THE COAL companies' sharply improved offer will probably end, after two months, the miners' strike. Question: Why did the companies increase their bid so sharply at a time when coal stocks are still comfortably high and when production in much of the country has hardly been affected?

One answer is the operators' interest in demonstrating reliability of supply to the new foreign customers who are becoming extremely important to them. Another answer lies in the complex and delicate relationship between the companies and the United Mine Workers. The companies have evidently decided to pay a premium to avoid humiliating the union. The miners' rising confidence in the UMW over the past several years has brought a remarkable decline in wildcat strikes and coal field chaos. That's worth a lot to their employers. From the companies' point of view, the new contract is not a bad investment at all.

But what about the national economy and the inflation rate? It is the wage pattern that carries the inflation along from one year to the next. The miners' cash wages under this contract will rise about 9 percent a year. That's no more than the average rise for all American wages over the past year. But this contract will keep the miners moving up at that rate for the next 40 months -- in effect, throughout the remainder of this presidential term.

Those are only the cash wages. There are also the fringe benefits. The much-disputed coal royalty payments into the union health and welfare funds, for example, will be continued and expanded after all. Fringe benefits, not only for miners but throughout the economy, are now rising much faster than cash wages. There's a simple reason: most finges are tax free, both to the employer and the employee. But, taxed or not, it's real money and will turn up in the form of higher prices in the months ahead.

The government has begun publishing statistics on the total costs of compensation to employers. Wages, in the first quarter of this year, rose at an annual rate of 11 percent. Total compensation, including the fringes, rose at a staggering rate of more than 15 percent. Part of it was the January increase in employers' Social Security taxes. But fringes like health insurance premiums were also rising. The trend in employee compensation seems clearly to be upward.

The Reagan administration's economic theory assumes that tight restraint on the money supply must slow down the inflation by curtailing high wage settlements.The miners' contract suggests that the assumption isn't holding in the coal industry. Nor, according to those dismaying figures on compensation costs, is it holding for the American economy as a whole.