Why US economy is in the dumps: intriguing but unconvincing view; Profits Without Production, by Seymour Melman. New York: Alfred A. Knopf. 300 pp. $18.95.

No doubt about it, the United States has had it tough, economically, over the last several years. The big problems have been inflation, which used to be terrible; unemployment, which is terrible now; and productivity, which has been rising, but with disgraceful lethargy, compared with other countries.

Professor Melman, like others before him, now believes that he has found the true explanation to these problems, but I think that readers who grope through these 300 pages of opaque prose are likely to conclude that he has not.

His odd thesis is that our worst economic problems result from two phenomena: the influence of the Department of Defense on the economy, and the tendency of modern business executives to pursue what he sneeringly calls ''moneymaking,'' instead of production.

Professor Melman, a professor of industrial engineering at Columbia University, is not new on this beat. He is a self-described man of the left who has for years blamed the Defense Department for US economic problems. He is also a longtime student of industrial production techniques. Melman has written on these subjects at length before, but in this book he synthesizes his thoughts to produce a large-scale explanation of why US industry is in the doldrums. The result: initially intriguing but, on examination, less convincing.

Consider first his analysis of the Defense Department's influence on the economy. When he points out that the department's purchasing practices do not encourage efficiency on the part of contractors - that they often strongly discourage it, in fact - he cannot be denied. Reports have shown that the Pentagon indeed pays thousands of dollars for simple parts costing pennies. This indubitably lowers America's productivity. To the extent that other industries could benefit from the technology that is wastefully produced under Pentagon contract, the productivity cost may be greater than it first appears.

But does this help to explain the various blights on America's economy? It doesn't appear to. The problem is that during the last 20 or 30 years, which Melman regards as the period in which American industry has gone to the dogs, the Defense Department has been a shrinking part of the economy. In 1960, its budget took 9 percent of the country's gross national product (GNP); last year it took about 6 percent, a 33 percent drop. Employment in defense-related agencies was 5.2 percent of the labor force in 1960, 3.1 percent in 1980. If defense spending is the root of all evil, then things ought to be getting better , not worse. Meanwhile, in the countries of Western Europe and Asia that Professor Melman cites as the industrial leaders of the future, defense spending as a proportion of GNP has been rising. Overall, US defense spending has declined from 34 percent of the world total in 1969 to 23 percent in 1978 (those years being the earliest and latest for which the Commerce Department has done the calculation). This does not exactly jibe with Melman's explanation of why US industry is becoming less competitive with the rest of the world's.

His other villain, the despicable tendency toward ''moneymaking'' among US managers, is even harder to make sense of. His assertion seems to be that American executives have found some way to make money without making products.

How can they do this? Professor Melman refers to ''short-term profit-taking opportunities afforded by tax laws, securities transfers, the milking of production assets, and other financial legerdemain.''

It's certainly true that financial tricks can increase profits, but not consistently in the long run and not for the economy as a whole; Professor Melman apparently believes that American managers don't understand this.

It's at this point that one begins to question Melman's understanding of business. One becomes suspicious when he refers to managers ''conditioned to maximize the 'bottom line' of a short-term balance sheet.'' Balance sheets are neither short- nor long-term, since they reflect a company's condition at a given moment, while the bottom line that managers try to maximize rests at the base of the income statement, not the balance sheet.

One's suspicions intensify when he upbraids owners of shopping malls for disdaining energy-saving devices, concluding with the ludicrous statement that ''these technological possibilities have been widely ignored, since the higher costs of mall operation justify higher rents and profits to the owners.''

In looking at what's wrong with our economy, this book aims to take on a problem that needs the strongest analysis we can give it. Its contribution is original, audacious, and unpersuasive.

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