THERE IS a crucial economic dimension to the Reagan strategy for dealing with Soviet power. It is that the Soviet Union, though a superpower, is relatively backward and cannot keep up in arms- building competition without suffering ever harsher internal strains. This has been, of course, a familiar element in Western thinking about the Soviet Union since 1917, and its implication--that the United States could spend the Kremlin into subordination, or at least into good international manners --has yet to prove out. It is being asked now, however, whether this time around the Soviet Union may not be near a bending point--some observers say breaking point--after all.

A certain answer comes from the new Soviet budget statements. The numbers can't be taken literally, but they, and the tone in which they are presented, show the way the wind is blowing. They indicate that some investment funds are being shifted to defense and that the people are being prepared for hardship ahead.

The extent to which this flows from a reaction to the Reagan defense surge is problematical. Soviet defense spending is not without peaks and valleys, but it is generally steadier than the Pentagon budget. Moscow is finding, however, that it is an expensive business running an empire--in Afghanistan, Cuba, Vietnam and elsewhere. Moreover, structural flaws in the Soviet economy are exacting a toll. The rate of return on capital investment is atrocious, demographic trends are tightening the manpower squeeze, and agriculture remains a disaster area: this year the Soviet Union, just to maintain a diet that is the scandal of the developed world, will buy more grain than any country has ever imported. Except for the party elite, the quality of life appears to be going down year by year.

There is no evidence that the United States can, by spending, alter the Soviet Union's strategic aims, given the way the Kremlin can play with its citizens' standard of living. There is, however, some evidence that it can aggravate the economic distress that the Soviet system itself nourishes. The trouble is that it costs. Look at the condition of the American economy and, in particular, at the contribution the defense spending is making to deficits, to tight money, to industrial bottlenecks and, not least, to the public's readiness to keep the Pentagon budget at the Reagan high.

Ultimately, a defense-spending contest is not, as some of the Reaganites would have it, a simple competition between economic machines. It is at the same time a competition in political and social elasticity. A prudent leadership will recognize the difference and the hazards of attempting to put the foot to the floor.