Mathematical methods of economics

MATHEMATICAL METHODS OF ECONOMICS*

JOEL FRANKLIN California Institute of Technology, Pasadena, California 91125

When Dr. Golomb and Dr. Bergquist asked me to give a talk on economics, my first impulse was to try to get out of it.

"Sol," I said, "I'm not an economist. You know that."

"I known said Golomb.

"If you avant ~ economist, I can get you one," I said. "I know some excellent economists."

"No," he said, ^C^G^w^e Walt a mathematician to tank about the subject to other mathematicians from their own point of view."

That made sense, and I hit on this idea: I won't try to tell you what mathematics has done for economics. Instead, I'll do Ale reverse: I'll tell you some things economics has done for mathematics. I'll describe some mathematical discoveries that were motivated by problems in economics, and I'll suggest to you that some of the new mathematical methods of economics might come into your own teaching and research.

One of these methods is called linear programming. I learned about it in i958. I had just come to Caltech as a junior faculty member associated with tub computing center. The director and I made a cross-country trip to survey tine most important industrial uses of computers. In New York, we visited the Mobil Oii Company, which had just put in a multi-million-dollar computer system. five found out that Mobil had paid off this huge investment in two weeks by doing linear programming.

Back at Caltech, Professor Allison Sweezy in economics and Professors Bill Corc~or~ and Neil Pings in chemical engineering urged me to teach a course in linear programming. When I told them I didn't know linear programming, they said: Fine, Joel, learn it. Seeing they meant business, I did study the subject and give the course. The students loved it, and so Ad L Perhaps you will have a similar experience.

One surprising thing I found was this. Ye mathematics was delightful I Mew it was useful, but I hadn't expected it to be beautiful. I