Of course the question was raised. Was all this new math really necessary? Mathematical economists were divided. Koopmans pointed out that the same objections had been brought up in other fields before such as the idea of negative numbers which was the topic of ridicule and doubt when they were discovered almost 2000 years ago. Of course we now know that negative numbers are very real and they have been with us for a very long time.
While the studies and math these men worked with have been with us for less than 100 years, perhaps they are the negative numbers of generations to come.
A for Will. Hey everyone else, you should read this one: it has a nice combination of being well-written and informative.
ReplyDeleteKoopmans' point is the one students use at all levels: why do we have to learn all this math if no one ever uses it (trust me, I've taken more math classes than you have, so I've used this excuse more than any of you). The truth is, everyone is trying to figure out how to get the math to help them through the next problem, and most of us don't succeed.
But ... there's an important point there for where we're going with the economics of growth. All it takes is one person to see how to apply known math to a new problem with an unknown solution. Then we can all copy their method, and move on to the next problem. That intellectual sharing/copying process has increasing returns to scale.
Of course, if you had my ECON 2500 class, you've been introduced to some of this already. We use separating hyperplanes all through the course (although I don't use that phrase), we do shadow prices, and we also talk about how profit maximization is the dual problem to cost minimization.
N.B. Lionel McKenzie, who worked in the same area as Arrow and Debreu, but is a little less known, passed away about 6 months ago.