guy named Melvin Reder, a labor economist, and he came in the ¬rst day

of class and put his feet on the chalkboard and said something deprecat-

ing about economic theory, so I never went back. The ¬rst term I spent

learning introductory calculus and probability theory. The probability

theory was actually taught by a guy whom I later learned was a world-

class probabilist. It was marvelous because he introduced everything via

examples, and then you could study for the exam because you had a

good feel for what probability theory was all about.

MD: Did you and Karl work together at Stanford?

Cass: No. One of the funny things about Stanford, and this may be

true in other graduate programs too, they preselected people that they

assumed were going to be stars. Karl was an undergraduate math major

at Princeton who basically went to Stanford because he knew about Ken

Arrow, and Karl was a preselected star. (He was not selected as top star

of the class; I forgot the name of the guy who was, but he turned out

to be a real bust.) Since I decided not to take economics the ¬rst year I

was there, I really didn™t have much to do with economics students, and

I only got to know Karl probably toward the end of my second year.

He introduced me to Serra House, and there Uzawa™s students all worked

together because we all knew each others™ problems, so we could com-

municate very quickly. But none of us actually wrote papers together.

Karl and I started collaborating on papers much later, in the early 1970s,

but, again, Karl knew my thesis and I knew Karl™s thesis throughout the

whole development phase, so basically who contributed what to what as

graduate students with Uzawa was always up in the air.

An Interview with David Cass 37

MD: And how were you led to your thesis topic?

Cass: Optimal growth? Well, it was basically the fascination Uzawa

had with the maximum principle.

MD: What growth theory did you know before that?

Cass: At that period there was a distinction between what we wanted

to do, optimal or prescriptive growth, and descriptive growth à la Solow.

He wrote a ton of papers, starting with the very famous paper on the

one-sector model, and then he wrote many others describing competitive

growth models that had more goods, and maybe some specialized techno-

logy, and he kept repeating how you describe a competitive equilibrium

and its ef¬ciency properties (something Malinvaud did much more ele-

gantly in his justi¬ably famous Econometrica paper). So that™s descriptive

growth theory. Then there was this famous paper by Ramsey, and Uzawa

was clearly fascinated by two-sector versions of the neoclassical growth

model. He wrote several papers on that. Then he decided to go into

optimal growth theory and produced a paper which was essentially a

two-sector model with a linear objective function. Basically, he re-created

the calculus of variations himself”he is a very original guy”and then he

discovered the maximum principle and became fascinated with it. Uzawa

also gave a seminar on economic history in which he went back and took

all the great names in economics, starting with Ricardo, Marx, . . . and

reproduced what they were doing as a growth model. I was very in¬‚u-

enced by Uzawa™s work. I didn™t even know about Ramsey at the time.

MD: That is interesting because sometimes one hears about Ramsey as

this hidden classic. But didn™t some people know about Ramsey? Didn™t

Uzawa?

Cass: No, I don™t think so, because I didn™t ¬nd out about Ramsey

until after I had written the ¬rst chapter of my thesis on optimum

growth. And then I was, to be perfectly honest, I was a bit embarrassed

about it.

MD: How did you discover Ramsey?

Cass: I don™t remember now. Maybe somebody mentioned it; maybe

Uzawa knew about it, but not really, because he thought my con-

tribution was absolutely seminal. In a way it is not at all. In fact I always

have been kind of embarrassed because that paper is always cited although

now I think of it as an exercise, almost re-creating and going a little

beyond the Ramsey model.

MD: Ramsey had no discounting and you did have discounting. That™s

one difference, right?

Cass: Ramsey had no discounting. He made a big point of talking about

the correctness of the social welfare function from a moral viewpoint, I

believe, maybe in his side remarks. Tjalling Koopmans was very sensitive

to this issue, too, when he wrote a paper of this sort. It turns out to be

38 Stephen E. Spear and Randall Wright

much harder to solve the problem with no discounting because, even if

the objective is written as a function of a functional, it is not well-de¬ned

because it may be in¬nite-valued, and you have to use a trick to make

sense out of it. You have to take the difference between utility of con-

sumption and utility of the golden rule consumption so that you get a

function that is well de¬ned. As a technical aside, it is very interesting

that the Ramsey problem is a counterexample to something which people

now always do. I think they do it in macro without even thinking about

it, when they do dynamic optimization, and they write down transversality

conditions as necessary, which I also said something about in my thesis,

and this is dead wrong. The Ramsey problem is a counterexample to this:

You have an optimum, but it doesn™t satisfy the transversality condition.

MD: Is this an issue only in the no-discounting case?

Cass: Yeah, that™s in the undiscounted case. It has to do with the con-

dition in capital theory that is called nontightness, which is a suf¬cient

condition for the transversality condition to be necessary, and basically is

an interiority condition that enables you to use a separating hyperplane

theorem. Now I have forgotten what the original question was!

MD: How you came to the optimal growth problem.

Cass: Actually, even though Uzawa always went back and read litera-

ture and was always motivated by literature, I didn™t pick that up from

him at all; I just decided to work on this problem because the techniques

were new and exciting and it seemed like an interesting problem. So I

taught myself the maximum principle, some differential equations, and so

on, by talking to people, seeing Uzawa working, and basically reading

math books. Our bible at the time was Pontryagin™s original book on the

maximum principle. That is really interesting too, because that book is

very geometric, and Pontryagin™s blind.

MD: Was it in Russian? You would have had a natural advantage there.

Cass: I could have read a little bit of Russian, but it was translated.

Anyway, he™s blind, and yet all of his thinking is purely geometric; he

pictures things. So I just put the two together, and then Uzawa thought

this was great. I™m not sure why, I guess probably because Tjalling

Koopmans was working on this problem and Tjalling was a bit of an idol

for Uzawa. Actually, Uzawa liked to one-up people. At some point he

was talking to Tjalling about the problem, and Tjalling was describing

what he was doing and Uzawa interrupted and said, “Well, I have a

graduate student who did that problem.” Then Tjalling got very nervous

about it, he was always very nervous about . . . , oh, authorship and who

was ¬rst and that sort of thing, and we had some correspondence.

Koopmans was also very interested in the no-discounting case, so he

solved the much harder problem in some ways, in addition to solving the

An Interview with David Cass 39

problem with discounting. Tjalling did all his analysis from ¬rst prin-

ciples; he derived all of the conditions.

MD: Then you went on the job market.

Cass: I™ll tell you a story about the job market that re¬‚ects the character,

the idiosyncratic character, of Uzawa. Uzawa originally engineered for

me to have a postdoc at Purdue, which was a pretty good department,

but then he had contact with Koopmans at the Cowles Foundation, who

were interested in doing some hiring. Uzawa decided that would be a

better job, but his idea of supporting a student on the market was that

it was immoral to have more than one offer. So I went to the winter

meetings in Boston with just an interview with the Cowles Foundation,

and a couple more that I had arranged that turned into disasters. I spent

most of the time in the hotel room watching football, and I was rooming

with Karl who had a million interviews! It came down to the last day of

interviews and everything depended on my passing an interview with the

Cowles Foundation, which was a lunch with Tjalling and Herb Scarf and

I don™t remember who else, very likely Jim Tobin. I talked a little about

my thesis, but Tjalling already knew about it, and he decided to question

me with “What will you be working on 10 years from now?” As with any

graduate student, I couldn™t even think two months ahead. I had no idea

what I would be doing!

For some reason, they couldn™t make me a regular appointment, and

I remember Tjalling had obligated himself to make an appointment that

it turned out he couldn™t make, so he signed me as a research associate

at the Cowles Foundation for one year, on a one-year appointment, with

the promise that it would be extended and I™d become an assistant

professor as well as research associate. You can™t believe salaries in those

days, even adjusted for in¬‚ation. My salary when I started was $8,000.

MD: Tell us about Yale.

Cass: Yale was a great postgraduate education. The Cowles Foundation,