STOCKHOLM, Sweden (AP) _ American researcher Robert M. Solow on Wednesday won the Nobel Memorial Prize in Economic Sciences for explaining how savings and technology make an economy grow.

Solow, of the Massachusetts Institute of Technology in Cambridge, Mass., won the prize for a mathematical formula published in 1956 that demonstrated how those two factors, along with labor and capital, affect a nation's economic future.

In awarding the prize, the Royal Swedish Academy of Sciences cited him for ''his contributions to the theory of economic growth.''

A native of Brooklyn, N.Y., Solow was the 15th American to win the prize since it was created by the Bank of Sweden in 1968.

Last year, James M. Buchanan of George Mason University, Fairfax, Va., received the prize for basic work on the theory of decision-making.

''My friends have been telling me for the last couple of years that I must be in the running for this. It's embarrassing to be told that all the time, so I guess I knew that, but it came as a complete surprise,'' Solow said at his harbor-side home in Boston.

Asked about the reasons for the volatility in the stock market, Solow blamed ''the combination of the balance-of-payments deficit and the federal budget deficit, which has put our country in the position of financing a consumption boom by borrowing from foreigners.''

He said ''we're going to be a number of years digging ourselves out of a hole that we dug for ourselves over the past six or seven years.''

Solow, a member of the President's Council of Economic Advisers under John F. Kennedy and a proponent of government regulation of the economy, criticized the Reagan administration for its refusal to raise taxes to combat the deficit.

The 63-year-old professor was among the first to recognize the role technological progress plays in bolstering the economy.

Assar Lindbeck, president of the Nobel committee which chose the laureate, said that by the 1960s, Solow's work had influenced countries to concentrate more resources on universities and research.

Members of the five-man committee called Solow ''easy-going and humorous'' and ''a very good teacher.''

Indeed, when his colleagues awarded him MIT's Faculty Achievement Award in 1978, they said he was especially valuable to the school because he divided his time among his students and his research. Solow continues to deliver introductory economics lectures at MIT.

The Academy's statement said Solow's ''theoretical model had an enormous impact on economic analysis.''

To this day, the World Bank and economists in countries around the globe use Solow's theories when projecting national growth, Lindbeck said. Solow was the second MIT scientist to win a Nobel Prize this year. Susumu Tonegawa, a Japanese researcher, won the prize for medicine last week.

Solow's work showed that even though in the short run a country can reach a higher level of growth by increased savings, technology and capital determine the long-range growth rate.

When Solow's ''Contribution to the Theory of Economic Growth'' was published in 1956 he already was a leading figure among economists seeking models of growth. By the 1970s, his theories stood alone as most accurate, said the committee's Ingemar Stahl.

Solow has devoted the last decade to researching macroeconomics, or the economic policies of nations, especially unemployment. He also is involved in research on the optimal use of natural resources and the environment, the Academy said.

The Nobel Foundation, a legacy of Swedish industrialist Alfred Nobel who invented dynamite, sponsors annual prizes in medicine, literature, physics, chemistry and work for peace. The prizes were established by Nobel's 1895 will.

The economics award was added in 1968 by the Bank of Sweden as a memorial to Nobel. The prizes are each worth the equivalent of about $340,000, which is split when more than one laureate is named.

The prize for literature will be announced Thursday.

Last week two Americans, Donald Cram and Charles J. Pedersen, shared the 1987 chemistry prize with Frenchman Jean-Marie Lehn. A West German, Georg Bednorz, and a Swiss, K. Alex Mueller, shared the physics prize.

The coveted Nobel Peace Prize was awarded to Costa Rican President Oscar Arias for his Central American peace plan.

All the prizes will be distributed Dec. 10 in Stockholm and in Oslo, Norway.