Economics for Mathematicians
Cambridge University Press, Dec 10, 1981 - Business & Economics - 145 pages
This is the expanded notes of a course intended to introduce students specializing in mathematics to some of the central ideas of traditional economics. The book should be readily accessible to anyone with some training in university mathematics; more advanced mathematical tools are explained in the appendices. Thus this text could be used for undergraduate mathematics courses or as supplementary reading for students of mathematical economics.
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Appendix argument Arrow's impossibility theorem assumption budget constraint bundle of commodities Chapter competitive allocation completely labelled facets condition consider constant consumed consumption contract curve convex cover convex function convex set core allocation Corollary cost decreases defined definition demand denote depends Edgeworth box eigenvalue Engel curve equates equilibrium Exercise factors of production follows Further Gale economy given gives Hence holds household h hyperplane implies indifference curves indifference hypersurfaces industry initial endowment input intensity vector investment irreducible l s j s n labour required Lemma Leontieff model Mathematical matrix maximize non-negative notation number of households output Pareto optimal Pj(m positive precisely price vector produced profit Proof quantity rate of interest replaced returns to scale satisfies Show simplex simplicial decomposition social utility Sraffa model strictly convex suppose Theorem 2.2 theory utility function utility subject vertices wage