4 - From virtual velocities to economic action: the very slow arrivals of linear programming and locational equilibrium

Summary

Introduction

Scenario

In the early nineteenth century, the principle of virtual work and other assumptions in analytical mechanics led to forays into equilibrium and optimization in economic contexts. Forays toward linear programming appeared in embryo forms at various times between the late eighteenth and the mid-nineteenth centuries, with a very clear formulation put forward by J. B. J. Fourier in the 1820s; but then they fell largely into desuetude. From 1900 to 1940, various studies concerning linear inequalities and/or convexity were carried out in many different branches of pure and applied mathematics; but they also did not launch linear programming, where progress remained slow until an extraordinarily rapid establishment after the Second World War. Similarly, some traces for nonlinear programming were laid, largely in connection with mechanics, but they were not seized when that topic advanced in the 1950s.

In another area, in 1829 two young French scientists, G. Lamé and B. Clapeyron, thought up all the basic ideas and applications of locational equilibrium; but their work made no impact, not even on the concerns of their own distinguished later careers. The topic saw only fitful and partial advances for the next century before establishment was effected.

Presentation

At the factual level this chapter is concerned with these three cases of mathematical economics, which saw their birth in France during this period and continued there and in other countries afterward. Each of them grew out of aspects of mechanics, which will be specified in the following section, along with an outline of the context of French science at that time.