Page "Herbert Scarf" Paragraph 1

Scarf never received formal training in economics.

Both his undergraduate training at Temple University and his graduate work at Princeton University were in mathematics.

For the past five decades, however, he has worked at the frontiers of both economic theory and operations research and has made a number of extraordinarily significant contributions to both of these fields.

He is internationally famous for his early epoch-making work on optimal inventory policies and his highly influential study with Andrew Clark on optimal policies for a multi-echelon inventory problem, which initiated the important and flourishing field of supply chain management.

Equally, he has gained world recognition for his classic study on the stability of the Walrasian price adjustment processes, his fundamental analysis ( with Gerard Debreu ) on the relation between the core and the set of competitive equilibria ( the so-called Edgeworth conjecture, named after the Irish economist, Francis Ysidro Edgeworth, Feb 8, 1845-Feb 13, 1926 ), his remarkable sufficient condition ( i. e., balancedness ) for the existence of a core in non-transferable utility games and general exchange economies, his seminal paper with Lloyd Shapley on housing markets, and his pioneering study on increasing returns and models of production in the presence of indivisibilities.

All in all, however, the name of Scarf is always remembered as a synonym for the computation of economic equilibria and fixed points.

In the early 1960s he invented a path-breaking technique for computing equilibrium prices.

This method is nowadays known as Scarf ’ s algorithm and has made general equilibrium theory applicable to large, realistic economic problems.

This work has generated a major research field in economics termed Applied General Equilibrium Analysis and a corresponding area in operations research known as Simplicial Fixed Point Methods ( or Algorithms ).

Scarf ’ s algorithm and its subsequent refinements and alternatives have become practical tools for assessing the consequences for the entire economy of a change in the economic environment or a major change in economic policy – to engage in comparative statics when the model of equilibrium is too large to be solved graphically or by simple numerical calculations.