that the second question comes in. Financial markets have shown clearly that they doubt Reagan's economics and his budget numbers. Their skepticism over 1982 numbers has contributed to their mistrust of the optimistic picture for 1983 and 1984.

Although yesterday's revisons to some extent recognize this, and certainly give a more realistic view of spending, the markets most likely will remain doubtful of the president's projections even if Congress is persuaded to pass the extra cuts.

Moreover, many economists believe that even if bond dealers and investors do take heart from Reagan's proposals, interest rates are likely to stay high and the economy weak for some time to come. The Federal Reserve's tight money policy is the reason; it shows no sign of abandoning this, and so long as money stays short, interest rates will stay high until the economy weakens.

The administration stands virtually alone in its forecast for next year's deficit. Officials still apparently assume that interest rates will fall swiftly and the economy grow sharply next year. Other forecasters, including the Congressional Budget Office, have been assuming a 1982 deficit of between $60 billion and $80 billion even with additional cuts this fall.

And there are a number of puzzles in yesterday's new array of numbers.

For example, yesterday's background document blames Congress for adding $6.3 billion to spending in 1982 by falling short of Reagan's proposals in the reconciliation act passed this summer. But the president supported and fashioned that act, and indeed claimed its passage in July as a success.

Moreover, the administration itself yesterday added $60 billion to its estimate of 1984 spending, with no explanation of the change nor explicit reference to it. Although the budget is still balanced in that year, on the administration's numbers, it is balanced with both spending and revenues taking a bigger share of gross national product than projected before.

All the more optimistic forecasts for the economy's growth next year assume that the Federal Reserve eases up on money growth, or else that there is an extraordinary increase in the amount of gross output that is consistent with a given supply of money in the economy.

It is more likely that money will stay tight, and the economy weak, at least until inflation comes down significantly. Further spending cuts to tighten fiscal policy just push Reagan economics closer to a traditional anti-inflation policy of slowing the economy and trying to squeeze out inflation by keeping unemployment high.