By P. H. M. Ruys, H. N. Weddepohl (auth.), Prof. Jacobus Kriens (eds.)

On February 20, 1978, the dep. of Econometrics of the college of Tilburg equipped a symposium on Convex research and Mathematical th Economics to commemorate the 50 anniversary of the college. the final topic of the anniversary get together was once "innovation" and because an immense a part of the departments' theoretical paintings is con centrated on mathematical economics, the above pointed out subject matter used to be selected. The medical a part of the Symposium consisted of 4 lectures, 3 of them are integrated in an tailored shape during this quantity, the fourth lec ture was once a mathematical one with the identify "On the advance of the appliance of convexity". the 3 papers incorporated hindrance fresh advancements within the family among convex research and mathematical economics. Dr. P.H.M. Ruys and Dr. H.N. Weddepohl (University of Tilburg) research of their paper "Economic idea and duality", the family among optimality and equilibrium recommendations in monetary conception and diverse duality strategies in convex research. The versions are brought with somebody dealing with a choice in an optimization challenge. subsequent, an n individual selection challenge is analyzed, and the next strategies are outlined: optimal, relative optimal, Nash-equilibrium, and Pareto-optimum.

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**Extra info for Convex Analysis and Mathematical Economics: Proceedings of a Symposium, Held at the University of Tilburg, February 20, 1978**

**Example text**

This procedure defines a correspondence K: X + X, called the input-correspondence: K(k) The input-correspondence of some program k E X owns all programs which, if invested in the production process, can produce at least sufficient outputs to guarantee the desired output in the succeeding period, and notably the output of the terminal period T. It consists of a cartesian product of aureoled, convex and closed sets, which are all but one inverses of components of the output correspondence F. The input correspondence K is constructed recursively from the terminal period T to the initial period O.

This is precluded, of course, if profits between consecutive periods (equal to unity) are equal to unit profits between any two periods, say t and s. In order to solve this problem, a (nonnegative) distribution of profits over time n := (nO,nl, ... ,n T ) is introduced, which replaces the unit profits in the duality operations and allows the price development to be consistent over time. Define the graph-duality operation with respect to n t by: } The consistency condition then implies that for all k E F(k): + > Pl·k l > PT·kT > PT·kT nO ..................

In order to show the existence of an optimum program in E, an abstract economy &0 := (X, P: X ~ X, F) is defined using the definitions above. 3 (i) hold. OJ .. OJ , i t follows that an optimal program in E is equivalently characterized by an optimal terminal bundle in the economy {XT,PT , YT,O(k O)}' Finally, if Yt,s or F are monotonous, Le. (F(k)-X) n X = F(k), then P may be replaced by P(k) := non P(k), without loss of generality. Since pE(k) C P(k) for all k such that P(k) ~ ~, it follows that an optimal program is always efficient.