A Circle Theorem in the Samuelson Domain

English auctions and the Stolper-Samuelson theorem

We prove that the English auction (with bidders that need not be ex ante identical and may have interdependent valuations) has an efficient ex post equilibrium. We establish this result for environments where it has not been previously obtained. We also prove two versions of the Stolper-Samuelson theorem, one for economies with n goods and n factors, and one for non-square economies. Similar as...

Protection and Real Wages: The Stolper-Samuelson Theorem

Beyond the Descartes Circle Theorem

The Descartes circle theorem states that if four circles are mutually tangent in the plane, with disjoint interiors, then their curvatures (or “bends”) bi = 1 ri satisfy the relation (b1 + b2 + b3 + b4) 2 = 2(b1 + b 2 2 + b 2 3 + b 2 4). We show that similar relations hold involving the centers of the four circles in such a configuration, coordinatized as complex numbers, yielding a complex Des...

Comparative Statics, English Auctions, and the Stolper-samuelson Theorem

We introduce a comparative-statics observation; we prove that the English auction is efficient in a model with interdependent valuations and n bidders; we generalize the StolperSamuelson Theorem to the case of more than 2 goods and factors of production and to non-square economies; and we illustrate how our comparative-statics observation is behind those seemingly unrelated economic proposition...

Complex Descartes Circle Theorem

We present a short proof of Descartes Circle Theorem on the “curvaturecenters” of four mutually tangent circles. Key to the proof is associating an octahedral configuration of spheres to four mutually tangent circles. We also prove an analogue for spheres. It can be traced back to at least Descartes that four mutually tangent circles have curvatures (reciprocals of radii) satisfying the relatio...