Math 21a, Fall 2014/2015, Multivariable Calculus, Harvard College

The 2014 Nobel prize in Economics went to the French economist Jean Tirole who worked on a theory of market failures. Summarizing in one sentence, Tirole showed that market regulation is complex and that rules should be adapted to each situation. His work contains quite a bit of mathematics on the 21a and 21b level.

Here is an example of a paper on Asset bubbles [PDF]. a topic which became relevant recently. How do bubbles form and aggregate? Which situations lead to bubbles and what is the nature and the consequences of bubbles? Here is a more recent paper on liquidity [PDF]. The mathematics of these papers deals more with discrete dynamical systems. given by vector fields F(x,y) = . One is first of all interested in places, where the vector field is <0,0>. These are called equilibrium points. Then one is interested in the stability of the equilibria and the dynamics X= -> F(x,y). We will mostly deal in 21a with situations where F(x,y) is the gradient of some functions f. The equilibria of F are the critical points of f.

Working in smaller dimensions and simple looking models whose understanding can have enormous consequences is typical.

Here are some links:

Press release
The Guardian
Wikipedia article (which unfortunately mostly focuses on awards and certificates and almost nothing about the work).
Spiegel mentions that this is the first time since 15 years that the prize goes to a European economist. But still, both origin or work of most economics Nobel prize winners are dominated by the US, as the chart in the "Spiegel News site" shows: