Map of Nenokuchi on Mathematically, however, Pareto assumed that the functions involved were differentiable. Differentiability means that the analyst is able to compute the first (slope) and second (slope of the slope) derivatives of these functions. The Paretian model differs from the Walrasian model in that the tastes-andobstacles structure of the former replaces the demandand- supply functions of the latter. Economics in the post-WORLD WAR II period retained the tastes-and-obstacles optimization structure of the Paretian system, but it essentially avoided its differentiability assumptions and effectively reproduced the same results without it. Seminal works of this period were those of Nobel Prize winners, Kenneth ARROW and Gerard DEBREU, in the 1950s. The question of whether their reliance on convexity (the property of a set of points that a line drawn between any two points on its boundary lies entirely in the set) is more general is a thorny issue. Some economists and many non-economists criticize the intense mathematics that has been used to refine GE models in the decades following the early Arrow-Debreu formulations as being mere mental gymnastics with no hope of application. Map of Nenokuchi 2016.
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