The simple theory behind the proposals President Reagan made last night is this: a reduction in the size of government and large individual and business tax cuts will almost instantaneously make the American economy more productive, simultaneously lowering both inflation and unemployment.

"The goal of this administration is to nurture the strength and vitality of the American people by reducing the burdensome, intrusive role of the federal government; by lowering tax rates and cutting spending; and by providing incentives for individuals to work, to save, and to invest," Reagan's economic recovery message said. "It is our basic belief that only by reducing the growth of government can we increase the growth of the economy."

Whether President Reagan's prescriptions work will depend on whether the nation's economic problems are in fact largely a consequence of excessive growth of government and increasing tax burdens. If they are not, the Reagan program risks generating more, not less inflation, or alternately, sluggish growth or outright recession accompanied by high unemployment, in the opinion of some economists.

Critics of the administration view, while agreeing that government expansion ought to be slowed and taxes cut, believe the country's economic problems stem from more fundamental causes that cannot easily be remedied. World oil prices have gone up independent of U.S. government spending; so have food prices, they say. The economy is now mature and grows slower than before; that is not the result of government spending, either.

Some of the uncertainty about exactly what the president's program might produce is reflected even in the payoff the administration promises. Only 10 days ago, the administration was on the verge of issuing a 1982 forecast showing a 6.5 percent inflation rate and a 7 percent increase in output. Now the oficial numbers for 1982 read 8.3 percent inflation and 4.2 percent real growth.

The Reagan view of the economy runs like this: the public demand for more and more services, income support and other government largesse has led to both a high and rising tax burden and large budget deficits. High marginal tax rates on individuals and business have discouraged work, saving and investment. At the same time, the deficits, financed by excessive growth in the money supply, have fueled inflation. and "the growing weight of haphazard and inefficient regulation" of private business by government has made everything worse.

The remedy is to attrack on all fronts at once, reducing spending, taxes, money growth and regulation all at the same time, the Reaganites believe.

But Reagan is not cutting everything but the same time. While he wants to slash spending by $41.4 billion for 1982, taxes would be cut by $53.9 billion.Some other changes, up and down, leave the 1982 deficit at $45 billion, $17.5 billion more than that proposed by President Carter in his final budget. Similarly, the 1983 deficit is projected at $23 billion instead of $8 billion even though economic activity that year is supposed to be more vigorous than forecast by Carter.

In other words, from a fiscal policy standpoint, the Reagan budget proposals add up to more stimulus for the economy than Carter and his economic advisers thought safe given the dangers of inflation.

Moreover, by 1983, to meet Reagan's own spending ceiling, the administration must come up with another $21.2 billion in budget cuts, none of which is so far identified. Another $10 billion in cuts must be found for 1984. If Congress doesn't make all the cuts Reagan has laid out, or those unspecified additional cuts, then the program could become risky indeed, some analysts said.

Meanwhile, the administration is urging the Federal Reserve to reduce money growth "from the 1980 levels to one-half those levels by 1986." That is roughly the sort of course the Fed has already indicated it wants to pursue.

The higher deficits for 1982 and 1983 will not cause the Fed any trouble, the administration argues, because the tax cuts will cause people to increase their savings, which can be borrowed to cover the added deficits.

The difficulty in all this is that attacking on all fronts means that a change intended to cure one problem may make another one worse. For instance, suppose individuals do respond to lowered tax rates by increasing saving. Whatever dollars they save, they are not consuming. Unless business steps up its investment spending very rapidly, economic growth could falter at least temporarily.

The greatest risk the administration program faces, however, is that the tight money policies it wants from the Fed will not finance both the real economic growth desired and even the reduced rate of inflation now forecast. If it is not enough, interest rates will rise and so will the risk of recession.

But Reagan's advisers foresee falling interest rates. They believe short-term interest rates will be about 9 percent late next year, compared to the 11 percent rate forecast by Carter. This is because they believe inflation will fall.

That decline in inflation occurs in turn be caused of a drop in inflationary expectatons brought on the Reagan economic program. In the administration's scenario. That change in expectations is central to the whole theory that is how less government translates into more production and less inflation at the same time.